The Blue Book by Reid Young.pdf

THE BLUE BOOK: An Advanced Strategy Guide for No-limit Hold'em Cash Games By

Reid Young

Copyright 2010, Reid Young

THE BLUE BOOK: An Advanced Strategy Guide for No-limit Hold'em Cash Games

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TABLE OF CONTENTS PLAYER TYPES

24

PRE-FLOP PLAY

28

FLOP PLAY

86

RIVER PLAY

139

TURN PLAY

166

TURNING HANDS INTO BLUFFS

177

OVER-BETTING AND UNDER- BETTING 209 ALL YOUR OPTIONS LEADING (INTO THE PFR)

226

QUANTIFYING LEVELING

236

MISCELLANEOUS CONCEPTS

243

MOVING THROUGH LIMITS

255

FOREWORD My experience with Reid has been a positive one. While he was a student of mine, Reid demonstrated a thirst for learning. He quenched that thirst by asking the right questions to the right people. As a result, Reid has become someone to whom people ask questions. Off the poker table, Reid has been great towork with as a part of Leggo. He has shown ambition, punctuality, and responsibility- qualities that most pokerplayers lack severely. I wish him and this book nothing but success.

- Aaron "Aejones" Jones, high stakes poker professional

PREFACE I regret that there will he a few odd soundingintroductions to the various subjects in this book. The subjects on which I write are quite interconnected, a flaw inherent of the subject matter, so there frequently will be oddly arranged ideas. I apologize in advance for any confusion this causes you as a reader and a student of the game.

There will also be a number of oddly placed questions, mostly rhetorical and colloquial, within this book. The reason for this stylistic choice is to attempt to grasp the active attention of the reader, just as your attention should be engaged in a poker game. I want you to actively consider every single thingl write about just as you would consider every single perceivable tendency of your opposition and every option available to you in a game. Eventually, when these questions have been properly addressed by both of us, you will become

a better player and a better poker thinker than your competition and that means more poker success for you.

Finally, I'd like to say that there are few joys as great for me as a student's success. I wish you all the best and great success in your poker endeavors unless we are in a hand together.

And for the 48456th time..

THE BLUE BOOK: An Advanced Strategy Guide for No-limit Hold'em Cash Games

INTRODUCTION The Blue Book isn't aiming to teach you what to think, but rather how to think. This book is aimed at poker players of all skill levels and I truly believe that it is a text that could and should be revisited throughout a poker player's career. The nuanced nature of the game offers near infinite faceted approaches and observations to the game. As your game changes, so will your responses to the questions herein asked. The questions in the text are designed to stimulate the growth of any level of poker player, from intermediate to advanced player.

When I first started playing poker, I would frequent the gambling section of many bookstores only to be disappointed to find the same introductory books and a lack of a volume truly reflective of the online player's approach to beating the games as they've developed in the last few years. The information that fills the

bookshelves has become outdated and less valuable to those intermediate players seeking continued growth for their game. The problem is that these poker books, often filled with over-simplified and outmoded thought processes, were mostly systematic in attempts to teach a casual player the art of survival in the average poker game. Nothing available comes close to touching on how to decisively win in a tough game, a daunting thought that now plagues many professional players as the general public and other players have become more educated. If information is power, I felt powerless playing poker once I moved past my first few limits and I didn't know where to go to imporve. With more people selling the same mass-produced and watered- down poker systems, the masses are able to absorb them. That is how I got stuck and bundled in as part of that group of stagnant-minded players. I have learned the systems that don't work in tough online cash games and I have since moved past them and onto working on the thought processes that you will need to engage in order to beat the higher games that are almost always entirely comprised of professional poker players.

his book will help to bring to light the fact that a uniform poker system cannot be applied to different types of players because each player is unique with his or her own playing style. My goal is to teach you the adjustments that you need to make based on reads you glean by playing with each different person. Every play you deconstruct and every adjustment you learn to make is going to add to your win rate. We're also going to delve much further into topics less explained by other poker literature in order to better understand our opponents' mistakes and our own mistakes.

- Reid Young, LeggoPoker.com coach "SHOOTAA" Note: He recently announced that he is no longer part ofLeggo.

GETTING STARTED: A HAND EXPLAINED I will be covering lots of topics in this book. As I've said, the topics are all interconnected. Below is a sample hand that shows how the ideas connect and how I constantly ask myself questions having to do with many different subsets of general poker theory and how these ideas often lead to a well informed and logically based decision given the limited information we have in a situation. Once you learn to see the game as a multidimensional playing field, a new world of poker will be at your fingertips. Let's start by taking a glimpse into my mind during a strategic hand.

Hand info: Type:

Cash Games

Game:

NL HokTem

Table:

Buddy

Blinds:

$10/$20

Posts big blind $20 Seat 3: VILLAIN($ 1,970) Dealer, Posts small blind $10 Seat 6: HERO ($2,030) Dealt to HERO [AsJd] Pre-flop: (Pot: $30) RAISE HERO, to $60 CALL VILLAIN, $40

Here, I make a standard raise pre-flop to three times the big blind with AJo and my opponent calls. He had been re-raising me a decent amount pre-flop, so I expect his range to include: • Several suited and connecting hands • Medium-to-high broadway hands • Occasional slow-played big hands

Flop: (Pot: $120)[6d,8d,Js] BET VILLAIN, $100 RAISE HERO, to 320 CALL VILLAIN, $220

My opponent leads into me on the flop, which is strange given how much he had been check-raising flops as draw heavy as this one in the recent past. He should realize that my range of hands for c-betting and calling a raise should widen to combat his high check- raising frequency and so I would expect his stronger hands to attempt a check-raise most of the time. Concurrently, there are many draws with which I might also raise his flop lead bet, so I am not expectim him to fold. As I do not see him taking his line with many legitimate hands, I expect him to at least call a raise or re-raise me with a weaker hand, if I elect to raise his flop lead. Given our recent history, I elect to raise with my top pair, top kicker. He calls, which, to me, represents the weak hand I believe him to have. This hand would be either some weak draw that he isn't comfortable getting all-in on the flop by calling an all-in bet after he

3-bets my flop raise or a slow played monster trying to induce a turn bet from what he views to be a range comprised mostly of draws and bluffs. There are several straight draws and a flush draw on the board and it's likely in his eyes that the combinations of my hands that are draws and pure bluffs that raise this flop are far more prevalent, combinatorically speaking, than the hands that I'm able to raise for value.

Turn ($760) [6d,8d,Js,5h] CHECK VILLAIN BET HERO, $500 CALL VILLAIN, $500

I bet the turn large enough to get value with what I believe to be the best hand and to charge his likely draw. The off-suit five coming on the turn brings some combinations of hands that are now a pair and gut shot, hands like 98 s, that he might play this way, and so I can bet a larger amount of money because he expects to have more equity against my range and is therefore able to put more money in the pot. Once I bet $500 into a

$760, he'll be getting 1260/500 or about 2.5-1 on a turn call. This makes it pretty easy for him to call with a lot of his range while leaving me a credible looking river bet that I could be using to bluff or to value bet. Remember, a larger portion of my perceived range is still draws. Once he just calls the turn, I'm expecting him to have either a flush draw that paired the turn or picked up a gut shot and now has enough equity to call, a weaker made hand that he wants to induce more action from the air portion of my range, or a pair and gut shot type hand.

River: (Pot: $1,760) [6d,8d,Js,5h,4d] BET VILLAIN, $1,090 and is ALL-IN

Immediately when I see the river card, I'm expecting to lose the pot to what I thought to be his very strong range and I'm feeling very frustrated with the deck for making me miss what I thought was going to be an easy value bet all-in on the river. Almost every single hand I thought to be in his range just hit! Flush draw, check.Pair-plus-straight-draw, check. He shoves

into me though, which is odd given our above analysis. This can only leave him with the pair and straight draw portion of his range, and I'll explain why. When he simply called my raise on the flop every single hand in his range with a seven or a flush draw that could make it to this river without making a turn mistake is discounted because I know he's a great player, so I know he won't be making the mistake of calling the turn without showdown value against me. If he were to continue with a flush draw like KdTd, I would expect him to get the money in on the flop or to check-raise me all-in on the turn because he's priced out of a turn call and might be uncomfortable check-calling the still unknown river on an already scary board with king- high.) If he has 5d7d, 9d7d, Td9d, Qd9d or QdTd I'm expecting him to get those all-in on the flop because of the massive equity those hands have against my range and with how often he should expect a three-bet on the flop to take down the pot, given how weak he is perceiving my range of hands. I would also expect him to check-raise most of his combination hands (flush draw plus pair or flush draw plus straight draw) because

I might bluff three-bet him on the flop given his high check-raising frequency over the last twenty hands. Also, I have the Jd in my hand, so there cannot be any hands in his range.

Next, let's consider the 7x hands that could possibly get to the river by taking his line of lead and call the flop and check and call the turn. He doesn't play 57 off-suit, abbreviated as 57o, 97o, J7 suited (abbreviated as J7s) type hands pre-flop out-of-position 100 big blinds effective (-$2000 effective stacks in this game) unless he's re-raising me pre-flop as a bluff. It's even less likely that he would bet and call those hands rather than check-call or check-raise with them. If he led into me and called my raise with a straight draw like that, then his outs might not be clean if he makes a straight on a diamond turn and I know he realizes this is a bad play and that he, being a skilled player, would not make it. Also, if he doesn't hit the turn in some way, he'll have to be either check-raising me without much equity if called or check-folding a lot of turns, and I know he knows he

can't win by folding. So the 7x hands are also out of his range, or at least extremely discounted.

We've narrowed his entire range down to weaker made hands. So now why is he shoving all in on the river, especially one he should expect me to bluff with my air almost always? From conversations we had about three months before this hand took place, I realized that he understands the value of turning made hands into a bluff. This board ran out in such a way that it looks like it heavily hit his range and I think that he's capable of realizing that if I'm going to give him credit for flushes and straights here that it's very unlikely, especially with how wide a range he perceives me to raise this flop and to bet on this turn, that he thinks I can call here. He's betting $1090 to win $1760, so if he's bluffing, it only has to work -38.2% of the time.

Given all of what we've considered during the hand and that I think my particular hand beats the few weak

made hands he might play this way (J9, JT, perhaps QJ and KJ). I decided to call. CALL HERO, $1,090 Showdown: VILLAIN SHOWS [Jh, Tc] HERO SHOWS [As, Jd] HERO wins the pot of S3,939.50 with a pair of Jacks

The above is the explanation of a $2,000 buy-in heads-up no-limit hold'em hand that I played against a friend of mine not too long ago. Does all this happen in my head every single hand of no-limit hold'em I play? Yes it does. In one's mind, you're obviously not writing paragraphs like you're trying to explain the hand in detail. If you're a smaller stakes or new player, this particular hand might not be a mental cake walk either. My goal is to get you to the point where it will be easy for you to go through these thoughts in every step of every hand that you will ever play after actively reading this book. By active reading, I mean that you should be doing some calculations in the margins, asking yourself questions about similar hands you've played, and

exploring the possibilities. Poker is a game of near infinite permutations. So limiting yourself to only the example in this book would be a serious mistake if you're seriously trying to take your game to the next level.

A Note on Ego The first thing that I discuss with all my students is how the presence of your ego may affect your poker game. If you can't admit to yourself that you're just a person, just like any other player, who will make mistakes in a game of mistakes, then much more likely than not, you're in big trouble.

However, ego can also be a good thing. It may help you to squelch fears about taking shots when you should, to face tough competition, and to give you the drive to better yourself to feed your need to be the best. Of course, let's not go overboard with this mentality if

we're always playing the best-of-the-best, we're going to lose money or win far less than we could be in easier equally available games at similar stakes. There's something to be said for grinding a smaller stake to build a bankroll to be able to play in a potentially softer and higher stakes game. There's also something to be said about spending a stagnant poker career bum hunting and only playing the weaker competition with every day filled with waiting for a recreational or bad player to take a shot at playing in your regular game. If all you do is wait around for soft competition, you will not improve as much as the other guys fighting in the trenches, and the money you can make in your poker career will be much less than the harder working players

So I propose that we practice a little balance with our respective egos. It's tough to say what the best mix of the two cases presented will be, but we can be sure that it's certainly not all of one or of the other.

CHAPTER 1: PLAYER TYPES This book has been made to show you that there is not a system for beating poker. There is no one move or play that will act as a panacea for all your poker problems. The reason that a system cannot be applied to poker is that the variables in the game are near infinite and always changing. This book has been made with the intention of teaching you how to actively think in order to adapt to those variables, not how to robotically respond to them with one of a few choices.

At first, the pessimists out there might be depressed about the above statements. However, I hope that you realize how this actually is fantastic news! This means there are almost infinite decisions in the game that give

you the opportunity to play better than your opponent. And as we know from other poker theory, causing our opponents to make mistakes and playing better than our opponents in a given spot are tiny steps taken on the way to winning. If we can make better decisions than the opposition in every spot, we'll be at the top of the game, continuously pushing the limits and bringing online poker to levels never before achieved by average, system-centric players.

If someone's betting frequency in a certain spot is too high, we will heighten our bluff-raising and calling frequencies. If an opponent always over-bets all in on the river, we will adjust and widen our river calling range and our range of made hands that we check to him. It will surprise you how long this list could go and how long your list will go after reading this book. For the reason that all of these dynamics feed off of each other, this book may seem slightly disconnected. Unfortunately, as above-stated, it's an unavoidable drawback about writing about the subject and one that

we'll have to get through together. For this reason, in some sections of the book I have written instructions to turn to another section in attempts to alleviate confusion caused by the interconnectedness of the subject matter when the surrounding theory has yet to be explained.

Our goal, as aspiring poker geniuses, is to be able to explore as many of these possible dynamics in such a detailed and thorough manner that we will play better and adjust better than the opposition. We will be able to dissect a player not as one of a few types, but as an agent of his or her exact actions. Our reads will become more than the usual phrase-long description per player and we'll win more as a result of our efforts. Each decision will be based on our opponent's range in an exact spot, not on a loose idea of his general image, which is nearly useless. Because poker is a game of imperfect information, the nature of our decision in each spot may be based on extrapolated data we have gleaned from other tendencies. The better we become at

extrapolation and observation, the better our decisions will be and the more we will win.

CHAPTER 2: PRE-FLOP PLAY re-flop play isn't the battleground for high stakes play. The edges are too small and the variance is too high. If it were the case, you would see the nosebleed players getting hands like A4o all in pre-flop and being ecstatic. So why doesn't this happen? It is because there are bigger skill edges and more variables to interpret better than your opposition post-flop. That said, pre- flop play is important because the decisions you make pre-flop will often impact how the largest hands you play will be played post-flop and because so much of getting out of tough spots where you are mistake-prone in poker is simply knowing how to avoid them. In order to avoid difficult spots, it will help us to know the general theory about the foundations of our pre-flop decisions.

Raising Pre-Flop I'm not going to go too far into specific hands to use in every instance pre-flop. Charts are frequently irrelevant or incomplete and so I'll just be giving you some food for thought so that you can make your own decisions that will work for any pre-flop situation, regardless of stack sizes and opponents. The game of No- Limit Texas Hold'em is very dynamic and so you need to be equipped to make your own decisions in different spots and to learn how to weigh and interpret the many different factors we will want to consider before choosing to raise a hand pre-flop.

Domination Generally, if we're raising pre-flop, we want to be called by dominated hands. For example, the case is rare that you would want to raise hands like K9o under the gun in a 6-max game. If you flop top pair with a hand like K9o after you've raised first to act in a tough game and get multiple streets of action, you're likely to be behind.

The decision to choose which hands to open are largely dependent on your opposition's pre-flop calling ranges. If we are playing at a table with a weaker player who calls 80% of his hands, then there will be more opportunities to open K9o. Why is this not a hard-set rule that we could add to a reasonably sized chart of some sort? A chart under thousands of pages long would be unintelligible because you still have to worry about players yet to act, all of whom may play in very different ways and have different mind-sets based on

previous hands played in the game or session. Will they often times re-raise your opens and play back at you with good (difficult to interpret) bluffing frequencies? Will they be calling with hands that dominate you so often that raising your particular hand will be a mistake? Will they be floating your flop continuation bets often and making post-flop difficult for you? Will you be out of position versus potential callers? If any of these are answered "yes," then it is likely your best play with K9o to fold pre-flop.

As stack sizes go up, domination becomes less important because your implied odds go up. For instance, the choice to call with suited Ax hands, often with position, will have a very dynamic value depending on stack sizes and how likely you are to get paid if you do make the nut flush. Hands like Q8s may make unlikely straights or two pairs for which an opponent may not give you credit, whereas 50 big blinds effective, the main concern by far is being on the bad end of a top pair versus top pair situation. Specific stack sizes with

which to call weaker hands vary based on the opposition's tendencies, the players yet to act pre-flop, and so many other factors that an attempt to quantify a correct stack size with which to begin calling such hands is almost certainly a non- fruitful exercise. The more imprecise variables that we attempt to quantify the less certain and the more general our idea of hands to play pre-flop in these spots become. The decision becomes one rooted more in theory than in a mathematically quantifiable objective choice.

Adjusting to the opposition's Pre-Flop aggression If everyone at the table is re-raising you often, then you will want to take steps to adjust to your opponent's pre-flop aggression. You should probably widen your four-betting range pre-flop and/or tighten your pre-flop opening range. Instead of having to fold hands like 64s

in a spot, we will have more hands like 99 that we may choose to four-bet with the intention of calling an all-in bet as a result of a tighter pre-flop raising range. Instead of folding our weaker hands, we might also choose to four-bet as a bluff. We will elaborate on these two specific adjustments later in the chapter, but before continuing to read, try to figure out why four- betting a hand as weak as 99 and calling an all-in is quite often a good play versus many people with the level of aggression in today's games. How many reasons can you think of before continuing to read?

The same logic that applies to raising pre-flop applies to re-raising pre-flop. Imagine a case where it is extremely likely that if you call with AQo, that you will be squeezed. Next, imagine a case where if you re-raise AQo pre-flop, the original raiser will fold hands like AJo and ATs. Finally, imagine both of these cases being true of the same hand and that player who we believe will fold AJo and ATs type hands raises and we haveAQo on the button. AQo is usually a clear call in this instance.

After calling the three-bet, you may choose the best of many ways to play back at a squeezer based on the squeezer's pre-flop and post-flop tendencies.

If the squeezer continuation bets missed hands every single time and will bet the flop and turn oftentimes on Axx and Qxx boards, then perhaps calling is the best option pre-flop with the hopes of seeing such boards or of trying to get your ace high hand to showdown. If he is squeezing hands like AJs and KQo and he is squeezing so often that it is hurting your ability (lessening your implied odds) to call with speculative hands such as small pocket pairs pre-flop in similar spots, you may want to shove as a way of balancing with the times you decide to re-raise hands like small pairs. Additionally, if he plays very well post- flop, then perhaps re-raising (usually all-in, unless you are so deep that you imagine him to be folding only worse hands) is the best play. The decision is going to be made based on your opponent's calling range when you re-raise, how often he will be folding to your re

raise, the money in the pot before your re-raise, what you must risk to re-raise, and your equity against his calling range with your specific hand. After a simple math calculation, you should know the weakest hands with which this play will be profitable at a specific time with a specific set of circumstances. There are examples of the math describing this type of play later in the book.

By going all-in, we will realize our equity against his weaker made hands like AJs and 88, as well as discouraging him from bluffing in the future, an often over-looked positive externality for when we shove and the squeezer folds. Even if we are called by a better hand in the specific hand we choose to back-raise this AQo, he will realize our ranges in this spot are balanced and well- suited or adjusted for his style of play. These adjustments will force him to readjust his pre-flop tendencies and allow us to call with more of our speculative hands in- position pre-flop knowing that he will have a more polarized range of hands for squeezing pre-flop. If he does not feel the need to adjust, we are

obviously content in taking his money by exploiting his pre-flop over- aggression in this instance.

Calling Pre-Flop (In-Position) When considering a call pre-flop, we should apply the same concepts that we believe our opposition is considering when choosing hands to open in singleraised pots pre-flop. Always ask yourself if you're dominating your opponent's raising range with your hand and how often you think you'll be able to take the pot away through some combination of floating and bluff-raising (see chapter 3 on flop play).

Other questions to ask when considering a pre-flop call include:

• How often you will flop something deceptive enough to win a large hand? • How often your opponent will pay you off when you have a deceptive hand? • How well do you know your opponent's post-flop tendencies? (the better you know them, the better you can play marginal hands in position with more information and the more mistakes you are able to force him to make against your range)

We talked about dominating hands already, so let us move to our next question: are there a lot of boards I'll be able to float using randomization by equity with this particular hand and will this opponent allow himself to be bluffed on later streets?

First, let's define what I mean when I say "randomization by equity." The term itself is something I believe Aaron Jones coined, but the concept is one familiar to all successful poker players. The idea is that at certain times every player should be bluffing in order to balance the times that he is betting for value, or in this case, the reverse, floating when we have made hands in our range of hands. Because we are able to choose the hands with which we will bluff and because we will be playing against observant opponents, it's sometimes necessary to randomize these bluffs in order to not give away information about how we play. It's important to distinguish between a "mandatory bluff spot," a time when you have one of the hands you have chosen to use as a bluffing hand in a certain spot, and a great situation to bluff. Consider Qcjh o n a K c T h 3 s 4 d board when your opponent called your flop bet. This example shows what we mean by "randomization by equity." You'll notice that Qcjh has a lot of equity against a flop calling range on this particular board, whereas a hand like 9s8s would have less equity because the cards are both below middle pair and there are no

draws that the river card will complete for this hand. However, against certain opponents, if the turn is an ace, you might do well enough betting your entire air range to show a profit given the large portion of a certain opponent's range that may be folding. For our floating example, we should choose hands that have the best equity to use to call flops and bet turns. Obviously, there are exceptions to the rule, including times when you believe your opponent is very likely to check-raise the turn and you have a lot of equity and do not want to fold your hand to a raise. This idea will be better explained in Chapter 3, which focuses on flop play, especially the sections on barreling and on floating.

JTo is a hand a lot of my students seem hesitant to call with in position, but it works out very well for our floating ranges as there are a lot of flops with which we connect and are subsequently able to float, especially against looser and more passive opposition. Now, choosing hands pre-flop partially based on their floating merit is a pretty involved and complex situation to

dissect, so we'll start out with a brief examination of a few boards on which we will play different hands in the same manner in order to emphasize the reasoning of both floating and of protecting our floats. By protecting our floats I mean that we will also be calling flops with made hands to mask the times when we choose to float. Calling with made hands and calling with weak draws play off of one another because one helps the other in ways I will soon discuss in a more in depth way in the chapter on flop play.

Essentially, a hand like JT has a much longer list of boards on which one may find oneself wanting to call with a made hand or to float. Some examples include 794, T83, Q83, KQ6, and KT3. Notice how even a hand as weak as Q8s has much more value than Q7s, not only due to its obviously superior high-card value, its ability to make higher top pairs, but also because of the vast amount of boards that may facilitate a profitable float against particular opponents. For Q8s, there are more boards with similar textures to T94 and J93 that might

roll off compared to a hand like Q7s and the more obvious 458 boards for Q7s to float or to check-raise. Q8s has the obvious gut shot to the four-straight flops, as in the Q7s example, in addition to the less obvious, and therefore, more valuable, two-card straight draws. Considerations like this are a significant part of determining profitable hands pre-flop.

With the knowledge that playing back on certain boards is more profitable when your hand has some added equity or outs to improve, caution should be exercised. If a board like J96 comes and we call our opponent's continuation bet with any hand, as a float or with a made hand, it is important to realize the perception of our range and how wide it will seem to many opponents. With such a wide perceived range, perhaps as wide as any gutshot in our pre-flop calling range, our opponent's betting frequency should increase, if he is in tune with the dynamics of such a board. The higher betting frequency from our opponent means more bluffs and thinner value bets on future

streets. It also means that we should adjust accordingly. We can out-manoeuvre our opponents who might consider expanding their ranges against a wide perceived floating range by incorporating a number of effective strategies such as: • Double-floating (floating again on the turn) • Calling down lighter • Raising turns and/or rivers both for value and as a bluff. In order to successfully double-float, the best tendencies of an opponent to see that makes the play profitable are going to be that opponent rarely checkcalling rivers with made hands, which is almost always the case on such draw-heavy boards, unless he has seen us double-floating in the past, and not three-barrel bluffing as often as he should be. It's quite intuitive that the more air in our opponent's checking range on the river, the more successful a bluff will be after a doublefloat. Our opponent should be less likely to check and call a river with a made hand because when several draws miss, our opposition's main concern will be balancing thin value-betting with his bluff range. He

should want to value bet instead of bluff catch with his made hands in order to get called lighter by us and to make more money from the times that we call with worse hands, which will happen quite often when many draws in his range miss the board. Additionally, over a general range of poker players, it is extremely unlikely that our opponent will view us as someone who is double-floating compared to the times that we will call down lighter because of all the missed draws on a given board, which means that most opponents will be giving up on blank rivers because they figure to be called too often to have their bluff show a profit. We will see in the chapters on turn and river play why giving up because you think you will be often called by better isn't necessarily a great idea (see Chapter 4).

In this more passive river scenario against the opponent who will give up his bluffs on a blank river, a double float becomes much more profitable. You have no more to do than a "simple" math equation determining how often a certain opponent will be

giving up by the river and if that percentage of times will warrant a double-float and a river bluff plus the consideration of the expected value of your gutshot or whatever weak draw with which you chose to continue. Note that when you are calculating the value of the play in its entirety that our turn play is independent of our flop float, which we already determined to be profitable, and so the flop float should not be part of your double- float equation. The word simple is in quotations because you will have to account for his change in bluffing frequency on certain river cards and therefore attempt a somewhat complicated calculation to obtain an accurate success rate for the play for all possible different river permutations. For example, the same opponent is probably extremely likely to bet flop, turn, and river with T8s on a J946K board as the opponent who check-folds the river on a J9469 board. These permutations, the specific cards on which a certain player continues a bluff or gives up are often going to cause a small error in calculation. However, if you find the correct opponent against whom to employ this play, you won't have to worry so much about the smaller

mistakes in your calculations because your profits should be quite large relative to the small adjustments or mistakes in the estimation of his bluffing range for certain river possibilities.

The best way to find the answer to how profitable a double-float is will be to do a few G bucks calculations (see chapter 4) in order to determine how often we will get to a river with the hand we decide to float the turn and our opponent will be checking that river, presumably always to fold his hand.

Another important consideration is if your perceived range after calling a turn is wide or full of stronger made hands and the relevance of this perception on your opponent's river bluffing frequency. If you decide to try to double-float on a drawy board, even the more passive opponents with the betting lead will realize that your turn call indicates a lot of pair-plus-draw type hands that might now be forced to fold on the river to another bet. If your range is perceived as such, it's less likely you

will induce a river check often enough in order to give yourself a profitable turn float followed by a river bluff.

Still another consideration is if your hand has any value in deception and if it will hit often and hard enough for this value to be realized. This consideration goes hand-in-hand with the above consideration because the more deceptive your draw is, the more disconnected the board will be. For example, floating twice with K8o on 567A and then rivering a 9 has little value in deception, whereas floating twice with a hand like Qh8h on Jh9s4c2h and then rivering a Td has an obvious increase in value, which is referred to as implied odds.

If we know we are playing an observant opponent, simply having our opponent know that more hands are in our pre-flop range in some spots will give us more credit for value hands when we choose to float because we are able to credibly represent a wider and more believable range of made hands. If we miss a draw when

calling down in-position, for example, with a small pair and a flush draw, there is nothing that says betting when checked to on the river or raising a river bet will be bad if we think our showdown value is no longer strong enough and as long as our opponents perceive that we are bluffing in close proportion to the frequency of us having the hands which we are representing and our opponents have a river bluffing range, or more specifically a folding to a river raise range (see Chapter 6 on Turning Hands into Bluffs). If things get too out of hand with our bluffing frequencies in these types of spots, we will be called down too lightly to show a profit with our bluffs. It's important to note why I said "having our opponent know" about our pre-flop range, especially before attempting to represent an unlikely hand. If he is not aware of our calling range in a particular spot, he might ascribe a different range to us and therefore give a bluff or value bet more or less credit than our actual ranges should dictate, depending on his thought process for the particular spot. People often assume that their opposition plays like they play and they interpret bets as their opponents would

interpret them, especially with no access to other information to the contrary and this false assumption is the cause of many mistakes. The idea that our range is different than what our opponent thinks it is the difference between an actual range and a perceived range. Getting the two confused is often costly and false assumptions are often avoided by avoiding fancier plays that require strong reads or evidence about an opponent's range to show a profit when no such information is known. Always keep in mind the difference between your perceived range and your actual range in every spot of every hand that you will ever play and you will be a lot more successful.

Calling Pre-Flop (Out-of-Position) If an opponent has an extremely tight raising range from a certain position or just in general, then calling out of position with hands like KTo and QTo may not be a part of a good game plan. The positive externalities of future bets you induce, or pots you are able to take away by representing wider ranges for value, may not be enough to offset the reverse implied odds of the situation. In other words, the idea of our pre-flop hand selection goes back to dominating hands. If we are always dominated or even often dominated in a spot, folding and sometimes three-betting the hand pre-flop may be the best way to play the hand against a particular opponent. The best way to avoid tough spots is to avoid putting yourself into the situation where they will often occur. However, it's important to distinguish between a tough spot and a non-profitable spot. Sometimes, a spot will foster so many difficult decisions

against a well- playing opponent that the expected value of the situation will plumet because our opponent will use position to outplay us, making sure we win the minimum and lose the maximum at all the right times. Difficult spots don't always mean money-losing spots; however, the two often go along with each other because the more mistakes someone makes in poker, the more money they will lose. Large and difficult decisions with a semi-face up range on the river after checking and calling flop and turn is a fairly common example of the quintessential "tough spot" in No-Limit Hold'em. Without position, our opposition controls the frequencies of betting as the board changes and so it's very difficult to play well versus someone who has a solid read of your range and who is able to exploit that read by three-barrelling and over-betting effectively, by which I mean your opponent will bet in a way that induces you to make a mistake by either calling or folding too often.

Another consideration when calling with weaker hands out of position is your opposition's barrelling frequencies. In other words, if we check and call a flop continuation bet on a board of Qh9s3c with KcTs, are the chances of the following scenarios taking place going to make the flop call profitable: our opponent giving up and we win by bluffing a river or by showing down the best hand, plus the implied odds of us turning either a king or a jack, and plus the chances he barrels us lighter in the future when we have a made hand, having seen us check-fold the turn in a similar spot with what should be assumed to be a draw, given the draw heavy nature of the board and the unlikelihood that we would hold a made hand of respectable strength, one that is unlikely to be sucked out on on such a board.

If your opponent is betting every turn or at least with great frequency, a better plan for the hand could be to check-raise his flop continuation bet in order to stymie our opponent and take away the initiative. A flop check-raise allows us to take down the pot immediately

some of the time, bluff the turn some of the time, and improve to the best hand if our opponent is not prone to three-betting the flop. The more likely an opponent is to three-bet a flop, the less profitable a check-raise bluff or semi-bluff will be on the flop.

The flop check-raise is a bit different of an approach than my default strategy to playing poker, but it is also an effective plan of attack in the right situation. Let your particular opponent be the determining factor of which default game-plan is best. By default, I prefer mostly the check-and-call method in these spots because I find it lower variance and easier to balance. However, a deceptive mix of the two is necessary at times to keep adjusting good players confused. By easier to balance I mean that it may be more difficult to start check-raising medium strength hands, like 98o in the instance of a Qh9s3c board and expect to be able to show down as often and as confidently (making less mistakes) than if you check-called it and avoid turning your range as faceup on future streets. There may be

times you check-raise 98o, the turn is a king and you decide to turn your hand into a bluff to fold out Qx and worse hands, only to run into Kx or a two-pair or better type hand, whereas, checking and calling the flop avoids putting in a lot of money out-of-position and without much confidence in your hand or knowledge about where it is relative to your opponent's range.

Whichever choice you are making about your strategy for playing a given hand, make sure that you are also making other choices to disguise your range in that same spot. For example, check-calling KJo on Qh9s3c and check-raising KJo on Kh9s3c might be bad against some people, mostly good hand-readers because of how weak future check-calls will seem and will be. Balance in these spots is extremely important, otherwise, you're running the risk of being exploited by good players. Choosing the hands to play pre-flop in order to balance these spots will strongly affect how your range appears to the competition when you call out-of-position.

I know that some people have commented on instructional videos that f vemade about how they wouldn't call hands like KJo out-of-position. Hopefully, this section sheds some light on my reasoning and shows how being able to balance my out-of-position play justifies the tougher post-flop spots.

Re-Raising Pre-Flop (In-Position) Generally, the best choices of hands to use to reraise in position are hands with which you would like more action (premium pairs, AK, etc.) and hands that are slightly too weak to call (hands you're relying on getting your opponent to fold). This strategy is more aptly described as three-betting a polarized range preflop, and it's the best way to play against a lot of opponents, especially ones from which we do not have much information.

The strategy behind using hands that are slightly worse than our calling requirements in order to bluff reraise pre-flop is that they will be the strongest hands we can use without "wasting" the value of our calling hands. Three-betting often with these types of hands will eventually create an image of re-raising lightly pre-flop to induce more action when we do happen to have good enough hands to take more action. The occasional bluff helps to balance our pre-flop re-raising range because sometimes we will actually have good hands for which we want action. If we are not bluffing some of the time, we become very easy to read and easy to play against, both of which are detriments to our win rate. Our expectation with a given hand, say 44, if we call pre-flop in position, may be higher than it would be three- betting that specific hand. The idea that other hands may have more value post-flop than by re-raising pre- flop as a bluff goes for similar speculative hands like suited connectors or weaker broadway hands.

Re-Raising Pre-Flop (Out-of-Position) We all know the importance of position in poker. If we do not have position, then our opponents have more information with which to make their decisions and they have an easier time deciding what to do with draws, especially weaker ones. They have the ability to float more often and to make cheaper raises as bluffs because we will often be put in situations where we would have to risk a significant percentage of our stack in comparison to their risk.

Though not a crucial consideration with 100 big blind stacks and below, when we three-bet out-of- position, we will be less able to call a four-bet from our opponent, given our positional disadvantage. For this

reason, most of the time we should still be using a polarized range to three-bet. Of course, there are always departures from the "rule." I say "rule," because without the necessary information on how to adjust, I believe a polarized three-betting range to be the most profitable way to construct a three-betting range. The point of this book is to show you that, in poker, the rules are not set- in-stone. So now the question is, how do we go about adapting to different re-raising tendencies of our opposition? Let us examine a few case studies to illustrate possible pre-flop adjustments to different player styles in order to eventually realize an overall game plan.

First, imagine an opponent who never four-bets pre-flop. He calls all three-bets in position and has been seen to call three-bets often over a large sample of hands. For someone like this, we should depolarize our range of hands we choose to three-bet for value. We can depolarize our range because now we are expecting to be called by more hands that we dominate. For example,

now we can three-bet hands like AJ and KJ because we believe him to be calling with hands like QJ and JT. The times that we will both make top pair and the money goes in are going to favor a depolarized range for us because those times will occur more often given our opponent's wider calling range, thus we make more money by adjusting to our opponent's pre-flop tendencies.

Next, let us examine someone who only four-bets us or folds to our three-bets pre-flop. If someone chooses to play all their hands pre-flop this way, unless he's four-betting and or calling all-ins so often that we would want to get AJo all-in pre-flop (if he's bluffing about 41 % of the time with lOObb with a semi-wide range for value, four-bet calling hands like 99), then there is no reason to depolarize our three-betting range here as we would be putting ourselves into situations to get blown off of the best hand pre-flop where we would make more bets on average by calling the same hand pre-flop. Having to fold a good hand pre-flop against

this opponent type also means that we are never going to have the advantage of dominating his range unless we adjust by calling those good hands like AJ and KJ pre- flop.

Another consideration when choosing hands with which to three-bet someone pre-flop is their raise size. The smaller the raise size your opponent chooses, the deeper the effective stack-to-pot ratio is, which means the more hands they should be able to defend, expecting more implied odds and, therefore, more profit when they make deceptive hands. The dynamic that a deeper pot-to-stack ratio creates is often extremely aggressive because of the nature of how profitable having a lighter calling range in this spot can be and how much more likely one is to get action by four-betting a big hand pre- flop. A lighter calling range for the opposition means that our three-betting range should be lighter, which means his four-betting range should be wider. This means that our opponent will be calling with hands that we'll be dominating more often should we choose to

depolarize our three-bet range. Because we are depolarizing our three-betting range, our opponent's four-bet bluffs will have a greater success due to the extremely unlikely nature that we are three-betting enough combinations of value hands strong enough to comfortably withstand action given our depolarized three-betting range. There simply aren't enough combinations to balance our three-betting range in that way in this spot; therefore, we have to widen our five- betting range, which usually means an all-in bet with lOObb stacks, or begin calling four-bets lighter, which can be tricky, especially when we are out-of-position. Calling four-bets sets us up for a tough spot because with the sizing of a smaller open, our three-bet and his four-bet will also be smaller, meaning that our five-bet shove will be risking a full buy-in while we expect to win significantly less bets if our opponent folds his hand. The dynamic that is present with good players when other good players are raising smaller pre-flop shows why a smaller pre-flop raise size is such a powerful weapon and certainly one with which I would recommend experimenting.

Notes on Small Pairs Sometimes you won't be able to call profitably with smaller pairs out-of-position against a good opponent. Your flop check-raise bluffs and lead bluffs won't work often enough to show a profit and you'll miss the flop too often. For these reasons, three-betting with your smaller pairs instead of folding them may enable you to squeeze a tad more value from the hand and make the play more profitable than a fold. If you make a set after your opponent calls, it will be extremely well disguised, and so you have great implied odds. If you have a problem barrelling weak draws too often against an opponent with good calling frequencies, with smaller pairs you will miss the flop about 88% of the time and avoiding a situation where you may be forced to barrel off a lot of your stack in order to have a chance at winning a hand may be the best plan of action. A positive part about playing weaker pairs out-of-position is that it's very easy to get away from the hand once you

miss a worrisome flop because there will usually be at least two over-cards on the board and your equity against your opponent's range, not to mention the decisions you will be forced to make on later streets will likely both be poor. In this pre-flop spot out-of-position against an aggressive and capable player with a wide and disguised range of hands where we are considering three-betting smaller pairs, this subset of hands follow our earlier discussed guideline of "hands that aren't quite good enough to call with are therefore the best hands to bluff with pre-flop."

Using the next best hands from the hands with which we may profitably call ensures that our three- betting range is as strong as possible. Smaller pairs, depending on our opponent's four-bet/calling range, can be great hands with which to five-bet shove as a semi-bluff. A lot of the time we are called, we'll be up against AQ or AK and will be racing. Try doing a few expected value equations and adding or taking away a few pocket pairs from our opponent's calling range and

notice how relevant it is to know with which pairs he's capable of calling an all-in bet after he four-bets preflop.

Four-Betting Pre-Flop If you are noticing that your opponent is employing a strategy involving three-betting pre-flop with more than his fair share of hands that would like to get all-in before the flop, there are many adjustments you will need to make in order to avoid being run over by him. As often as you want to steal the blinds to bolster your win rate, good players aren't going to lay down their hand every time for you and give you what could be their pots.

We already discussed calling more hands in position in order to play post-flop in such a way that negates as much of your opponent's re-steal equity as possible. Another way that one is able to negate this

edge is by having a balanced four-bet range, both with value hands and with bluffs.

Choosing a four-betting frequency is going to be dependent on the three-bettor's three-betting range at the time of the hand in question and his five-betting range given the game flow and the player's tenancies. Many dynamics can come into play that will affect your opponent's decision to three-bet, all of which were explained earlier in the 'Re-Raising Pre-Flop' section, and most of which will be more important than looking at his statistics in order to solve for a 'perfect' four- betting range. Again, the meta-game considerations, especially in any spot where your data-mined statistics are often over too small of a sample size to be significant, are going to out-weigh the information given by hands played in previous sessions.

Another, and somewhat odd, type of four-bet to work into your game is a four-bet shove. The only time I think using this play has merit is when you have called

an opponent's opening raise, either with a weaker hand or with a slow-played hand, and another opponent after you squeezes the two, or more, of you with around 100 big blind effective stack sizes. If the first opponent, the original pre-flop-raiser, folds, then deciding whether or not to shove a hand like pocket 3 s is as simple as solving an easy expected value problem based on how often the squeezer is bluffing and with what hands he has in his value range. For example, take the following case at 5/10 no-limit with $1,000 effective stack sizes: the cutoffraises to $30, we decide to call with TdTh on the button, the small blind folds, the big blind squeezes to $120, and the cutoff folds. We are now presented with three main choices, assuming we've ruled out folding: call the squeeze, make a small re-raise, or go all-in. If we call the big blind's squeeze then we turn our range somewhat face-up due to the fact that we'll have speculative hands in this spot more often than slow- played hands simply because of the more combinations of speculative hands compared to premium hands. Our range also appears weak if we choose to call the big blind's squeeze in light of the the fact that we'd usually

re-raise our premium hands in order to balance with the times we'd re-raise as a bluff pre-flop. Re-raising small pre-flop also causes problems by failing to cause our opponent to make some mistakes because a smaller four-bet allows our opponent to play better against our range. For example, our opponent might five-bet shove something like AJ with which he expects to have some folding equity that he might also fold to our shove because with hands such as AJ he expects to be dominated or racing against our shoving range. Given the flaws in the other two choices with which we are presented in this spot with around 100 big blind stacks. I'm of the opinion that making an all-in bet is the easiest way to balance the range of hands with which you choose to continue as well as the best way to force your opponent to make mistakes against your range. Here's how the math works out in this particular spot with TdTh, assuming this player squeezes 12% of the time in this spot on average and that he's planning on calling a shove with 99+, AQ+, which is 5.2% of hands.

Our read of his range in this spot means that he's calling (5.2/12)* 100% = 43.33% of the time and folding 56.67% of the time.

TdTh is 44.2% vs a range of 99+,AQ+. EV(shove) = (percentage of times we take down the pot) (the pot if villain folds) + (percentage of times our opponent calls) (total pot when villain calls * (our equity when called the amount we risk to shove) EV(shove) = 0.567 (185) + 0.433 (2035 * 0.442 - 970) EV(shove) = 104.83 + (-30.56) EV(shove) = $74.27

As with all the expected value calculations and scenarios we examine, I recommend running them many times with different numbers that represent different assumptions about our opponents' play in order to familiarize yourself with different possible situations that may occur while you're playing poker.

Five-Betting Pre-Flop Let's first examine the simplest scenario in which we might find ourselves five-bet shoving, a heads-up five-bet all-in. Assume we're against a reasonably aggressive and balanced player who will be four-betting us as a bluff 60% of the time as we are considering five- bet shoving with pocket 3s. The other 40% of the time, he has his value range, which consists of 99+, AQs+, and AK. PokerStove shows us that pocket 3s is 30.594% to win against this particular balanced heads-up opponent's value range. Assuming that our opponent will four-bet us to 240 over our 100 three-bet, our expected value equation looks like this in our fictitious heads-up match:

EV(100bb) - (percentage opponent folds) (pot we win when opponent folds) + (percentage opponent calls) (total pot * our equity when called - what we risk) EV(100bb) - 0.60 (340) + 0.40 (2000*0.30594 - 900) EV(100bb) - 88.752

Our expected value equation shows that we should make just over $88.75 on average with our five-bet shove against this opponent at this time in a heads-up match.

Let's change the stack sizes and the pre-flop sizing a bit and see what happens as stacks get a bit deeper, at 150bb effective stacks. We'll keep the same hand and assume that he has the same range for calling a shove. We are also changing our three-bet size to 110 and our opponent's four-bet size to 250.

EV(150bb) = 0.6 (360) + 0.40 (3000*0.30594 - 1390) EV(150bb) = 27.128

150bb effective, we would win just under $27.13 by five-bet shoving pocket threes. The reason our expected value changes so much is because we are risking more to win very close to the same amount that is in the pot pre-flop. What this means is that our opponents should realize this situation and be four-betting as a bluff more

often and thereby making more money, expecting us to tighten our five-betting range significantly. If that is the case, well have to change our expected value equation a bit. Obviously, filling the pages of this book with expected value calculations would show how to adapt and adjust in all the different spots, but doing the calculations is something relatively simple that you should be able to do and to get used to doing. Experimenting with different calculations will make you remember the numbers you calculate and teach you how to work with expected value calculations if you're unfamiliar with them.

Due to the aggressive nature of today's games and the fact that there is so much dead money in the pot, you'll find that the option to five-bet the pre-flop four- bettor presents itself regularly and from many different positions. First of all, let's see how often our opponents have to fold here to make a bluff profitable.

Full Tilt Poker Table (6 max) - $5/$10 - NL HE Seat 1: HERO ($1,053) Seat 2: VILLAIN 1 ($1,067) Seat 4: VILLAIN 2 ($863.10) Seat 5: VILLAIN 3 ($1,057) Seat 6: VILLAIN 4 ($1311), is sitting out VILLAIN 2 posts the small blind of $5 VILLAIN 3 posts the big blind of $10 The button is in seat #2 *** HOLE CARDS *** Dealt to HERO [Ac,3c] HERO raises to $30 VILLAIN 1 has 15 seconds left to act VILLAIN 1 raises to $105 VILLAIN 2 folds VILLAIN 3 has 15 seconds left to act VILLAIN 3 raises to $250 HERO?

I have played with both VILLAIN 1 and VILLAIN 3 for many hands and both view me as mostly straightforward, but aggressive and capable of making crazy plays at good times; although, bluffing here might be a bit optimistic!

I know that VILLAIN 1 three-bets about 8% of his hands on the button and that he's probably calling with JJ+, AK if I shove, which accounts for 3% of hands. That means he'll be folding [l-(3/8)]* 100 percent of the time, or 62.5%. We also know that VILLAIN 3 is a very aggressive regular capable of recognizing that VILLAIN 1 and HERO will both be folding enough of the time to bluff some percentage of the time, let's say pessimistically 60%, since it's likely more often than 60% of the time since it's such a good bluff spot and there are few combinations of value hands relative to how often VILLAIN 3 is likely bluffing. For value, let's assume that he's raising 99+, AQs+, AKo and that he will fold 99 and half his TT combos to HERO's shove, because it looks so strong. So we'll give VILLAIN 3 a total range 40% comprised of half the combos of TT, JJ+, and AK and 60% of his range comprised of bluffs. Simply put, we believe he will fold to our raise 60% of the time and call with the top 3.2% of total hands the other 40% of the time.

In order to calculate the expected value for this situation we have to break down the calculation into a number of smaller equations and add them. The formula for this expected value calculation is:

[ calculation missing from the book ]

This expected value equation shows that the expected value is the sum of a number of situations, i situations, multiplied by the probability of that situation occurring. All the probabilities summed should be equal to 100% because we're calculating the expected value of a particular situation in full.

First, let's outline the four situations that are taking place.

1.

The button folds and the big blind calls.

2.

The button calls and the big blind folds.

3.

Both the button and the big blind call.

4.

Both the button and the big blind fold.

Now that we've defined the four values that we'll be adding, let's calculate the probability that each occurs and then the value of each of the four possible outcomes.

1.

BTN folds and BB calls. The button's folding

percentage facing a five-bet shove, given all the hands he is three-betting, is 62.5%. The big blind's calling percentage is 40%, the amount of the time we estimate him to be bluffing. In order to get the likelihood of both events occurring we have to multiply the two and by doing this, we get 25%. We'll use the same methods for the rest of the calculations.

2.

BTN calls and BB folds. Because the big blind's calling

range is now affected after the button calls, we must recalculate his new folding range in order to get

the proper probability. The probability of the button calling is still 37.5%. Given a button call, a showing of extreme strength, we're narrowing the big blind's calling range to half the combinations of QQ, KK, and AA. So if at first the big blind is calling with the top 3.2% of hands, half of the TT combinations and JJ+,AK, and his new calling range is 1.1% of hands, that means he'll be folding (2.1/3.2)* 100% = 65.63% of the 40% of the time he was going to call, calling 34.38% of the time of that 40%. So again, we multiply the probabilities and to get the likelihood of the big blind calling, 0.34375*0.40 *100% = 13.75%. So he folds 100% -13.75% of the time, or 86.25%. The probability of the button calling and the big blind folding is therefore: 0.375*0.8625*100% = 32.34%.

3. BTN calls and BB calls. We have already determined the big blind's new and tighter calling range given a button call and the probability that he calls after the button has called to be 13.75% of the time. So the

probability of the button and big blind calling is 0.375*0.1375* 100% = 5.12%

4. BTN folds and BB folds. The probability that both villains fold is simply the respective likelihoods of them folding multiplied together. 0.625*0.60*100% = 37.5%.

Just to check if we have all the events' likelihoods correctly calculated, we'll add up all the probabilities. 5.12% + 32.34% + 37.5% + 25% = 99.96%, which is an acceptable error given rounding throughout our numerous calculations.

Next, we should calculate the probability that Ac3c wins versus each of the calling ranges that we have constructed in scenarios 1-4.

1. Ac3c vs 1/2(TT), JJ+, AK 30.2% vs 69.8%

2.

AC3c vs JJ+, AK 29.9% vs 70.1%

3.

Ac3c vs JJ+, AK vs 1/2(QQ), KK+ 19.8% vs 27.5% vs 52.7%

4.

We win the pot 100% of the time.

As shown before in our expected value calculation, we need to multiply the probabilities of each event happening by the expected value of each event.

EV(1) = 0.25 (2244 * 0.302) - 1037 = -89.83 EV(2) - 0.3234 (2389 * 0.299) - 1037 = -104.36 EV(3) = 0.0512 (3206 * 0.198) - 1037 = -20.59 EV(4) - 0.375 (105 + 250 + 5) = 135 EVtotai = EV(1) + EV(2) + EV(3) + EV(4) EVtotai = "$79.78

So we have shown this particular five-bet shove to be slightly negative expectation, but with slightly different circumstances, with more aggressive players

involved or a different hand that does better against our opponents' calling ranges, this play, although high variance, could certainly have positive expectation. The perception of your ranges after you are called making this play will get you much more action on your stronger hands. While it's difficult to factor a specific value for this perception into an expected value formula, it should certainly be mentioned and a consideration if the parameters for this play end in a neutral or even slightly losing expected outcome.

Slow-Playing There are times when slow-playing a hand pre-flop may be more advantageous than re-raising it for value. Simply put, when you think your opponent or players yet to act will make a bigger mistake against your specific holding than if you re-raise with it, then it could be better to slow-play.

Other advantages to slow-playing pre-flop include the fact that it makes you less predictable not only pre- flop, but also post-flop. Firstly, if you call with large pairs some of the time pre-flop, especially in late position, you will be less susceptible to light re-raises, squeeze plays, because your opponents will have to be wary of your slightly stronger range. If your opponents are not wary, then they are making more of a mistake against your range by re-raising with the same frequency pre-flop, which means you will win more money from them. Additionally, you will be given a bit more credit if you choose to bluff-raise a continuation bet on a board like 2d3d8h because your opponent will have to include some slow-played large hands in your range.

Obviously, the benefits to slow-playing pre-flop are many, but when should we slow-play and how often? The 'when' is a bit more complex than the 'how often,' as it is essentially a function of the 'how often.' So let us first examine the 'when.' An example of a likely

profitable time to slow-play pre-flop is when you have been three-betting so often that you can tell somebody is about to do something about it by four-betting you as a bluff or with a wider value range with the intention of calling an all-in bet with something like AQo. Because people are expecting you to three-bet all of your good hands due to your aggressive pre-flop image, when you call with a strong hand pre-flop you will appear extremely weak to observant players. If your range appears weak, good, aggressive players will attack with a wider range of air and believe you less often when you do end up playing back at them.

Before you choose to slow-play a big hand pre-flop, you should weigh the value of a slow-play against the possibility of somebody four-betting your three-bet and going with their hand if you move all-in. Even if someone is folding pre-flop, a four-bet is usually around twenty-two through twenty-seven big blinds, which is a lot to win without a showdown. You should compare those numbers and the chances of an opponent four-

betting and folding to an all-in to how often someone is squeezing and calling a back-raise all-in. Alternatively, if you choose to call, you should use how often your opponent continuation bets after squeezing and how often they follow through on the turn when called on the flop as a basis for your comparison. When considering the two pre-flop options, its interesting to see how squeezing combined with continuation betting, when sized by a good player, is going to be about the same amount of big blinds as a pre-flop four-bet. The similarity in sizing makes it fairly simple to compare the two scenarios with certain opponents.

Another good time to slow-play pre-flop is if you are against an opponent who folds too many pre-flop re-raises. If you are not getting action on your good hands versus this particular opponent, then you may want to start calling with your strongest hands in attempts to induce more action post-flop and re-raise more often with bluffing hands. We have already touched on this topic when examining re-raising pre-

flop. We can summarize the above by saying that if it is unlikely that our opponent will call our re-raise with a worse hand when we have a premium holding, then it is usually a better play to call pre-flop with that hand and to slow-play in order to maximize the hand's value.

The same strategy of how to determine if this reason to slow-play is more profitable than re-raising pre-flop applies as in our first comparison about our two different choices of whether or not to slow-play. We should compare the likelihood of someone stacking off lightly post-flop compared to how often they are giving us action on our re-raises with their worse hands pre-flop. For most people, this comparison will become a function of how often you have been seen re-raising pre-flop by the player(s) in question, but you will find that some players will not adjust and they will simply wait for JJ+ or AK before continuing pre-flop. It's also important to realize that our two examples are not mutually exclusive, meaning that both can possibly happen at the same time.

You should be careful not to slow-play too often, especially if you are liberal with your re-raising pre-flop. The more often you slow-play pre-flop, the weaker your re-raising range will be perceived as a direct function of the amount of slow-playing that is taking place and shown down. In other words, if your opponents know that you never re-raise with A A, then they do not have to put AA in your re-raising range, and it becomes a bit weaker and you become a bit easier to read.

It would be somewhat difficult to notice that you were completely without a particular hand in your pre- flop re-raising range, only a near unrecognizable drop in your pre-flop all-in percentage that could be attributed to any number of other dynamics. The sample size of this event taking place with showdown would be extremely small, even over a large amount of hands. Also, any competent opponent would assume that slow-playing such a strong hand pre-flop isn't your standard way to play that particular premium hand.

However, assessing a single hand is not the point of considering this example. We are talking about a game of ranges, not one of hands, and if your opponent sees a single hand slow-played pre-flop, he will likely, and probably should, extrapolate this slow-play sighting to the fact that your re-raising range is a bit weaker than he would have thought had he not previously considered you to be slow-playing hands pre-flop.

The dynamic created by slow-playing pre-flop is a good example of how everything in poker balances and how dynamics always play off of one another. If you choose to play a hand a certain way, then it should probably be less likely you're playing it the same way in a similar situation later against observant and capable. Each time you show down a hand your ranges become more divulged to your opponents and your knowledge of their views of your ranges become more divulged. Almost every time you choose to do something in poker, your choice is going to affect your later actions and your opponents' perceptions of those actions. So

the better you learn to adjust and to play according to your opponent's adjustments, the better your ranges will do against your opposition's ranges.

CHAPTER 3: FLOP PLAY Many of the ideas written in this section will also apply when the same concepts are considered for play on the turn. For example both floating and raising as a bluff will be touched on in the chapter on turn play, but the majority of the theory herein discussed for those types of plays will hold true for play on later streets.

The Anatomy of a Continuation-Bet: Betting the Flop as the Pre-FlopRaiser For those of you who are newer to poker and are unfamiliar with the definition of a continuation bet, a continuation bet is a bet that follows a pre-flop aggression in order to represent a strong range of holdings post-flop.

There are many questions that surround the anatomy of a flop continuation-bet in a single-raised pot (ex. we raise pre-flop UTG and the button calls). Here are the questions that we plan to examine every single time we ever consider a continuation bet along with their respective explanations:

1. How does my range rate against my opponent's range?

In general, and depending on many factors, the pre-flop-raiser will be able to represent a stronger range before the flop than a caller. There are several reasons for this perception of strength compared to a caller's range including our opponent's pre-flop ranges and tendencies. A simple example is that if our opponent always re-raises with hands QQ+, then we can take those out of his range when he is unable to do so with our range. Our opponent also has to worry about being in a dominating situation with reverse implied odds. Basically this means that our opponent will sometimes fold hands like K9o pre-flop when we're raising with hands like JTs that he actually beats at the time because he's playing against our range, not our specific hand,

and the same worry will occur post-flop if he re-raises hands like AQ and AK most of the time in a certain position. For example, this fear of pre-flop domination will give us more folding equity on king-high boards and allow us to win the pot with a simple continuation bet versus many of our opponent's holdings, as his range will be less rich with Kx hands.

2. What are the effective stack sizes and how will this affect action on future streets considering our flop continuation bet sizing?

Often in a hand, our goal will be to set up an all-in bet by the river or a least the threat of an all-in bet if we are bluffing. The first step is choosing a flop bet size that works for this purpose if stack sizes are such that your flop bet size will be a determining factor. 300 big blinds deep, we aren't going to start by betting four times the pot as a continuation bet. It's important to note that if you and your opponent are deep-stacked that continuation betting a large amount, something like

three times the pot. is a terrible idea for a myriad of reasons. In fact, we'll want to choose a standardized flop continuation bet in most spots against most opponents. One important departure from this norm is if we are called by someone playing a stack significantly shorter than the somewhat normal lOObb buy-in. If we can threaten their stacks at a lower cost, why not do it? Our bluffs are cheaper and our ability to threaten our opponent's stack by the river remains while we risk less money. A word of warning is that any change in bet-size may have an unpredicted effect against a certain opponent, so be sure of whom you're dealing with first and their possible interpretations of your changing bet size.

3. How often will my flop bet force me to continue on the turn?

See Chapter 5 on turn play and barreling

4. How does the recent history of our match effect the credibility or lack of credibility, of my continuation bet?

If your opponent perceives you to be continuation betting a large percentage of hands, he or she will be more likely to widen his or her calling and/or raising ranges. The proper readjustment to the type of opponent who calls more often is to value bet thinner and to bluff less often. You may also be bluff-raised more often, which means that you may want to pot control your medium strength hands to avoid a tough decision later in the hand, especially if you're out-ofposition against your opponent(s) and he/they are capable of raising flops with a well-balanced range, making it tough to make a good decision against their flop-raise. By polarizing your flop continuation bet range against this type of opponent, you avoid the tough decisions that come with playing marginal hands in large pots against a well-balanced range.

5. What types of boards are better to induce more or less folds?

The percentage of times that your opponent folds is largely dependent on the board texture and his pre-flop position. Generally, the drier the board, the more often most of your opponents will fold. The quintessential example of a dry board is Ad9s3h. There is no connectivity and so it is unlikely that you will be called by a draw, in the conventional sense of the word, as 5d4d or JsTs are basically the only reasonable "draws" to be had on that board. Compare this board to something like Qs8h4s where there are tons of straight draws and a flush draw your opponent may hit. It's also a bit more likely that your opponent would just call you pre-flop than re-raise you with a hand containing a queen. This makes his range slightly richer in Qx hands than it may be in Ax hands. Obviously, these examples are speaking in generalities and each player's ranges will be different, the idea is that there are few or no examples or cases to examine that will hold for every single player. I'm

simply teaching you what to think about as you consider a continuation bet and you're the one meant to apply these many considerations to a particular player on a particular board texture at a particular time in- game. Your opponent's position pre-flop is also going to be a major factor in how often a continuation bet will take down the pot and how well his pre-flop range will connect with certain board types. If your opponent is in position and you're opening in late position, his calling range should be fairly wide given the position from which you have opened and the position from which he has called. The earlier the position you open from, the less likely you will be to win the blinds outright and this means that your opponent's calling range should adjust to your stronger pre-flop range from early position. Your opponent should be calling less often for fear of being dominated and having poor reverse implied odds post-flop. The later the position of your opponent, the less people he has to worry about re-raising pre-flop and so there should be more speculative hands his range that expect to see a flop fairly regularly with less of a

compounded worry of each individual behind him reraising. In short, we have determined that you will see more folds to your continuation bet the less connected the board

6. How should I react against a flop raise of my continuation bet?

Generally, if you have to ask yourself this question and are legitimately confused about the answer after having continuation bet a given hand, you have made a mistake by continuation betting in the first place. Ideally, we want to be able to predict our opposition's raising frequencies well enough, bet hands with which we know how to react, and check hands with which we know how to react to a bet in order to check-raise, to check-call, or to check-fold. Against a very good player who balances his flop calling and raising ranges well for bluffs and for value, there are inherently going to be tough decisions for his opponents after they continuation bet. You're just going to have to outwit people here, or "soul read,"

as we like to say, usually based on some combination of the opponent's tendencies, meta-game considerations, and stack sizes.

For other considerations on raising flops and what to do when raised, such as how your opponent, history, flop texture, certain hands, and position should affect your decisions, see the below section on bluff-raising and how to react to frequent flop raises.

7. When should I not continuation bet? What should I do with my hand if I check the flop as the pre-flop- raiser?

This is a question for which the answer will be dependent on your history with your opponents and your reads on their tendencies when the pre-flop-raiser checks to them. Your decision here is somewhat based on what your actual hand is and has a lot to do with how you think your opponent will view you at this

point in the game. On very connected boards on which you may often give up, it may be a good time to checkcall as a trap, and likely continue to do so on future streets depending on the board if the following criteria are met:

• Your opponent bets when checked to very often • Your opponent is capable of betting all three streets for thin value, thinner perhaps than he might call you down with

An example of a questionable continuation bet could be if you raise As2s and the flop comes AdTs8d and you feel you'll be confused if your continuation bet is raised. This board on which your opponent's range may play aggressively and trickily may be a good time to check and represent a slightly weaker hand like JTo. You'll also get more value if someone is trying to bluff you off of a Tx hand and believes that they need to bet the flop, turn, and river with a bluffing hand to fold out the weak-made-hand you're representing with a flop-check.

If the board turns out to be unfavourable by the river, then check-calling again may become more of a read- based play than a trap. As more and more of your opponent's perceived range connects with the board, you should usually be more likely to fold a marginal hand, especially in the cases when playing an opponent you believe to be randomizing bluffs by equity. If our opponent randomizes his bluffs with how well his hand connects with the board, then the more draws that hit the board, the stronger his range will be. However, if our opponent simply bets when checked to every time, the scarier the board gets, the more likely he is to keep betting his pure air range and therefore over- compensate for how often he is actually value-betting. When done properly this play should induce an overaggressive opponent to have too much air in their range by the river, making call downs extremely profitable, especially as the board gets scarier, which will induce your opponent's air combinations to bet with extremely high frequency.

If your hand is as strong as JsJc on a Jh8d2d flop and your opponent bets into you after you've checked the flop, realize how likely it is that your opponent has either a bluff or a draw because he likely would have reraised QQ+ pre-flop and you block most of the Jx combinations with your specific hand. In this case, you should adjust your play based on his likelihood to continue (semi)bluffs. If he'll call a check-raise and bluff shove over a turn bet with all of his draws, maybe check-raising the flop and belting the turn to induce a raise is the best line. There are definitely many different lines that could prove the most profitable against a particular opponent at a particular time.

Some of you may realize that check-raising the turn will likely fold out his weaker draws and pure air that would continue to bluff if the board gets scarier. The reason we raise here is that we may also choose to take this line with a draw of our own. Hoping to fold out better high card hands that are also drawing or even pure bluffs that our opponent could have on the flop,

given our show of extreme weakness by checking such a coordinated board. Raising also might induce lots of action from a hand like a flush draw on the flop that may choose to take a free card later on in the hand instead of continuing to bluff on blank turns and-or rivers

If we are check-raising or check-calling in this spot with only strong hands, an observant opponent will notice and adjust his game plan. Think about how profitable a play that check-raising as a bluff can be here if your opponent is bluffing nearly 100% of the time when you check, betting only his best hands for value for worry of not knowing what to do if raised, and checking back everything else. You win extra money from a lot of his range that would have probably otherwise folded the flop. Even if your opponent is only betting all his gut shots and flush draws when you're checking, realize how much of his range only those few hands make up compared to the value portion of his range. Against other and more aggressive types of

opponents, their range will be extremely wide in this instance and will be comprised of mostly hands that will fold to a check-raise.

To practice the effects of a check-raise versus different opponent types, try the following:

1.

Write out villain's flop range from the JJ example on a

piece of paper and list all possible outcomes for when we check to him (note the fewer combinations of Jx hands, which may influence our decision to bet or to check on the flop).

2.

Now write out his range of hands for when we

continuation bet below the first range you've written.

3.

Compare the ranges and the combinations of hands

you've written to see the likelihood of a bet in each case. Which is more profitable? How situational is your comparison? How often will your opponent continue in

each case? Give yourself different "reads" on your pretend opponents and manipulate his ranges accordingly. This exercise will mimic how you should be thinking while playing poker.

In position, especially when our opponent assumes that we are going to continuation bet, we might want to balance a checking back range in order to avoid the tough spots he'll create by check-raising if he is assuming that the majority of our air range will be betting a certain flop texture and not continue after being raised. This worry can be compounded on draw heavy boards on which many turns would be scare cards for our specific hand. If our opponent has more information about our frequencies than we have on him in a certain spot, then we need to change something in order to avoid him taking advantage of our tendencies. In this case, continuation betting some boards textures too often may be easily exploited by smart and aggressive opponents.

It's important to include some hands that would almost welcome two streets of action in a check back range in order to bluff catch confidently on the turn and on most rivers and to have our opponent realize that simply because we have checked back a flop that betting the turn and river with his entire range isn't necessarily going to be profitable. Because checking back stronger hands will make your opponent more hesitant about bluffing you on the turn and river, you should realize that your flop continuation bet range will be perceived as more polarized, and probably weaker on the boards on which you choose to check back given that your best chance to win the pot may be by continuation betting your air on the flop when it's very likely you'll be bet into on the turn. If your opponent can assume that you are continuation betting the majority of your air and you are checking back most of your medium strength hands, then it's not a far leap of logic to assume that you will have air very often when you are continuation betting certain board textures as it's extremely likely that the air portion of your range will far outweigh the strongest portion of your range in terms of which you

are combinatorially more likely to possess on the flop. For this reason, it's important to mix in some delayedcontinuation bets, or checking back air that we plan to bluff with if checked to again on the turn.

Checking back the flop as the pre-flop-raiser is a useful play to utilize if you feel exploited on the flop or like you're getting the worst of a continuation bet dynamic on a certain board texture with a marginal subset of your pre-flop raising range. Because you have the need to check back marginal hands in your range, you should also have stronger hands to balance with these marginal hands and total air hands to strengthen your delayed continuation bet range. If you don't know how to react to flop check-raises, but feel comfortable against a turn and river leading range on most turns and rivers, then checking back the flop is almost always the obviously correct choice for the situation. If you're mixing up your play with good and bad hands, you'll have to be wary of how to navigate your opponent's adjustments. His main weapons to combat frequent

flop-checks instead of continuation bets would be leading and check-raising later streets, both of which he should be doing with a range of bluffs and a range for value. How often and with what types of hands you should be checking back the flop is dependent on how often you expect to be check-raised on a given flop, your ability to withstand that potential check-raise with your specific holding, and how often you expect to be lead into on certain turns and rivers. You will also have occasion to bluff-raise some turns and rivers that hit your checking back range hard and that are unlikely to hit your opponent's calling range. A common example of this scenario is when we raise on the button and we are called by one of the blinds. If we are lead into on a draw heavy board on the turn, after the flop goes checkcheck, on lower board pairing turn cards, say cards 2 through 9, those cards are still well within our range given our well-balanced flop checking back range given how smaller flop pairs are frequently vulnerable to heavy action; whereas, our opponent will have a range mostly comprised of stronger made hands, semi-bluffs, and pure air, all of which become bluff-catchers to our

turn raise. Almost all of these hand types will also be put into very difficult river spots, especially because we, as the pre-flop-raiser, control the betting size and frequency on certain river cards.

8. How does my position influence my continuation bet frequency?

We touched on this question while explaining what to consider after question 5. To elaborate, if you have position on your opponent you will have more information to use when making your strategic decisions post-flop. For example, if your opponent has a strong leading range, then you can discount his future value range that checks to you because some of it should be leading into you to balance his blurt leads. If your opponent rarely check-raises, you're able to bet your weaker made hands and weaker draws on the flop without fear of being put into a tough decision against a well-balanced range of hands. These two examples

illustrate scenarios in which a continuation bet will generally be met with less resistance by your opponents.

Also, realize that you're opening wider ranges from later positions as there are fewer people who have yet to act and there is a higher likelihood that you will steal the blinds and antes uncontested. This means when you're called and see a flop, your opponent may be smart enough to realize that he may be able to get away with some bluffs if you're opening very a wide range and continuation betting too often for how much air is in your range. It's difficult to come up with an exact number for the percentage of times you should check back, either with made hands or to give up. In order to balance your play due to the many dynamics one should consider when you are thinking about checking back.

9. Which of these considerations matter for this/these specific opponent(s)?

The answer to this question is a concept that took me quite a while to understand. Sometimes, your opponent will allow you to do whatever is best for the situation you're facing. In other words, due to lack of perception, monetary attachment, or ability to make adjustments, your opposition's tendencies will make it so that your flop decisions as to whether or not to continuation bet will be drastically skewed to one end of the betting or checking frequency spectrum and you will have an easy flop decision about whether or not you should continuation bet. There are times when you can routinely bluff and your opponent will fold everything but top pair or better. Other times, your opponent will never fold, so you just have to wait until you make a hand to value bet and maximize value when called. Better opponents are going to use a hybrid of these two cases to make it difficult for people to play well against them. However, if you spot a person who plays closer to one of these ways, adjust accordingly and you will be doing much better than using some default well- balanced range. It's tempting to romanticize the idea of balance and being more balanced than your opponent

means that you will win more money than they will. Balance is an extremely important idea, but against someone who isn't paying attention to how you play certain hands, it's nearly or completely irrelevant to balance, assuming playing an exploitative style will net the most profit. Remember, poker is not a game based on systems and set ranges in certain spots. Almost everything in the game should be adjusted at some point or another based on the information at your disposal.

Flop Texture During the section on continuation betting I briefly mentioned flop texture as a determining factor of how to react on certain boards. It is an important factor because some boards play differently than other boards and you need to know why they are different. The most important takeaway from a discussion of flop texture is the fact that different boards foster action with different combinations of hands. Some boards give many combinations of hands enough equity to call or semi- bluff raise, to continue in some way, while other boards that are more disconnected, are likely to foster straight forward play for a few reasons:

1. Disconnected boards do not present many possible value combinations and therefore, are generally bad boards on which to bluff (or at least with the same frequency with which you'd bluff a more connected board).

2. Your bluffing frequency should be a function of how often your opponent will fold to your bluff. How often a good player will fold is based on how often both of your perceived range hits a given board, along with meta-game considerations and several other factors.

All other things being equal, flop texture is going to have a lot to do with how often someone will give you credit for a hand and so very connected boards require a different kind of balance than less connected boards. Your opponent should be checking the more connected boards, anticipating being played at if he elects to continuation bet. Because he's checking to give up some of the time, he should also be checking some good hands and the adjustments continue.

Floating Floating is a call on one street typically, not necessarily, with decent equity against an opponent's range in order to take the pot away on a later street by bluffing. Floating is a more specific type of call because the play will only be profitable in terms of future expected value and in terms of how often you'll be able to take the pot away from your opponent if he makes some display of weakness and you are better able to bluff on a later street. Let's clarify our definition a bit more and examine how to employ floats in our game plan in order to win more and to make our strategy difficult to combat. The idea of a float is that it is a multi-street play, so it cannot be discussed in full in one chapter of this book the way I have chosen to order the chapters. So for the reader's ease of comprehension, I will herein discuss floating in full detail of its implications for multiple streets of play and for future hands.

Future Expected Value of a Float Obviously, we might hit our weak draw and stand to win a large pot because of both the deceptive nature of the draw and the likelihood of its connectedness with our opponent's range of hands if he continues to bet into our newly strengthened hand and range. Something that may be less evident about the theory and reasoning of floating is how the image of these floats will garner us more action in the future.

Consider the following scenario:

•

The cutoff opens and we elect to call with Qcjd on

the button •

Flop is Kd9c4s

•

We call a flop continuation bet

•

We decide to fold to a turn bet on the 2d

Next time we're in a similar turn situation, realize how much more likely it is that we will be further ahead of our opponent's range with a hand with vulnerable showdown value. If we call on the turn with a hand like 8s9s, especially against the right type of opponent who is adjusting to what happened in the Qcjd hand, then our equity versus his range should be significantly higher. If our opponent perceives our range to be comprised of a lot of floats and not many kings, given our passive pre-flop play, he should adjust his turn barrelling range to one that is extremely wide in order to fold out our queen high and jack high floats. If we

know that our opponent is making this adjustment and we may assume he's a thinking player, then we should widen our calling range, expecting to be bluffed on the turn and possibly the river more often given our recent history of our earlier "failed" float.

The above example shows that the results of floating are much more than a hand-by-hand expected value calculation. We'll be making money from folding turns we miss with our floats, even though we lose that specific hand, because we'll be fostering action against observant opponents on boards on which we have hit against their increasingly wide turn and possibly river barrelling ranges.

Displays of Weakness If our opponent checks on a turn which misses our float, it often brings up a question of whether or not it's best to:

A.

bet as a bluff with our floats to balance with the

times we're value betting or

B.

take a free card to realize the equity of our draw

with 100% certainty and make a decision about bluffing the river if we are checked to again.

The answer to the question of "should we bet?" is the combination of many smaller questions that will often corroborate one another to yield us a clear turn decision.

Question #1: How often is your opponent check- raising the turn or check-calling to induce you to betting from your hands that floated the flop?

If the answer is "never," especially in regards to the check-raise part of the question, then the decision to bluff becomes a much easier one. A turn check from an opponent likely to take this line with his entire range is the perfect opportunity to make a very profitable turn bet because we will always realize the equity of our draw since we'll never be raised off of it, and we'll gain folding equity by betting into our opponent the times he has chosen to give up on the hand. However, most opponents who realize what's happening when your bet frequency is high in spots after you might float and bluff when checked to will incorporate some type of balance in these turn spots, either by check-calling or check- raising more often, in order to thwart your attempts to exploit his turn tendencies.

The better and more balanced opponents you will likely face will incorporate check-calling and check- raising on turns following flops which have a large potential to be floated because they realize the board texture and how it will affect your turn betting frequency. In general, the drawier the flop, the more often you should expect an opponent capable of floating to bluff at some point later on in the hand, assuming most people use hands that hit the board to randomize their floats. The idea of a wider bluffing range on draw heavy boards also means that this type of player should be value betting thinner at some point in the hand in order to balance his bluffing range and to avoid being exploited by observant and capable opposition.

Given the conclusions we have arrived at about board texture and turn play when we're in position, does this mean our opponent should be barrelling these draw heavy boards as a bluff with a wider range and/or higher frequency when we are the out-of-position player? Perhaps. We have to resolve the conflict of the

math problem of the likely positive expected value of betting almost our entire range in a given spot to fold out weaker draws with the worry of widening our turn range so much that our river bluffing range includes too much air when it is in fact perceived as tighter. For example, if a great bluff card falls and we bluff after having bet the turn with a hand that is totally disconnected with the board and we are called by a better hand, which is much more likely given our wider range, then our perceived range is open to a few different interpretations by our opponent, specifically either our opponent will consider if we will be bluffing too often or we will be bluffing less often after the hand in question is shown down, if you're being double floated or semi-bluff-raised on the turn, your attempts at barrelling even lighter than the default ranges you have constructed that mostly rely on a combination of randomization by equity and scare cards falling are likely to cost you money in future hands if you cannot out-adjust the opponent who sees evidence of your extremely wide turn betting range. The problem with over-stepping the boundaries of bluffing our fair share

of hands, ones that connect with the board, is that we cannot be certain how the information we are transmitting about a wider range will be interpreted by our observant opposition.

Our opponent may counter our heightened propensity to bluff the turn and to bet the turn for thinner for value by checking turns in order to check- raise a balanced range of bluffing and value hands, in this dynamic, our opponent does not sacrifice balance for exploitation, at least in such a memorable way that might help us to play better against him in the future. He also does not turn his hand somewhat face up by check-calling the turn, allowing us to play as well as possible against the weak range of hands with which he will be most likely to take this action. Of course, it's possible to check-call strong hands on the turn, but if he chooses to trap in this manner, then it's more likely he is sacrificing value that he would get from betting the turn and then the river or by check-raising the turn with such a strong hand. If we are more likely to check back

turns and bluff the river when checked to, our opponent will be able to make lighter river calls taking into consideration our perceived range, his hand, and his pot odds, but he will not be able to abuse the aforementioned turn dynamic. So far we have outlined a few reasons both to check the turn and to bet the turn on draw heavy boards. Let's ask a few questions so we can weigh the value of each option and so we can make the best decision about which dynamic to exploit versus certain opponents.

Reasons to bet turn: If we're bet into by a tough and well-balanced opponent on a river after checking back a float without showdown value, we will have a pretty tough choice for which the outcome is likely close to breakeven or slightly losing for us. Our opponent controls the frequencies with which he is taking this line and it is unlikely that we'll be able to play very well against it, especially if he leads us to make false assumptions on the river such as "he will bluff all of his missed draws when checked to." Other reasons to bet

the turn are that we aren't able to threaten stacks by checking the turn against this opponent, unless we check-raise the river. If we wait until the river to bluff, we'll have to balance that by checking back some good hands on the turn from which we'd like value, which we'd get by betting the turn and river. Also, such a large portion of our opponent's range on the river will be bluffs that we may have gotten more value by betting the turn and inducing a bluff-raise to fold out parts of our assumed-to-be draw heavy range.

Reasons to check the turn: We should get more information about our opponent's hand and learn how successful a bluff will be given his reaction to the turn and river cards and how they improve or hurt our opponent's perceived range comprised of draws and weaker made hands. Against a predictable opponent for whom we have solid reads, our river decision will be easy and likely quite profitable.

Question #2: When we are in position, will our opponent check his entire range again on the river?

If your opponent will check his entire range on the river to induce a value bet from your probable worse hand that you chose to pot control on the turn or a float that probably missed again on the river, then you should probably lean towards betting the turn with your floats more often when you can represent a wider and stronger range of hands, especially if your opponent is capable of employing the dynamic choices of using a balanced river-check-raise range. Of course when we are bluffing a wide range of hands, we should also be value betting a wide range of hands. If your opponent picks up on the fact that you're balancing your turn betting range by value betting thinly, then you may want to readjust your turn betting range, since you should expect to be called or check-raised with a wider range on the turn given how wide a range your opponent knows you have on some turns. Another

consideration in this dynamic has to do with our next question.

Question #3: How many floats are in your perceived range on certain turns?

On a board like Kc9c6h versus your late position flop-call, there are many more combinations of floats than strong value hands in your range. If you're against a perceptive opponent, you should be increasingly wary of bluffing later on in a hand and of his likely adjustments to the board texture to thwart the profit margin of your wide range of floats. You can also tailor your range to your opposition's adjustments by floating fewer hands and bluffing less often if he is playing back often on turns. Therefore, you may choose to fold something as weak as 7s5s on this board, considering:

• Your pair outs are less likely to be good by the river and those outs are less likely to be live and/or more likely to be conditional

•

You're going to be barrelled too often on the turn

compared to the times you're going to get paid if you make your hand

•

The times your opponent will check and fold this

very drawy board on the turn

•

Our equity against our opponent's range with our

particular float is decidedly weaker than other floats in our range such as QJ and JT

If our opponent is planning on check-calling turns and/or some rivers to induce us to bluff when he has a weaker made hands (ex: 98s) on the turn, then we have a decent amount of equity with our stronger floats. If we expect him to frequently check-raise our turn bet or to check-call the turn and river if the river is a blank, we might be best by avoiding a turn dynamic by checking back the turn and bluffing rivers with what we determine to be an optimal frequency against our

opponent's possible holdings and river check-raising frequency. However, if we know he doesn't expect us to be floating, then betting is generally going to be our best action. These ideas obviously follow from our above examinations from the opposite point of view.

In summary, betting the turn is advantageous when the following are true:

•

We have a high likelihood of folding out some hands

with very weak showdown value (such as ace high) because we can usually better threaten stacks by threatening multiple streets of action

•

Our opponent is rarely checking and calling good

hands on multiple streets

• We do not expect to be check-raised on the turn

The more likely you are to be check-raised, the less you should bluff a medium-strength draw for all the reasons discussed. A medium-strength draw's value is different for each opponent you play. The reason for the varying value of a turn (semi-)bluff is that your equity against your opponent's range of hands he could checkraise your (semi-)bluff on the turn will change depending on the range with which they decide to attempt a turn check-raise.

A decision for your opponent to check-raise a turn will mostly be a function of game flow, board texture, and stack sizes. Examining the following will help you to determine the likelihood of you being check-raised on a turn against an opponent you may trust to play the same way in similar situations:

Question #4: Has he check-folded a turn before?

If he has, it may be more likely you will be check-raised, depending on the opponent, of course.

Question #5: Are there several combinations of possible floats on the flop that he expects you to call with and then bluff the turn?

If yes, then he will probably be check-raising the turn more often than on a different board.

Question #6: Are stacks such that he can fold out your medium strength draws?

If once you bet turn you are committed to calling his raise, regardless of its size, with a naked flush draw for instance, then it's most likely he'll bet the turn himself if he wants any folding equity. Another consideration is a short stacked scenario is that if his turn raise size is straddling the border on committing

you to the pot with a lot of your weaker draws, then he might not think he would be able to credibly represent a bluff. In this one, his turn check-raise should be viewed as very strong. This means that, in general, people should be bluffing weaker draws to balance with their stronger value hands (anything you would want to call a check-raise or that would like to be check-called twice) on the turn. This also means that stronger draws that are not strong enough to bet/call the turn, like a baby flush draw, should be checking back in most cases.

If you check-call a weaker made hand after continuation betting a board with a highly connected board texture (a dubious decision in many instances that will be ignored for the sake of the point) and a strong draw hits the river, you may want to check and call another bet if you believe it's highly likely that the strong draw hitting will narrow your opponent's value range and make him bluff his weaker missed draws more often (probably close to 100%). If he is only betting top pairs and better on the turn for value, but all

gutshots as a bluff, then you should see that his river range is probably very highly skewed towards bluffs on a large number of rivers.

Betting also helps us to avoid being bluffed by a bet-check-bet line. Say we call a Kd7h9c flop with 5c6c and a turn 2d goes check-check. If we're betting into our opponent as a bluff on a non-8 river, we have a pretty tough choice. Our opponent controls the frequencies with which he is taking this line and it is unlikely that we'll be able to play well against it. We would also bet the turn if we aren't able to threaten stacks by checking the turn and when we want to avoid having to balance by checking back good hands on the turn from which we'd like value. I believe the dynamic created on the turn by floating, on both sides of the aggression and both in position and out-of-position shows why the spot is so interesting from both points of view. Because both players have so many considerations in order to exploit their opponent and to avoid being exploited, it's a dynamic on which it

is well worth spending the time to anticipate adjustments and to quantify the adjustments your reads lead you to make with mathematics. Turn play is still an unsolved ground in No-Limit Hold'em. After this section on floating, it is easy to see why there is much work to be done considering the dynamics of turn play!

Question #7: Do we have showdown value with our float?

Let's say that the cutoff raises and we call with AdQd on the button. The flop is JhTd4c. And we call our opponent's continuation bet hoping for a turn diamond, ace, king, or queen. We also intend to continue on some other turns that miss our opponent's semi-bluffing range because we have good equity against a lot of his turn betting range, hands like Jc9c. Because we are ahead of most of our opponent's semi- bluffing range, we deduce that we have some showdown value with our hand.

The answer to this is also a function of how likely your opponent is to check the turn and/or river in order to induce bluffs from you when your range has a lot of draws in it. If he checks the turn, he'll likely be checking a blank river to induce a bluff with his weaker made hands. When considering a bluff when checked to on the turn or on the river, you're getting the worst of both worlds as it's unlikely you fold out anything better by betting as a bluff and the fact that you'll have the best hand often enough in order to show down profitably makes inducing a bluff on the river the likely best play. Because your opponent is expecting you to bet air like 9d7d, KdQd, and 9h8h, if he checks the river with a weak made hand, then he will almost always be calling your bet. If he is checking the river, it's with a plan to either call or to fold and because we beat all of our opponent's failed turn bluffs, we should just take the showdown with our AdQd.

Bluff-Raising Sometimes boards will come down that hit your perceived range very hard and you will have a hand that has completely missed the flop, if you have a very marginal hand and you're against an opponent who is capable of barrelling as the board gets scarier for the range of hands you're representing by calling a flop continuation bet, you may want to raise the flop as a bluff.

Generally, a flop call, especially on a drawy board, represents a range with marginal strength because many players will give lots of action with a draw on such a board if they think they have good equity versus a calling range as well as some folding equity. Against players who continuation bet and barrel too often, but often enough that you will make mistakes on future streets, you may be best off choosing to raise the flop as a (semi)bluff.

As far as sizing goes, assuming 100 big blind stacks, you do not have to raise to a very large size to put your opponent to a test for a large portion of his range of borderline hands. A borderline hand is a hand like JsTd on QsTs4h that your opponent continuation bets, expecting you to call with almost all of your range. A large benefit of having a flop-raise dynamic is that you take away his ability to get value in spots like this one with marginal hands and force him to play a more pot controlling style or a guessing game in which you control the frequencies on future streets, which, if you play well, shouldn't end well for him. Let's say we call a $30 raise pre-flop in position and decide to raise a flop continuation bet of $50 to $150. Immediately we are risking $150 to win $140 (assuming we aren't either of the blinds) and so our bluff only has to work slightly more than half the time in order to be profitable. If we assume that after our opponent three-bets the flop that we have an easy decision to fold or to continue (note: by an easy flop decision that I mean we would almost never raise a hand like KhQh on QdTd3h and subsequently

fold to a flop three-bet or ever raise 8c7c and shove over a three-bet), then we won't be put into tough spots that may lead to larger post-flop mistakes. Typically when we are in position, we will be able to play better after the flop action should our opponent elect to call our raise and so raising in position as a bluff should be more profitable than out-of-position.

Ways in which our opponents will combat our flop-raises have been touched on when I mentioned the pot-control method of polarizing continuation bet ranges. Other methods our opponent may use to combat this certain flop dynamic include:

•

Check-raising flops, both for value and as a bluff

•

Three-betting our flop raises, both for value and as

a bluff •

Stop raising as much pre-flop with marginal hands,

thereby attempting to avoid marginal spots post-flop

Check-Raising Flops Once our opponent realizes that we are raising flops so often that it's unlikely that we are always holding a good hand, he should be mixing up his play and include some flop checks with both good and bad hands. If he can't win in one dynamic, he may try to exploit another dynamic in the same spot. A part of this different dynamic could include checking hands that he wants to check-raise bluff. Hands like gutshots that have some equity, but not enough to continue if raised after a continuation bet, might be best used for this play because we don't mind folding them if three-bet on the flop. To add to the efficacy of our flop-check-raise-bluff, if our check-raise is called on the flop when we are using a gutshot to bluff, then we have many turns which we may credibly represent when our perceived range is strengthened in addition to the times we hit our gutshot and make a strong hand. Different players will induce flop-bluffs to check-raise-bluff on different board textures and so it's important to pay attention to your

opponent's range in these types of spots because it will directly affect the range of value hands that you will be comfortable with when facing heat if you do choose to value bet a flop when checked to by the pre-flop-raiser.

Three-Betting Our FlopRaise As a bluff or for value, our opponent should start three-betting, or re-raising, our flop raise because our flop-raising range should be wider given that we're widening our flop bluffing range. By anticipating that our opponent will eventually make a play against our flop-raise with a wider range, whether it be with a bluff or with a made hand with which he's taking a stand, our value range should be widened accordingly.

Not Raising as Often PreFlop (Polarizing Pre-Flop) If our opponent is anticipating being put into marginal spots post-flop with his marginal made hands, then he can choose to raise a more polarized range pre- flop. This will assure that he will more often hit a flop either hard or not at all, rather than hitting something mediocre. A key strategy for dealing with difficult spots in poker is to avoid them in the first place.

CHAPTER 4: RIVER PLAY Note: I have chosen to discuss river play prior to a discussion of turn play for reasons that will be evident after the reading of this chapter.

The concepts presented within this chapter will help you to: •

Call people down more profitably

•

Understand how much of someone's range you're

attempting to fold out on a given turn or river •

Understand whether or not a certain bet size is

more profitable with a bluff or with a value bet

Like turn play, river play is going to be an extension of the previous street of play. By the river, we'd like to be able put our opponent on a fairly narrow range of hands based on the way that he played pre-flop, on the flop and on the turn. Narrowing down our opponent's range is going to be important for value-betting and for bluffing. It is a process that is going to improve with experience and by paying close attention to the examples and questions that I am giving and discussing in each chapter.

It's important to remember the general theme of this book: there is no one answer to beating No-Limit Texas Hold'em. Everyone plays differently, often in-line with their personality or temperament. Therefore, your reactions to their perceived ranges, predicted reactions, and adjustments against your ranges will certainly impact the best strategy for playing each hand. All of these ideas rolled into one equation may sound a bit optimistic, but Galfond Dollars will allow us to do just

that if we have the correct data to enter into our expected value calculations.

Galfond Dollars Explained In order to understand what we mean by Phil Galfond'sGalfond Dollars, or G Bucks, we should first define Sklansky Dollars, or Sklansky bucks. Sklansky bucks, as first defined by David Sklansky in his book The Theory of Poker, shows us the expected value of a single hand against another hand. For example, if we are all-in pre-flop with Acjs versus KhKd in a $2000pot, $1000 of which is our money, we expect to win $572 on average. The expected value equation for this hand versus hand match-up is

EV = (% win of A J) (total pot) - (what we risk) EV = (0.288)(2000) - (1000) EV = $576-$1000 EV = $424

The calculation shows that on average we expect to lose $424 of our original $ 1000 investment into the pot.

Galfond Dollars are more applicable to an actual poker game because with G Bucks we consider an entire range of hands against a specific hand. The information we get from G Bucks calculations is a lot more applicable because we are attempting to put our opponent on a range of hands and not a specific hand. This process of hand-reading will allow us to make better plays against well-balanced players. Wellbalanced players will make certain plays with more than a single hand, some as a bluff and some as a value bet. A G Bucks calculation will allow us to decrease our margins of error as well because our calculation is set up in terms of combinations of hands better than a specific hand.

Usually, it is advantageous in practice to choose our lowest and "purest bluff-catcher." A pure bluff-catcher is a hand that meets the following criteria:

•

weakest hand with which we get to a certain point

in a hand

•

does not block any of our opponent's semi-bluffs

•

only beats a bluff

When we use pure bluff-catchers in our G Bucks calculations, we create a starting point in our minds on certain boards from which we are able to adjust based on a number of factors such as card removal and bluffing frequencies. If we have 8c8d by the river on a 2c6c7hKdQd board facing a river bet we can take a club out of villain's range as well as the 8c and 8d and which lower his bluffing frequency due to card removal and how many 8x hands villain has by the river that were semi-bluffs continuing river aggression hoping to induce a fold from a hand below Kx. We should also

account for the fact that our opponent may not continue bluffing the river each time he gets to the river. These points will be expanded, but first let us go over a simple example of a G Bucks calculation.

Our Hand: JhTs Board: Jd8h3d8d2c

Play History: We have been bet into on every street, including a $200 bet into the $300 river pot. Current Action: We are on the button versus a cut-off pre-flop-raiser; we were heads-up to the flop and are now facing a $200 river bet.

The scenario gives our opponent a good incentive to bluff because he should suspect that we are still drawing and he will be able to make us fold with a river bluff a good percentage of the time. We will assume for this example that he will bluff the river with 100 percent of his turn range.

We can deduce Villain s range to be:

•

all straight draws, including gut-shots

•

all diamond hands he'd open pre-flop

. KJo+

. 88 •

JJ+

. Ad

Against this range, we win about 33% with JTo. It is actually a bit more, but we will use 33% for the sake of simplicity

If we win 33% of the time, we will lose 67% of the time. Now we have the information needed to create an expected value (EV) equation

EV(Call) = (percentage we win * 0.01)(total pot) (percentage we lose * 0.01) (what we risk by calling) EV(Call) - (0.33)(500) - (0.67)(200) EV(Call) = 165 - 134 EV(Call) = 31

So by risking a river call of $200 into this $500 pot against the range we assigned to Villain, on average we expect to win $31.

What if Villain chooses a different bet size with this range than $200 in our example? How should we react? We can set our EV equation equal to zero and solve for X in order to figure out the maximum bet size we are able to profitably call because the EV of calling and folding will be the same at the point of indifference, the breakeven point between calling and folding. The calculation here is assuming that the EV of raising as a bluff is less than zero.

EV(Call) = 0 0 = (0.33)(300 + x) - (0.67)(x) 0 = 99 + 0.33x - 0.67x 0 = 99 - 0.34x 0.34x = 99 x = 99 / 0.34 x = 294.12 Check: 0 = (0.33)(300 + 294.12) - (0.67)(294.12) 0 = 197.06 - 197.06 0=0

These calculations show that the maximum bet size we are able to profitably call is $294.12. Does this mean that if Villain bets enough on the river, we should be folding our entire range, or at least JTo? That depends on a number of factors and a calculation of a rangeversus-range analysis that I will not be explaining in this book because it is extremely tedious and inaccurate given small mistakes we make with our opponent's range and our range in a given spot. It would be like trying to calculate the probability of an outcome step-

by-step where we were not even sure of the likelihoods of the other events involved. I would recommend taking the time to consider adjustments to make to someone over-betting their entire range on a given river, especially when a lot of your range will be somewhat face-up bluff-catchers. Over-betting, for this reason, and the nature of the unpredictability and the timing of the play, becomes something difficult to play well against.

Because these calculations are somewhat tedious and complicated, it is very difficult to do them in the middle of a game, especially if you are multi-tabling and have other decisions occupying your time and concentration. I have found that the best way to get a grasp on when you should call and fold in certain spots, other than intuition gained from playing thousands of hands, is to do some calculations away from the table. I have provided a few examples that deal with common spots and that show how slightly different cards may

significantly affect the choice of the best river play in a given situation.

For all the following G bucks calculations, we will assume that we are playing 5/10 NL and that we are in the BB and the SB is raising us to $30 pre-flop, continuation betting $50 on the flop, betting $135 on the turn, and betting $280 into us on the river for a total pot of $430 ($710 with our call). We are also not concerned here with calling the turn bet, we are only looking at these calculations as independent river decisions (numbers may differ slightly from rounding error and pre-flop range assigned to the SB). When "Board A" is part of a different board's range, that just means that you should append the earlier board's range to that example's range. Notice what changes from board-to-board. One board may be the exact same except for an added flush draw on the turn or a third card of a suit on the river. The idea is to show the relative impact of each board change to our specific hand, assuming our opponent is using a randomization

by equity to determine his turn and river bluffing frequencies.

Board A = 2s3sQcAsJc Hero's hand = 8h8d Villain's range = KQ+; 45-46; 56; JT+; Ks5x+; spade hands; Ax; 22-55; 4x; 5x; 3 off-suited pure air hands. 8h8d is good on Board A 23.5% of the time and bad 76.5% of the time. EV (Call) = (%win) (total pot) - (% lose) (the bet to call) EV (Call) = (0.235)(710) - (0.765)(280) EV (Call) = 167.1 -214.1 EV (Call) = -47.0

Board B = 2s3sQcAcJh Villains range = Board A's range without air hands; club hands; 8h8d is good on Board B 29.1% of the time and bad 70.9% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.291)(710) - (0.709)(280) EV(Call) = 206.3 - 198.7 EV(Call) = 7.6

Example 2 Board A = 4h9dQcKs3h Hero's hand = Tc9h Villain's range = T5+; J5+; Kx; AQ+; 44; 99; QQ+ Tc9h is good 42.1% of the time and bad 57.9% of the time. EV(Call) - (%win)(total pot) - (%lose)(the bet to call) EV(Call) - (0.421 )(710) - (0.579)(280) EV(Call) - 299 - 162 EV(Call) - 136

Board B = 4h9dQdKs3d Hero's hand = Tc9h Villain's range = Board A; diamond hands Tc9h is good 35.7% of the time and bad 64.3% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.357)(710) - (0.643)(280) EV(Call) = 253 - 180 EV(Call) = 73

Board C = 4h9dQdKs3s Hero's hand = Tc9h Villain's range = Board B Tc9h is good 46.5% of the time and bad 53.5% of the time EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.465)(710) - (0.535)(280) EV(Call) = 330 - 150 EV(Call) = 180

Board D = 4h9dQc8s3s Hero's hand = Tc9h Villain's range = 48s-49s; 98; Q5+; 44; 99; QQ+; KT-KQ; Tx; Jx; 75-76 Tc9h is good 53.2% of the time and bad 46.8 of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.532)(710) - (0.468)(280) EV(Call) = 378 - 131 EV(Call) = 247

Example 3 Board A = 3s4sTdJh8c Hero's hand = 9c9h

Villain's range = spades; A2; A5; Q9+; AT+; 52s-62s: 56-57; 67; 3c4c; T3s-T4s; J5+; T8; 33-44; TT+; QT-KT 9c9h is good 42.4% of the time and bad 57.6% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.424)(710) - (0.576)(280) EV(Call) = 301 - 161 EV(Call) = 140

Board B = 3s4sTdJh8s Hero's hand = 9c9h Villain's range = Board A; 8sXx 9c9h is good 34.9% of the time and bad 65.1% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.349)(710) - (0.651)(280) EV(Call) = 248 - 182 EV(Call) = 66

Board C = 3s4sTdJs8c Hero's hand = 9c9h Villain's range = Board A; Some one card flush draws 9c9h is good 43.5% of the time and bad 56.5% of the time.

EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.435)(710) - (0.565)(280)

EV(Call) = 309 - 158 EV(Call) = 151

Example 4 Board A = 2sTc9h2d2c Hero's hand = 9d5d Villain's range = 86-87; JK-JK; 99+; J8-Q8; J7; Txs; T5o+ 9d5d is good 48.7% of the time and bad 51.3% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.487)(710) - (0.513)(200) EV(Call) = 146.1 -102.6 EV(Call) = 43.5

Board B = 2sTc9hAd2c Hero's hand = 9d5d Villain's range = Board A; Ax hands 9d5d is good 34.2% of the time and bad 65.8% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.342)(710) - (0.658)(200) EV(Call) = 102.6-131.6

EV(Call) = -29

Board C = 2sTc9hKd2c Hero's hand = 9d5d Villain's range (1) = Board A Villain's range (2) = Board A; Qx; Jx Range (1) 9d5d is good 23.6% of the time and bad 76.4% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.236)(300) - (0.764)(200) EV(Call) = 70.8 - 152.8 EV(Call) = -82 Range (2) 9d5d is good 42.7% of the time and bad 57.3% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.427)(300) - (0.573)(200) EV(Call) = 128.1 -114.6 EV(Call) = 13.5

Board D = 2sTc9h6d2c Hero's hand = 9d5d Villain's range (1) = Board A; 66; -6X

Villain's range (2) = Board A; 66; -6X; 7X; 8X Range (1) 9d5d is good 44.7% of the time and bad 55.3% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.447)(300) - (0.513)(200) EV(Call) = 134.1 -110.6 EV(Call) = 23.5 Range (2) 9d5d is good 60.8% of the time and bad 39.2% of the time. EV(Call) = (%win)(total pot) - (%lose)(the bet to call) EV(Call) = (0.608)(300) - (0.392)(200) EV(Call) = 182.4 - 78.4 EV(Call) = 104

To break away from the purely theoretical instances in which our opponent may be assumed to be betting 100% of his turn betting range on the river for value or as a bluff like in the above examples, we may choose to discount our opponent's river range for certain cards and quantify it in an expected value equation using mathematics. For example, it is intuitive that most

people will not bluff blankrivers as often as rivers that complete some sort of draw on the board. The type of G Bucks calculation in which an opponent's river range is discounted is what will most often mirror reality and the betting describe problems faced in actual poker games.

In order to make such a calculation, let's arbitrarily assume that our equity is 31.3% against an opponent's river betting range of 100% of his hands which bet a certain turn card. On a blank river, let's assume that our opponent is only bluffing with half of his air hands and so we must discount his river betting range to account for his assumptions about our calling frequencies when all draws miss on a certain river. Let's say that if we call when our our opponent isbetting 100% of his turn range, we are beating 62 combinations of hands out of a possible 198 combinations, which is where we got that we are 31.3% to win against 100% of his turn range on the river. Because we have a pure bluff catcher, we know that he will never be value-betting a worse hand than

the one which we are holding. Therefore, we may simplydivide the 62 combinations of hands we beat in half, so now we only beat 31 combinations of hands, given that he's giving up with his bluffs on a blank river half of the time. We then subtract those 31 combinations from our total of a possible 198 combination to get 167 combinations. Now when we call the blank river, accounting for a discounting of his bluff range, we will win [(31/167)*100%] = 18.6% of the time.

This idea of discounting our opponent's river bluffing range is an extremely relevant and important one because the rivers on which our opponent bets 100% of his turn betting range are not as frequent as timeshe will choose smaller amount of his turn range with which to continue bluffing. However, counting combinations of hands can be tedious, especially when ranges are wide and there are many combinations. Let's look at another example to show us how to circumvent the tedious nature of this EV calculation.

Let's assume that we will win when we call a certain river bet 136/428 times, or that we beat 138 of our opponent's possible 428 combinations of hands for which he isbetting the river. In other words, we will win 31.8% of the time if we call the river. Again, our opponent may not necessarily bet certain rivers with 100% of his turn betting range. Let's again discount our opponent's range and pretend that he is giving up half of the time, in order to make the math easy to follow. After discounting his river betting range as we did in our above example, we have determined that we will win 68/360 times (18.9%). For an actual hand, counting out all of these combinations is extremely time consuming. Here's a little tip to avoid wasting time counting hand combinations. In this example, we know our hand's equity against the 100% of a player's turn betting range is 31.8%. Let's treat this number like 318/1000. Now let's say we would like to discount his river betting range and assume that he's only betting with half of his bluffs, making this number 159/841. Now we will win 18.9% of the time if we call the river

bet. Does our answer look familiar? Now you know a simple way to short-cut the time-consuming nature of counting individual hand combinations when doing such a calculation.

I'd like to stress the point that I made at the beginning of this book: Poker played against thinking and adapting players cannot have a system to follow that will always make you a winner.

While G Bucks calculations will help you to derive your own turn and river betting ranges in order to maximize value from bluffing and from value betting, the ranges you derive will not be set ranges you play with against everybody or the ranges that your opponents will use when attempting to bluff or to value bet you. It's doubtful that you will even be able to have the same range against one opponent from one hand to the next because of how he will adjust to what he sees that you show down. The point of learning these calculations is so that you realize the implications of

bleeding off bets when someone is three-barrelling too often and of ideal spots for thinner value bets. You will get a better grasp on three-barrelling and how often it should work in certain spots and which hands to use in order to bolster an aggressive image that will get you paid in the future. All of these adjustments are not static. The adjustments are dynamic and each one will add to your win rate when you learn how to adjust better than the other players with whom you are playing. You'll realize that almost everybody's ranges are constantly changing from different happenings in the poker game and that your goal isn't to solve their game given a single hand in a single situation. Your task in becoming a better poker player is to out-adjust and to out-think the opposition, therefore causing you to make fewer mistakes and consequently, win more money in all situations.

When determining how often a given opponent is bluffing on the river, it's often helpful to assume that his use of a "scare card," often one that also improves his

semi-bluffing range, usually ensures that he will be bluffing with the part of his bluff range that missed the scare card. Usually, the scarier a card is for a caller's perceived range, the more of a person's range that will be bluffing that card in a given spot because that person is expecting you to make a mistake on that card with your range by folding too often.

Sometimes you will bet so thinly in a given spot that your opponent will call you with a better hand. At first thought, this may seem like a bad result. In actuality the play is going to be great for our bluffing range because our opponent will make two key realizations about our ranges:

1.

Our ability to bet such a wide of a range of hands for

value. 2.

The number of hands with which he gets to a

certain spot that are considering a call that are in jeopardy of becoming bluff catchers on a later street because of how thinly we are able to bet for value.

The knowledge of our thin value bet makes it very difficult for our opponents to adjust to our barrelling range. The definition of a value bet is "betting a hand that when called wins the pot at least half of the time. There are times when you will have a hand that when called you win more than half of the time, but when you are called some of your range will overlap with a few hands that are better hands than your hand in your opponent's range; however, this should not deter you from a value bet just because you might lose the pot when called.

The most important takeaway from this chapter, other than general knowledge of how to calculate people's ranges and how they do against your specific hand at a specific time, is that some people have different bluffing ranges from street to street. One person's flop-bluff range might be significantly wider than his turn-bluffing range and his turn-bluffing range much wider than his river-bluffing range. Against this

type of person, folding hands as strong as top pair by the river could be a good play due to his very small river-bluffing frequency compared to his river-valuebetting frequency. These player types are less common in the highest games and more common at smaller stakes games because good players realize the implications of balancing thin value bets with bluffs.

A transitional experiment into our next chapter is to attempt G Bucks calculations for the turn. While a specific turn spot in itself may seem interesting, the problem itself becomes much more dynamic when we consider our opponent's varying interpretations of what to do on different river cards with the different parts of his range. All of the different possible river cards may inspire our opponent to choose to give up with bluffs, value-bet thinly, over-bet for value or as a bluff, or choose a certain bet size. A slightly negative expected value turn-call may lead to a highly profitable river scenario if we can correctly assume 100% of our opponent's turn betting range may bet on certain rivers

that fall often enough to offset our slightly bad turn call. We may also be able to make a slightly bad turn-call if we have reason to believe that our opponent will give up a bluff on most blank rivers. Much like our river calculations, practice with the calculations will help you to intuit decisions in these varying and close spots that come up on certain turn cards when you are considering a call of an opponent's bet.

CHAPTER 5: TURN PLAY Having extensively explored flop play and river play, we'll move on to our next challenge: turn play. Our turn play is going to be an extension of our flop play in many instances, particularly when we have the initiative. Our turn plays are also going to be derived based on the assumptions gained by the way our opponent's pure bluff catchers should react given certain rivers, covered in chapter 4. We'll have the initiative on the turn if (1) we continuation bet as the pre-flop-raiser and were called, (2) we bet-three-bet the flop and are called, (3) if we check-raise the flop and are called, or (4) if we lead the flop and are called. So let's go through each of these scenarios and see how our turn play should change based on a number of factors.

We continuation bet as the pre-flop-raiser and we are called This is probably the simplest scenario to analyse; although, it will change based on your opponent's flop tendencies. For example, if your opponent raises all of his flush draws on the flop, but calls your continuation bet when you bet into him, then a flush isn't likely to be in his range if a flush draw hits on the turn with three cards of a single suit out on the board. This read on our opponent means that our turn barrel, a continuation of our flop aggression, will be scarier to him because our perceived range will improve more than his range. This read-based example sets the foreground for a general rule of barrelling the turn, although we'll see that sometimes there are exceptions to the rule and that reads may be taken too far, especially if our opponent is capable of varying his play.

It is advantageous for us to continue to barrel the turn if our perceived range improves versus what we view our opponent s range to be. This idea is especially true if the turn improves our equity by giving us a gut shot, a flush draw, or a weaker pair that we expect to be behind our opponent s flop calling range because we now may append the chances of our hand possibly improving on the river if we are called on the turn to the success of our turn bet.

Our aim is to construct an estimate for a turn betting range based on what we have determined our river ranges should be in the certain spots in order to show a profit while preserving a balanced range against the more observant opposition we encounter. By using G Bucks, we are able to decide in a fairly accurate way how often and with what hands we should also be betting the turn. I used the phrases "loosely construct" and "fairly accurately" for a few reasons. The first reason I use these phrases is because we will not be able to

predict with 100% certainty in what way a given player will play his range in a certain spot or in what way that player will adjust to some glaring (in his perception) tendency or something that we have shown at a showdown. The second reason is because we should be adjusting our ranges on certain turn cards because they will force our opposition to make more mistakes given how his imperfect knowledge of our ranges will coincide with how a scary turn card improves our perceived range over his own range. The consideration of a turn scare card being in our range compared to considering a non-scare card skews the math of a turn call to the negative in many cases, especially in the cases where our opponent's hand is likely to improve to a hand that bests our possibly turned hand.

An easy example for a spot that many people like to use a slightly wider turn betting range is when a scare card comes that rarely improves our opponent's range for example, consider the following scenario:

Pre-Flop: We raise 5h6h UTG The cutoff (a very aggressive pre-flop player) calls our raise, we are heads-up Flop: The flop comes 2h2s9c We continuation bet We are called Turn: Turn is the Kc, bringing a flush draw to the board

We decide that betting again will fold out enough of our opponent's range on the turn to show a profit. The turn bluff combined with the fact that we have the added possibility of a scary river card falling means that we can again bluff and induce a mistake by our opponent, possibly adding value to our turn bluff. I say that it is possibly adding value to our turn bet because our opponent may decide that if we are bluffing the turn king and club draw that we will continue our bluff on a club river 100% of the time; therefore, his turn call commits him to a river call. We almost never expect our

opponent to have a Kx hand given his pre-flop and flop play and because of the fact that the king helps our perceived range, it should give pause to most of his range. If we are intending to barrel hands like QJ and turned flush draws in addition to 9x hands and better on this turn, our opponent will see that any 33-88 hand is close to drawing dead or, at best, a small favourite against the hands we are representing on the turn. Additionally, our opponent will realize that he'll have to navigate a lot of tricky rivers if he is somehow ahead on the turn.

For those rare times that we are caught using this play it actually helps us to get thinner value in the future which is always nice. With every piece of information that our opponents pick up from us, we also have the ability to react, both to our play as well as to our opponent's responses and actions. Keep in mind that everything your opponent notices gives you an opportunity to better readjust than your opposition and therefore play even better and make more of their

money more often. However, if it gets to the point where your opponent thinks you are going to barrel such scare cards with your entire range and you actually are, against a good hand reader, you're going to lose a lot of money and quickly. A better opponent may adjust to your adjustments better than you adjust to his adjustments. For these reasons, I caution you to use this adjustment sparingly.

Unlike the above example where we expect to have more folding equity because of our strengthened perceived range, there are times where we will rarely have folding equity because of our unimproved perceived range on the turn. Consider the board Th9h7c2c. If we have the same pre-flop action as in the previous example and our flop continuation bet is called with a hand like Qcjc, we have a fairly standard and clear turn second barrel; although, this bet probably does not have as much folding equity as a bet on the Ac turn. For the reason that we expect to be called more often on a blank turn, we may have a few hands in our

range given the flop action with which we could adjust our ranges a bit and choose not to barrel this turn blank.

Pretend on this board that we have Acjd and that we continuation bet the flop because we rarely expect to he raised by our opponent. If we check and our opponent bets, then we might expect to have to make multiple streets of difficult calls on a very coordinated board that is likely to become even more coordinated in such a way that the board would allow our opponent to better bluff us off our ace-high hand. Because we have determined our perceived turn betting range to be extremely wide and it is not likely to contain many hands that will check on the turn and expect to continue, we might decide to check Acjd to induce bluffs from draws. Since we do not expect to fold out many or any better hands by betting the turn and we have fairly good equity going into the river, this is a good hand to choose to check-call the turn. If we double barrel on this board with any (semi)bluff in our range,

we are probably going to be relying on a river scare card or a river card that improves our hand to either fold out or to get value from our opponent's hand, given the high likelihood of our opponent putting in more money on such a draw heavy board on the turn.

These two examples are not considerations in what I would call a "standard G Bucks calculation". In other words, I would assume that for most players that their 5h4h does not bluff the turn in the first example and that Acjd does bet the turn in the second example. However, small deviations from the normal perceived ranges an opponent would expect from you are the definition of how you win money in poker. The previous two examples illustrate how we cannot actually derive or solve a turn betting range solely based upon our above discussed river ranges calculated using G Bucks. The examples also illuminate the fact that some small deviations are actually going to be better for your win rate. These deviations are solvable if we assume we have perfect knowledge of our opponent's adjustments

to our perceived range on a given turn in addition to his likelihood of making a good play on certain rivers when certain cards come, meaning his ability to predict accurately the nuanced variances in our chosen range of hands.

You are certainly welcome to attempt the multiple equations to figure out a range of hands to use in a very specific spot against a very specific opponent, stack size, and position, but the truth is that these calculations are so convoluted and involved that they are essentially pointless, other than their ability to give us, as players, a general idea of how often and with what hands we should continue in certain spots. So many unquantifiable factors have to be considered that you are probably best off learning the implications of certain rivers and guesstimating the best turn play given your hand, the board, meta-game, your opponent, and your perceived range. You can fairly well analyse turn bluffs and valuebets in a vacuum, apart from every other factor. However, considering the implications of getting

to the river with too little or too many hands will likely overcomplicate things and bring up glaring mistakes to which your opponent will easily adjust once you attempt to take on the permutations necessary to calculate the value of a certain barrelling opportunity or call-down in its entirety.

You can also use these same ideas when you are facing action from another player on the turn. If you have a good grasp on your opponent's ranges on the river, you will likely have a good grasp on when to call and when to fold the turn if you have studied G Bucks enough. However, making a close turn decision, especially out-of-position, will lead to many tricky river decisions, which means a lot of mistakes. Even if we know our opponent's turn range for betting hands, we may not know how often and with what hands he bets the river. For that reason, our turn decisions, especially those made out-of-position, should warrant more caution.

CHAPTER 6: TURNING HANDS INTO BLUFFS In order to understand the seemingly complicated concept of turning hands into bluffs, we first need to debunk the definition of the term 'showdown value'. There are two quite different definitions of the term in the poker community. One definition is correct; the other is not, because it describes a very limited case.

Showdown value (n.) Definition 1: A pair or ace high that will win sometimes if your opponent is bluffing or gives up.

This term is absolute in nature, meaning that if your cards connect with the board, you have showdown value.

Definition 2: A hand that is rated ahead of your opponent's range often enough to dissuade you to bluff

This is a relative term and can change based on your range of hands you 're able to represent and the range of hands that your opponent can represent. For example, having As2s on Ks9c2dQh4h after you check and call a flop bet, the turn goes check/check, and you're considering your river action is much different to floating a continuation bet on JhTc4d with AdQd, checking back a turn 2c when your opponent (the pre- flop-raiser) checks and you are considering whether or not to bet when you are checked to on a 5h river.

The difference in these two definitions is that the first one is going to give you the wrong impression about the value of your hands and of your opponent's likely hands in a given spot. Sometimes you should be turning a made hand into a bluff (i.e. a worse hand is extremely unlikely to call your bet) for the reason that your hand has no showdown value (in the sense of the second definition) and that the range you represent by betting is extremely strong for this reason. Now that we have the definitions out of the way, let's rewind and simplify things a bit.

Let's assume that we can rank our range on a given board from 0-10, 0 being absolutely nothing and 10 being the nuts. Sometimes what we're ranking 0 is going to be a paired hand and sometimes what we're ranking 7 (say top pair with a good kicker) will rarely be called when we bet. Are you starting to see where this is going?

Sometimes when we bet our weakest hands in our range (what we're ranking 0-2), our range is not only

lacking air, but also is perceived as much stronger when we bet. This heightened perception of strength is because now a bet represents a stronger part of this non-air range, one that is often ahead of our opponent's checking range on the turn. This dynamic is another positive externality to all of our out-of-position floating. The cards that might come on the turn or river to improve our perceived range against our opponent's range that allow us to bluff some of the time either by raising our opponent's turn or river bet or by betting the river after he checks the turn. Notice how the hands with which we are choosing to bluff, those ranked 0-2, are actually made hands. This idea might be confusing because of how some people wrongly define showdown value, but by looking at ranges and not at absolute hand values, the matter becomes much simpler.

If an opponent catches onto our strategy of betting all of our 0-2 (bluffs) and all of our 7-10 (value bets) ranked hands, then he will realize that checking rivers turns our hand face up as something in our 3-6 range.

Our opponent will be able to use this knowledge to his advantage and it will allow him to value bet very thinly and effectively. If we check and call some of our moderately good hands, hands we would rank close to 7 (those that beat some hands that our opponent would value bet into us when we check the river, especially given our 'turning hands into bluffs' dynamic), then we might even get more value from the "7" ranked hands in our range than if we lead out on the river with a bet given our opponent's interpretation of our river range.

An example of the idea of checking moderately strong hands on the river to induce a value bet from worse while keeping worse hands from folding if we lead the betting on the river can be illustrated by the following scenario:

•

We are in the big blind

•

A very loose and predictable player opens on the

button

We call Asjs •

We check and call a Kc9s3h flop

•

A turn 4s checks through

•

We check a river Jh. expecting our opponent to

value bet any Jx hand in his range as well as some nonzero amount of bluffs from his air range in attempts to fold out 9x and below

Given our earlier analysis of this player's range, we expect him to fold almost all hands worse than Asjs if we bet the river ourselves. By checking we will maximize the value of our hand as well as balance our river checking range with the times we are checking weaker hands with the intention of folding to a river bet. Another important question that you should be asking when considering balancing a river checking range is when and with what parts of our range should we check raise rivers?

In order to be able to check and decide to call, to fold, or to check-raise when faced with a river bet with some of our hands, we should choose to use the weaker of our hands to check-raise the river as a bluff because the stronger ones will possibly beat some of our opponent's value betting range. With our strongest hands, say those ranked 10, we may choose to go for a check-raise for value if we determine it to be more valuable than simply betting the river. So when check- raising the river in spots where we'll typically bet with the very bottom of our range, we should use our extremely strong hands to check-raise for value and use the weakest hands in our river check-raising range as bluffs.

Hand 1 To explain the hand below, I'll break it down into a street-by-street analysis and explain why I took each action and the theory behind the actions starting with the flop play. These examples will help you familiarise yourself with 'turning hands into bluffs' examples.

Seat 1: VILLAIN 1 ($1,015) Seat 2: VILLAIN 2 ($1,207) Seat 3: VILLAIN 3 ($1,045) Seat 4: HERO ($1,985) Posts small blind $5 Seat 5: VILLAIN 4 ($2,000)Posts big blind of $10 Seat 6: VILLAIN 5 ($970) Dealt to HERO Thjh Pre-flop: (Pot: $15) FOLD VILLAIN 5 FOLD VILLAIN 1 FOLD VILLAIN 2 RAISE VILLAIN 3, to $30 CALL HERO, $25 CALL VILLAIN 4, $20

Flop: (Pot: $90) 9s3cKh CHECK HERO CHECK VILLAIN 4 BET VILLAIN 3, $60 CALL HERO, $60 RAISE CILLAIN 4, to $180 CALL VILLAIN 3, $120

CALL HERO, $120

On the flop, the button pre-flop-raiser continuation bets a somewhat disconnected king high flop, which he will do with most of his range, expecting to induce folds often from the other two players in the hand.

Because I know this and because I have a gutshot and back-door flush draw, I decide to make an out-of- position float and call his continuation bet hoping to turn a queen, jack, ten, or heart or that the turn will check through and I'll have the opportunity to bluff the river if I'm still unimproved.

However, the big blind raises both of us and after the button calls I have another decision. A raise represents a very strong and narrow range of hands where my perceived range is quite wide, which generally makes it a bad time for a bluff. Because the big blind is raising in such a spot, where his range is extremely wide

compared to the hands that he's representing. I decided to make another float with my hand.

Also, the button's flop call is going to help me to represent strength because I know he's capable of floats with similar hands as well as calling with many weaker made hands and my over-call on the flop looks that much stronger given both of the other player's perceptions of my range given the perception of their respective ranges. In other words, the big blind is mostly going to give up with his bluffs and the button is going to pot control almost all of his hands on the turn, since his range is largely weaker made hands, and allow me an excellent river bluffing opportunity.

Turn: (Pot: $630) 9s3cKhTc

On the Tc turn I get what I was hoping for because my perceived range improves again and both players elect to check. This turn play, a show of weakness by both players, means that on the river, even if the big

blind had something as strong as KJ, given everything that has happened in the hand so far, if I bluff, he'll have a very tough call, and probably a losing one against my actual range.

River: (Pot: $630) 9s3cKhTc8s BET HERO, $460 FOLD VILLAIN 4 FOLD VILLAIN 3 RETURNED

TO

HERO, $460

On the river the button knows that if I bet that I have done so with the knowledge of what has happened in the rest of the hand and he will also have to give me a lot of credit for betting into two people when their ranges look strong and probably also fold nearly his entire range, making this river bluff an extremely profitable and creative play

Hand 2 A street-by-street analysis of the following hand will show a very important concept about turning hands into bluffs and how there are good and bad times to put the theory into practice.

Seat 1: VILLAIN 1 ($1,045) Seat 2: VILLAIN 2 ($1,849.25) Posts small blind $5 Seat 4: VILLAIN 3 ($3,135) Posts big blind $10 Seat 5: HERO ($2,137) Seat 6: VILLAIN 4 ($400) Dealt to HERO AdQc Pre-flop: (Pot: $15) RAISE HERO, to $30 FOLD VILLAIN 4 FOLD VILLAIN 1 CALL VILLAIN 2, $25 FOLD VILLAIN 3

Flop: (Pot: $70) 8dAh9s CHECK VILLAIN 2 BET HERO, $50 CALL VILLAIN 2, $50

On the flop, my opponent check-calls, which is no surprise given the drawy nature of this board and with the fact that I expect him to play almost all the hands that would connect with this board given our deep stacks and his increased implied odds with his drawing hands post flop.

Turn: (Pot: $170) 8dAh9s4c CHECH VILLAIN 2 BET HERO, $120 RAISE VILLAIN 2, to $400 CALL HERO, $280

I get check-raised on the turn, which doesn't make sense for many hands given that we're so deep and that raising the flop in order to begin building a pot is usually the best way to make money. Because my opponent knows this and I assume he likes money, his turn raise appears incredibly weak to me and I'm often expecting to see some sort of weak straight draw that is attempting to fold out a similar type of hand of mine.

River: (Pot: $970) 8dAh9s4c2s BET VILLAIN 2, $810 CALL HERO, $810

The river blanks off and it's very conceivable that he's bluffing again in order to fold out hands that I may have floated on the turn against what he thinks is a strong line and the implied odds that he thinks I would think I would have to make a light turn call profitable. Villain shows bottom pair, which is a poor way to play his hand in my opinion and shows a very important

concept you should always consider when you want to turn a hand into a bluff. My opponent didn't realize how wide of a range of hands he was representing on the turn and used a hand that was actually closer to the middle of his range in his bluff range, rather than use a hand at the bottom of that range like a missed straight draw. Not only is the fact that he's representing a wide range of hands make his bluff suspect, but also it's unlikely that he would play a strong hand this way, especially with deep stacks. Results: VILLAIN 2 SHOWS 7s8s HERO SHOWS QcAd HERO WINS POT $2,587

Hand 3 In this hand, I am turning a hand into a bluff that will be forced to navigate some tricky rivers and may be well-behind our opponent's turn value-betting range.

Seat 1: VILLAIN 1 ($1,000) Seat 2: VILLAIN 2 ($1,163) Seat 3: VILLAIN 3 ($1,969) Seat 4: VILLAIN 4 ($1,000) Posts big blind $10 Seat 5: HERO ($1,182) Seat 6: VILLAIN 5 ($1,005) Dealt to Herojsjh Pre-flop: (Pot:$15) RAISE HERO, to $30 FOLD VILLAIN 5 CALL VILLAIN 1, $30 FOLD VILLAIN 2 FOLD VILLAIN 3

Flop: (Pot:$95) Ah9c7s CHECK VILLAIN 4 CHECK HERO BET VILLAIN 1, $60 FOLD VILLAIN 4 CALL HERO, $60 Turn: (Pot: $215) Ah9c7s8h CHECK HERO BET VILLAIN 1, $160 RAISE HERO, to $1,092 and is ALL-IN FOLD VILLAIN 1 RETURN HERO, $932

In order to avoid making a mistake on this street and on the river, I decided to bluff-raise the turn, expecting to fold out most of his range because of my pre-flop raise and my flop check-call, I'm not representing any air. On the turn, I believe the range of hands I'm representing, mostly turned two pairs and straights, are well ahead of his turn value-betting range in this spot and so he will be force to fold too often given his assumptions about my range.

Hand 4 In this hand, I'm playing a smart and observant opponent who has seen me turn hands into bluffs in the past. Therefore, I know in some cases I can get value from a wider range of hands on the river if he is expecting alot of my hand combination that bet to be both made hands and bluffs. In terms of shifting my river betting range more towards the 6-10 portions of my range and away from bluffing the 0-2 portions of my range.

$5/$10 NL Hold'em Cash Game, 2 Players BTN: $2,183 Hero (BB): $2000 Pre-flop: JcKd dealt to Hero (BB) BTN RAISE, to $30 HERO CALL, $20

Flop: (Pot: $60) 4c6hKc (2 Players) HERO CHECK BTN BET $40 HERO CALL $40 Turn: (Pot: $140) 9s (2 Players) HERO CHECK BTN CHECK River: (Pot: $140) Qc (2 Players) HERO BET $110 BTN CALL $110 Results: (Pot: $360, Rake $0.50) BTN MUCK 9c8s HERO SHOW JcKd AND WINS POT

Because this opponent assumed that I would be bluffing my 4x hands and my missed straight draws on the river, he decided to make a call with a weak holding in terms of absolute strength, realising that my range does not rely on absolute strength, but the perception of absolute hand strength. In other words, because he

believed that I might check some of my 7-10 hands in order to induce a bluff or a value bet from a worse holding from him, this discounts the combinations in my perceived value range. This opponent also knows that I will be betting most of my hands worse than 9x on this river, the 0-2 portion of my range, and so he makes an adjustment and calls with a much weaker hand, hoping to catch me bluffing with a worse made hand. Unfortunately for him, I had a hand that is in my value range this time. Having seen this adjustment my opponent made against my range, I can value-bet the river more thinly and more accurately because I know he'll be calling me with a wider range. If he assumes I'm making this adjustment, then he may realize that my river checking range should appear extremely weak to him and he may take the opportunity to bluff.

Hand 5 Here is an example of a good time to turn a hand into a bluff where an opponent tried to bluff me. Unfortunately for him, I made the nuts on the river.

$1000.00 USD NL Texas Hold'em 6MAX Seat 1 is the button Seat 1: VILLAIN 1 ($1368.25) Seat 2: VILLAIN 2 ($1097.00) Seat 3: VILLAIN 3 ($1000.00) Seat 4: VILLAIN 4 ($650.00) Seat 5: HERO ($2153.25) Seat 6: VILLAIN 5 ($1015.00) VILLAIN 2 posts small blind $5.00 VILLAIN 3 posts small blind $10.00 Dealt to HERO: TcQc VILLAIN 4 folds HERO RAISE, to $30 VILLAIN 5 CALL, $30 VILLAIN 1 FOLDS VILLAIN 2 FOLDS

VILLAIN 3 FOLDS

Flop: 6sjc8d HERO BET, $50 VILLAIN 5 CALL, $50 Turn: As HERO BET $120 VILLAIN CALL $120 River: 9h HERO BET $280 VILLAIN 5 RAISE $815 HERO CALL $535 Results: VILLAIN 5 SHOWS Tdjd HERO SHOWS TcQc HERO WINS $2042 from the main pot

What makes this play interesting is that there isn't really any air in either of our ranges. If he assumes that I am randomizing my barrel range by equity, meaning that I'm choosing the best hands out of my range with which to semi-bluff the turn, then the only total air

hands I should have are KQ and missed spade draws, few of which are not paired or better by this river. I should also realize that he can't have any air by the river and so without knowing what he's capable of, this would be an optimistic call with something as strong as A8. Because my calling range is so narrow compared to how wide my river betting range seems to be, his shove seems like a fantastic play. His raise may only fold out my air hands which he already beats and not be worth the risk if I don't believe him to play his strong hands the same way and if I know he is capable of turning hands into bluffs. It's up to you to figure out if the proportion of someone's air range and their madehand-folding range to the hands with which they will call a raise and if risking the extra amount of your stack, often a lot of money by the time you choose to raise a river bet as a bluff is going to be a profitable investment. In order to calculate the best play, you should set up a simple expected value equation. Let's describe the set-up to our equation and then look at an example.

When your bluff works, he folds and you win the pot X% of the time. When your bluff fails, subtract your river raise amount Y% of the time for when he calls and you lose your river raise. For an example, let's assume that we are facing a $200 bet into a $300 pot on the river and we go all-in for $800 as a bluff, which will work 60% of the time. Is this bet profitable? Let's follow our description and make an EV calculation.

EV = (0.6*500)-(0.4*800) EV = 300-320 EV = -20

Our expected value equation, in which we win the $500 pot 60% of the time and lose our $800 raise 40% of the time, shows that the expected value of our bluff is - $20.

Figuring out this expected value problem is going to be paramount when you're deciding whether or not to turn a made hand into a bluff. You can guesstimate

your opponent's calling range by looking at your perceived range against his and factoring in any outlying tendencies that may change things a bit. Like if your opponent makes huge folds too often or calls too often or if he's tilting and more likely to call or to fold.

The Combinatorics of Turning Hands into Bluffs Against better players, you will often find yourself in tricky spots where your range is fairly defined and they are able to exploit this by turning something into a bluff some unknown % of the time in order to force you to make a mistake in a certain spot. The following example is a hand that I played against a very good high stakes NL player. I posted this hand on the LeggoPokker.com HSNL forum,feel free to go visit the forum and give the hand your two cents.

Here is my post:

"I'm not sure if he knows who I am on stars, but I'd say for the majority of my play on Full Tilt he regards me as a decent/solid regular capable of doing some weird spewy crap at times. I'm also about 80% certain he can turn at least some of his hands into a bluff (I guess multiply his bluff range by 0.8 or something, I don't know)."

$1000 USD NL Texas Hold'em Seat 2 is the button seat 1: VILLAIN 1 ($1806.00) seat 2: VILLAIN 2 ($3155.00) seat 3: VILLAIN 3 ($2112.75) seat 4: VILLAIN 4 ($2108.00) seat 5: HERO ($2341.00) seat 6: VILLAIN 5 ($2346.00) VILLAIN 3 posts small blind $5 VILLAIN 4 posts big blind $10 Dealt to HERO: KsKc HERO RAISES $30 VILLAIN 5 FOLDS

VILLAIN 2 FOLDS VILLAIN 3 CALLS $25 VILLAIN 4 FOLDS

Flop: 8d9s3h VILLAIN 3 CHECKS HERO BETS $50 VILLAIN 3 CALLS $50 Turn: 8h VILLAIN 3 CHECKS HERO BETS $140 VILLAIN 3 CALLS $140 River: 7d VILLAIN 3 CHECKS HERO BETS $380 VILLAIN 3 RAISES $1125 HERO? $745 to call.

"What range do you give him by the turn and how much of that is he turning into a bluff (if any) on the river? Iguess that about takes care of my reads... Oh I'd also like to add that I took a while to size my river bet and that he check-raised somewhere between quick and relatively quick.

I'm not sure how he's interpreting this river bet size either or if that affects his check-raise range at all."

After posting, I then proceeded to read about 20 HSNL regulars and other people say 'instafold', 'easy fold', and 'fold'. After getting all the responses that I had expected to see I then felt it was time to add my opinion of the outcome of this hand.

Pot on the river = $1950 To call his raise = $745 Pot odds -2.62:1 (I have to be good 27.6% of the time in order to break even on a call)

We'll give my opponent in this hand a single hand that he could turn into a bluff, a pocket pair, for six combinations. There are two combinations of A8s remaining and one of the 87s (we'll say four just to discount offsuit 87, which is very generous towards his value range) and three combinations of 77. Even with these ridiculously generous assumptions that help my colleagues to prove their dissimilar point of view, there are still 10 combinations of value betting hands versus six combinations of bluffing hands (1.67:1).

If villain can get to the river with 77, 33-66, TT, and one third of the JJ combinations also get there that can possibly bluff, then he onlyhas to be using one of those hands to bluff, out of 5.33 hands, which seems fairly reasonable if not even too optimistic.

It is very unlikely that people often slow-play sets 200bb deep on this board. I think any non-zero chance of villain slow-playing can be explained away by attributing the pot odds equivalent possibility of him

turning another combo of a hand into a bluff here and so it's a moot point. In other words, I am being generous with how the math problem could be written in order to alleviate any worry or rebuttal a sceptical person mayhave about this hand.

If he's turning one of his missed (non-boat) pocket pairs into a bluff on the river, it means that I will win (6/16) * 100% = 37.5% of the time when I call his river raise.

The way that our assumptions set up the expected value equation for this problem, is an extremely close spot. I believe that the math is skewed to ease the minds of sceptics, but VILLAIN 3 is an extremely good player and good players will make your decisions very close and difficult, attempting to force you into making a mistake. While this spot is a close decision, it revisits an important concept about turning made hands into bluffs: against great hand readers, you would have to be able to credibly represent value hands that you would

play the same way as the strongest hands in your range. In these spots, balance is extremely important. I've probably missed some value by checking sets three times to an aggressive opponent in those specific hands. However, later when I check-raise the river, that same opponent has to give me credit for me having a stronger range than a lot of people would have in the same spot because of the way he saw me play my strong hand earlier. Turning made hands into bluffs is not only an interesting concept, but also a great help to your poker game against other thinking players and a good lesson in balance. It also forces you to play actively and to always consider your range in every spot that comes up throughout every hand you play, which will rapidly improve your poker play compared to auto-piloting through matches.

CHAPTER 7: OVER-BETTING AND UNDER-BETTING ALL YOUR OPTIONS It is very important that you are asking yourself each time that you choose a play, "what options do I have and which is the best decision for this spot and what are the implications of my decision now on future hands that I play?" These considerations apply not only

for the specific point in the hand that you are in, but also for later on in that hand and for your game as a whole. If you are caught in a bluff now, will your opponent call every value bet you make for the rest of his life? If so, your bluff is more profitable because of how your opponent will interpret your range in the future in similar spots.

Two options beyond to bet or not to bet in a certain spot that people don't often consider or understand why they should consider are over-betting and under-betting the pot.

Over-betting: Betting over the size of the pot. Complex definitions aside, over-betting is something that a lot of people do not have in their game. It's a complex topic from a theory perspective. Mathematically, it's difficult to play against for your opposition, especially in the spots we will discuss. That's why I believe it to be a good weapon that should be in your ever growing repertoire of potential best play decisions. When our opponent's range is capped, i.e. he likely has a certain "best" hand from the way he has played his hand to this point, an over-bet will make his future decisions in the hand very difficult. Often when we decide to over-bet into a capped range, the cap for our opponent's range will be a relatively low strength hand compared to all the hands we are able to represent on

certain boards. His decisions will be especially difficult due to the fact that our range, because it's so balanced and how the board has run out, will be uncapped. The way certain boards run out mean that we can have the nuts and a lot of hands close in absolute strength, while our opponent is far less likely to have the nuts. Another positive aspect of over-betting all-in mostly seen in reraised pots or on the river in single-raised pots, is that it stops our opponent from bluffing us off a potentially better hand (ex. his smaller straight draw raises our river bet with a missed ace-high draw) and we make a mistake by folding.

Hand 1 Seat 1: VILLAIN 1 ($2,481) Posts big blind $10 Seat 2: VILLAIN 2 ($470) Seat 4: VILLAIN 3 ($3,999) Seat 5: HERO ($2,634) Seat 6: VILLAIN 4 ($990) Posts small blind $5 Dealt to HERO Tcjs Pre-flop: (Pot: $15) FOLD VILLAIN 2 RAISE VILLAIN 3, to $30 CALL HERO, $30 CALL VILLAIN 4, $25 CALL VILLAIN 1, $20 Flop:

(Pot:

$120)

9c9dTh CHECK VILLAIN 4 CHECK VILLAIN 1 BET

VILLAIN

$70 CALL HERO, $70 FOLD VILLAIN 4

3,

Turn: (Pot: $260) 9c9dTh5h CHECK VILLAIN 3 BET HERO, $180 CALL VILLAIN 3, $180 River: (Pot: $620) 9c9dTh5hKc CHECK VILLAIN 3 BET HERO, S2,354 and is ALL-IN CALL VILLAIN 3, $770 and is ALL-IN RETURN HERO, $1,584 Showdown: SHOWS HERO Tcjc SHOWS VILLAIN 3 KdKh VILLAIN 3 wins the pot of $2,157 with a full house, kings full of Nines

This hand ties together a few concepts and introduces a new one: how over-betting a medium strength hand turns the hand into a bluff and when to make this play. Granted, this particular situation is fairly rare as we must be making a thin turn bet that is followed by a river card that hits our range so hard that

our perceived range becomes much stronger than our opponent's range. Given our strength, we should then make a bet in order to fold our opponent off of nearly all of his holdings. The math for this concept is fairly complex and variable for each opponent, and so I won't be going into it in this book; however, it's intuitive that risking slightly more than a pot-sized bet in order to win the pot 95+ percent of the time is an obviously profitable investment. Much of the reasoning behind this calculation being so convoluted and probably meaningless is because when one over-bets, it's often difficult to determine a near-exact calling range for your opponent.

In the above hand example I am checked to on the turn and decide to bet in order to balance with the times that I'm betting my large amount of straight draws in this spot and to get value from worse hands that are inducing my draws to bluff. I can be expected to be called by many worse hands because my opponent is a thinking player who is aware of my range well enough

in this spot in order to make a light call on the turn after he checks to me. Once my opponent called the turn and from the way he had been playing, I was nearly certain that his range was capped at AA and was most likely another Tx type hand as I would expect most of his premium hands to be betting or check-raising this turn when he is planning to continue betting for value. I would suspect that he would choose to use his weaker hands to induce bluffs for the reasons discuss in the section on floating in Chapter 3.

On the river, my opponent checked again and rather than making a smaller bet like $280 that would possibly open me to a check-raise bluff or that would likely only be called by a slightly better hand, I decided to over-bet shove the river, representing any hand better than AT. I have all of KJ. KQ. 9x. and QJ combinations in my range in this spot and given the way he played his hand on the turn, my range of hands is significantly ahead of his range of hands on the river. I felt that in order to only represent the aforementioned range it was

necessary to over-bet, thereby polarizing my range. Because the only air hands I could have had were the four combinations of 87s. I also expected to get a lot of credit in this spot. Unfortunately I ran into his rivered full-house and I lost the pot. Aside from my loss of this hand. I think that I make quite a bit of money on average from this play versus this opponent in this particular spot.

If we bet larger than the pot, then our opponent will have had to win a larger percentage of the time to make his call profitable because he has worse pot odds. With a semi-face-up weak range, this will be extremely difficult to do for him because we are the ones who control the frequency of our over-bets. It would be very difficult for him to trap us or to have correct slow-play frequencies to counter our over-betting strategy without losing value in other spots when we decide to take a showdown with our weaker hands or not to bluff the river.

Hand 2 Here's another example of a time that I over-bet because my perceived range by the river is quite wide. Because most of my opponent's range is Qx and so many draws missed the board on the river, I need to offer my opponent a worse price on his river call in order to make my river bluff profitable. Try assigning me a range in this spot and assume that I can over-bet KQ+ for value while the rest of my air makes the same bet.

Full Tilt, $5/$l0 NL Hold'em Cash Game, 4 Players LeggoPoker.com Hand History Converter BB: $680.25 Hero (UTG): $1,000 BTN: $2,104.75 SB: $1,756.50 Pre-Flop: Jc8c dealt to Hero (UTG) Hero raises to $30

BTN folds SB

calls

$25 BB folds Flop: (Pot: $70) 3cQc9d (2 Players) SB checks Hero bets $55 SB calls $55 Turn: (Pot: $180) 6h (2 Players) SB checks Hero bets SI50. SB calls $150 River: (Pot: S480) 9h (2 Players) SB checks Hero bets $765 and is ALL-IN SB folds Results: $480 Pot ($2 Rake) Hero showed Jc8c and WON $478 (+$243 NET)

Another great time to over-bet is when your bet is only going to be called by a great hand regardless of the

amount you bet. This premise of over-betting works especially well because most of the time a board runs out in such a way that this situation arises, it is also quite similar, perhaps the same, as when your range is uncapped and your opponent's range is capped.

Eventually, in these situations, people will feel obligated to take a stand with the top of their range and make a call to avoid folding 100% of their range in these spots.

Hand 3 It's important to over-bet for value as well as with bluffs in order to balance your over-betting range.

PokerStars, $10/$20 NL Hold'em Cash Game, 5 Players LeggoPoker.com Hand History Converter Cutoff: $475.00 Button: $497.00 SB: $915.65.00 BB: $1,688.00 Hero(UTG): $2335 Pre-flop: KcQc dealt to Hero Hero raises to $60 (UTG) 3 folds BB

ll $40

Flop: (Pot: $130) 9dTd6h (2 Players) BB checks

Hero bets $100 BB calls $100 Turn: (Pot:$330) Jc (2 Players) BB checks Hero bets $260 BB calls $260 River: (Pot: $850) As (2 Players) BB checks Hero bets $1,915 and is All-in ($1,268 to call) BB folds

Under-betting: making a bet that is very small relative to the pot size. Under-bets are primarily used for two reasons:

1.

A cheap bluff.

2.

When we're coaxing our opposition into making a

bad call with deceptively good pot odds against our range and/or to induce a bluff-raise from him in the same spot. In both cases, this type of bet size is best used when there is little or no air in our range and our opponent's range is extremely weak in comparison.

For value, we want to choose a bet size that is almost bordering on what anything might call, knowing it's almost always beat. Our opponent might justify his call by telling himself that he is getting information about our range and that he will make money from the combination of his marginal or bad call and his newly acquired information in the long-run. He might also just be curious and call with something that's almost never good. Under-betting is not meant to be a blocker bet. The difference between the two is that a blocker bet is meant to get calls from weaker hands and to allow us to comfortably fold our hand to a raise. We have already said here that our opponents range should be extremely weak before we decide to under-bet for value, and its quite unlikely we'll be raised on the river for value. Also, if we are raised, the matter of comfortably folding goes out the window because we are now facing a very strange line that represents not very many good hands, especially hands that most people are capable of raising for value. This is fairly often a desperate bluff from an opponent misinterpreting our small bet size for

weakness. After you under-bet and call a raise, you might get owned by a river check-raise here or there, but I've definitely won some big pots with very marginal holdings facing river raises that made no sense for my opponent's range.

Realizing all your options is crucial. Consider, for example, a scenario in which we're under-betting for value and then three-betting as a bluff over someone's river raise in order to fold out their entire range. Consider bluffing someone's over-bet. There are many more possibilities than you have likely considered in this game. Be vigilant and mindful while playing poker and while you're away from playing the game and you're sure to find different and new spots to explore that may confuse your opponents.

CHAPTER 8: LEADING (INTO THE PRE-FLOP-RAISER) Leading into the pre-flop-raiser, affectionately known as "donk betting" or "donking", is a strategy that has become more prevalent as people have started to understand continuation bets a bit better. As we have discussed, it is often a mistake, especially against a great and well-balanced player, to continuation bet too often, especially with weaker made hands that are going to be put into tough spots if they get raised. If it is difficult for us to have a clearly correct turn play after we check-call the flop, then sometimes leading can create a clear turn play when check-raising or check-calling the flop may lead to confusing turn and/or river spots.

An examination on leading and literature surrounding the topic are almost non-existent in the poker community. Therefore, by working on your leading game, I think that we all stand to up our win rates by quite a bit as adjustments to leading are yet to be examined in full or put into practice in many games. It is also important to note that because our perceived range is much stronger on these boards, on which we will soon elaborate, it is reasonable to assume that a decent hand reader will be folding quite a few hands if he believes that we have a balanced leading range. In order to create the perception of a balanced range, we cannot always lead air and always check-raise the nuts. If we play our hands in such an unbalanced way, we will become easy to read and we will be called down too lightly to make our bluffs profitable against perceptive players and good hand readers.

So with all the ideas we just examined we can begin to construct a leading range. It is important to realize

that the boards on which we are choosing to lead are often ones prone to changing quite a bit as the hand progresses, so our perceived range may quickly become so strong relative to our opponent's flop calling range that if we were leading a weaker made hand, then there may often be times we might want to lead our weak hand again as a bluff. If we were leading with one semi- bluffing hand and another draw in our perceived range gets there, we may choose to lead again, continuing our (semi)bluff.

I think the best way to start thinking about leading ranges is to look at some leading examples and then to add other hands into our range on a specific board type in order to balance bluffs with value bets. Remember how we extrapolated our turn betting ranges, albeit somewhat loosely depending on the specific turn card, from a good river bluff range? We are going to use a similar technique to determine good leading ranges.

Example Pre-Flop: We call a button raise in the big blind with Qsjc Flop: Ts8s3h

Notice how almost the entire deck is a scare card for a significant part of our opponent's flop calling range after we lead the flop. Any 7, any spade, 9, T, J, Q, K, or A are scare cards that may hit the turn and give our opponent pause with much of his flop calling range. We also improve in terms of absolute strength on a lot of these turn cards as well as improve our equity versus our opponent's flop calling range. If our lead is called on the flop we know that other than the five cards known to us at the time that there are a remaining 47 cards in the deck and of those 47 cards 25 of those cards (53.2% of the deck) allow us to semi-bluff or value bet the turn according to our plan of creating a range of hands with

which to continue on the turn based on improvements in our equity. If we are called on the turn, the river will be a scare card or a card improving our hand quite often as well (24/46 cards or 52.2% of the time).

Even if our opponent has a hand as strong as 8x, he will often be put in extremely difficult spots as the board and our range appears to lessen the absolute strength of his hand. If he has a straight draw we dominate J9o for example, we could make a dominating hand which he may give action to on the turn. When determining to continue bluffing the river, assuming we continue to bluff the turn the 53.2% of the time that we improve, we will have to determine our opponent's likely worst hand for calling a river bet of a given size and weigh the sizing with our bluffing and value betting combinations of hands versus the combinations of hands with which he gets to the river in a G Bucks calculation (see Chapter 4: River Play).

Part of the problem of how amazing leading as a bluff can be on some boards is that we also need to be leading good hands in order to protect the times that we lead with hands like queen high or a small spade draw, otherwise we are able to be raised off of our hand too often and our opponents will be able to adjust to our skewed frequencies and exploit our play. Inherently, leading a balanced range, as compared to a check- calling range, is going to be difficult because leading medium-strength hands is usually not advantageous against the range that gives our lead action, especially across multiple streets. If we lead a medium-strength hand, then our decision of what to do when raised is a bit more complex and will likely lead to mistakes against our opponent's hand. If we decide to call, future streets can be difficult on coordinated boards out-ofposition. If we decide to three-bet the flop, it's unlikely that our medium-strength hand does well against a range of hands with which our opponent will commit his stack. The problem in this case is that taking all of the medium hands out of our range polarizes our leading range to very strong value hands, or at least

hands with which we believe we are able to make the best decisions on future streets, and semi-bluffs. Currently, a leading game hasn't been explained or perfected by many players and so people are still playing poorly against leading when their opposition is probably leading far too many hands as a bluff compared to the times that opponent is leading for value. It's just like betting when checked to by the pre- flop-raiser on certain boards, it works so often that balance isn't an issue against 99% of people, and that's something that we can exploit if we are in that enlightened 1% of poker players.

On the other side of the action, when facing a lead it's important to realize the mentality of someone leading into the pre-flop-raiser and their game plan and reasoning for leading. To sum up the game plan we above outlined, balancing for most players isn't necessary because their opponents allow them to play in an exploitative way.

Assumptions by our opposition that we will react just as poorly to leads as their average opponent gives us the opportunity to force them into making a mistake.

Two ways we able to force such a mistake are by:

1. Widening our bluffing ranges on "scary flops" which they will often lead

2. Widening our calling ranges on "scary" turns and rivers which they will often continue to lead on after we have called a "scary flop"

Both of these actions would be taken because we expect our opponent's leading ranges to be unbalanced and mostly composed of weaker semi-bluffing hands. Adjustments made in a poker game should be based on a function of how often our opponent's leading range is a bluff and how often he is capable of three-betting the flop as a bluff or floating out-of-position and bluffing a later street.

You have already read how to calculate the expected value of a play against a given range of hands

and I believe that leading ranges and folding ranges to flop-raises or giving up on certain barreling cards is so subjective that any sample exercises I could do here would be almost entirely useless in the way that a single G Bucks calculation is nearly meaningless. Now that you know what to do try some expected value equations against different leading ranges, what percentage of hands in that range will fold to a raise, what percentage of hands in that range will re-raise a raise, and what percentage will call. By practicing the outcomes of several different plays against several different ranges, you won't have to discover in-game what the best play is after the chips go in the pot, which is often the most pricy way to learn poker.

CHAPTER 9: QUANTIFYING "LEVELING" Poker players love to talk about leveling one another into a call or a fold in certain spots. By "leveling", most people mean that they are trying to make an opponent react a certain way based on the perception of a certain action. People accept the mentality that they have tricked someone if a certain outcome happens and think that they have failed if their trick "does not work".

However, poker players should be thinking about their opponent's possible range of hands and how their ploy will skew their opponent's range in a certain

direction not just a specific hand. Leveling is like the Sklansky Dollars terminology for what we come across once we address the combinatorics and ranges involved in one's interpretation of any given action, given previous actions.

By breaking down the word leveling and by better examining what it is meant to represent in terms of read based mathematics, we are able to make better decisions, ones that are more rational and more profitable rather than superstitious and impulsive. Once an opponent reaches a certain inflection point and we think that he is adjusting his ranges in a way that allows us to make a different play more profitably than another play, we should obviously choose the latter play. This inflection point is what is often called leveling by poker players, but the name for the inflection point confuses some people into thinking that all adjustments are spots on the other side of an inflection point that should change how a range is played, instead of how a range is adjusted. Over-adjusting to meta-game will cause you to

lose money in some spots that might be avoided or even more profitable by a smaller adjustment of your range.

Take the example of the beginning of a heads-up match, the match begins and we know that our opponent is capable of calling three-bets lightly, especially early in a match, and so our plan is to start off three-betting a depolarized range. We are dealt AJ and decide to three-bet and our opponent folds to our raise. A few hands later after some raising and folding pre- flop, no re-raising, we are again dealt AJ. Again, we decide to three-bet, but this time our reasoning is different because we believe that we have come closer to an inflection point where our opponent's pre-flop adjustment to our range might make our three-bet more profitable than our first three-bet. Along with the read that we have suggesting that he is capable of calling hands which we dominate such as AT, A9s and KJ, we realize that he is likely at some point to four-bet us lightly. This pre-flop adjustment is inevitable given that we have already three-bet him a few times at the very

beginning of the match and because we know he is a good player who won't allow himself to be run over by re-raises. Some players four-bet early as a bluff to set a tone for the match and to send a message while other players do it out of frustration, but the fact is that we expect this player to be bluffing here more often than an average time when he is re-raised pre-flop, and so for all the times we re-raise this player, this situation may be one of the best times to five-bet shove. At the beginning of the match, we were uncertain of his four-betting range, but knew a bit about his calling range. Now we are not only confident three-betting this hand to get called by worse hands, but also fairly confident in that we have a profitable five-bet shove as we approach (or reach) the inflection point or the "breaking point" when he decides to four-bet our three-bet as a bluff.

Let's say that away from an aggressive dynamic that our opponent will be four-betting us as a bluff 35% of the time and calling an all-in with a range of 99+, AQs+ and AK. Our expected value for five-bet shoving Acjh here (after our opponent four-bets to $240 over our $100 three- bet) lOObb effective is:

EV (shove) = 0.35(340)+0.65(2000*0.30326-900) EV (shove) = 119 + (-190.762) EV (shove) = -71.762

After we have already three-bet him once in the match and we expect him to adapt by four-bet bluffing about half of the time and still call the same range of hands for value, our EV of shoving with Acjh changes to:

EV (shove) = 0.50(340) + 0.50(2000*0.30326 - 900) EV (shove) = 170 + (-146.74) EV (shove) = 23.26

Notice how we're not calling the pre-flop situation one when we are leveling our opponent into four-bet bluffing us. Rather than thinking we are catching our opponent bluffing pre-flop this exact time that we three-bet we are adjusting the percentage that he bluffs a few points higher given how we think our opponent thinks. This adjustment to the percentage of times he is bluffing is the best way for us to quantify his thought process and how it will affect the hand. By imagining the dynamic as one strictly based on leveling, we may incorrectly assume that he won't be bluffing enough of the time here to shove or that he is bluffing so often that we could shove a worse hand that wouldn't do well enough against his calling range to make a five- bet shove a profitable play in this spot.

I've already written about why trying to quantify the expected value of a hand in which one or more of the players in it over-bets is probably not worth the inaccurate attempt, but I will write that the more often one over-bets, the more likely an over-bet will be

called. If you are representing an extremely narrow range of hands very often, an observant opponent will realize that you're betting with more than just your share of cards in a certain spot an capitalize on that realization by calling more often. While it's difficult to say how much more often and quite dependent on the particular opponent in question, it is intuitive that the more often and in succession that you are able to overbet, the more likely it is that one of your opponents will take a stand and you will be called, and the more expected value the play has when you're betting for value.

By adding and removing combinations of bluffs and value-bets from villain's range based on the flow of the game we are able to make rational and more profitable choices instead of going with an intuitive gut feeling that may lead us astray. We want to escape the need to play a guessing game and embrace a mathematically supported plan based on our reads of our opponent's (future) adjustments.

CHAPTER 10: MISCELLANEOUS CONCEPTS Representing a Bluff There are situations where calling a raise may actually represent a stronger hand range than re-raising. Calling may represent a stronger range because because in many spots, you forfeit the illusion that you are trying to get folding equity and you might be turning your hand face up as extremely strong. Here is an example of a hand where the value range that we are representing is extremely narrow and so calling our opponent raise and failing to represent air may be a large mistake that costs us lots of value.

Full Tilt, 6-MAX, DEEP $5/$10 - No Limit Hold'em Seat 1: VILLAIN 1 ($1,000) Seat 2: VILLAIN 2 ($2,000) Seat 3: VILLAIN 3 ($5,253) Seat 4: VILLAIN 4 ($1,005) Seat 5: HERO ($1,958) Seat 6: VILLAIN 5 ($2,819) VILLAIN 4 posts the small blind $5 HERO posts the big blind $10 VILLAIN 3 is BTN Dealt to HERO: 7h7s VILLAIN 5 RAISE, to $30 4 Fold. HERO CALL, $20

Flop: 3h3c7d Hero checks VILLAIN 5 bets $50 HERO raises to $180 VILLAIN 5 has 15 seconds left to act VILLAIN 5 has requested TIME VILLAIN 5 raises to $415 HERO has 15 seconds left to act

The important concept to realize by studying this hand is thai we should three-bet in this spot both as a bluff and for value. Because calling makes it so unlikely that we have any air in our range, a three-bet will also help us to get more value and build a pot versus our opponent's non air range. He also may choose to float because the range of hands that we're representing is so polarized and fast played, something which many people are not willing to do for fear of losing action. There were my intentions when I decided to check-raise the flop versus this particular opponent.

HERO raises to $720 VILLAIN 5 has 15 seconds left to act

VILLAIN 5 has requested TIME VILLAIN 5 calls $305 Turn: Ts HERO has 15 seconds left to act

Because we said that some of the time our opponent will be floating and because we have purposefully left just enough money for a pot size bet, we should consider checking the turn in case he wants to bluff us there or in case he has a weaker draw such as 56hh that could improve to a worse made hand on the river Our turn check may also plant the idea in his mind that we intended to give up on the turn if called on the flop and widen his river calling range.

HERO checks VILLAIN 5 has 15 seconds left to act VILLAIN 5 has requested TIME VILLAIN 5 checks River: 4s HERO has 15 seconds left to act HERO bets $1,235, and is ALL-IN

VILLAIN 5 calls $1,235 Showdown: HERO shows 7s7s VILLAIN 5 mucks KcKs HERO wins the pot ($3,972) with a full house: Sevens full of Threes

In this example of why it's important to represent air, we are bet into by an opponent who isn't representing a wide hand range for value given the combination of how wide his flop check-call range is, the unlikelihood that the turn 2h improves his specific hand, and the fact that this opponent would be most likely to check-raise strong hands on a draw heavy flop. We obviously have a profitable turn call and possibly a profitable river call if our opponent chooses to continue his bluff. Because calling should mean to our opponent that most of the time we have showdown value, he may be unlikely to continue blufiing on rivers that don't improve any of his perceived semi-bluffing range. For this reason, and to balance the times we would like to bluff-raise this opponent when he takes a line that

represents nothing, we should raise our hand for value and hopefully induce a larger mistake from our opponent like a call without the correct implied odds or three-betting the turn as a bluff. In this hand, we successfully induced the latter and made much more money while preserving a balanced strategy by representing air with our turn raise.

Full Tilt 6-MAX $3/$6 - No Limit Hold'em Seat 1: VILLAIN 1 ($1,318.50) Seat 2: VILLAIN 2 ($600) Seat 3: VILLAIN 3 ($444.90) Seat 4: HERO ($756.75) Seat 5: VILLAIN4 ($210) Seat 6: VILLAIN 5 ($975.95)

VILLAIN 4 posts SB $3 VILLAIN 5 posts BB $6 HERO is BTN Dealt to HERO Qc9s Folded to HERO HERO raise to $15 VILLAIN 4 folds VILLAIN 5 has 15 seconds to act VILLAIN 5 calls $9 Flop: 3dQhTc VILLAIN 5 checks HERO bets $24 VILLAIN 5 calls $24 Turn: 3dQhTc2h VILLAIN 5 bets $54 HERO raises to $132 VILLAIN 5 has 15 seconds left to act VILLAIN 5 raises to $936.95, and is all in HERO calls $585.75. and is all in VILLAIN 5 shows 9hjh HERO shows Qc9s $219.20 returned to VILLAIN 5 River: 3dQhTc2hAd HERO wins the pot ($1,513.50) with a pair of Queens

Using other Players Perceived Ranges to Strengthen our Perceived Range This hand shows how sometimes our opponent's perception of how we should be interpreting how other players react to our range may force them to make false assumptions about the strength of our perceived range. Giving us too much credit for a strong hand.

$2000.00 NLHE Seat 1: VILLAIN I ($2284.00) Seat 2. HERO ($3179.00) Seat 3: VILLAIN 2 ($2492.00) Seat 4: VILLAIN 3 ($3997.00) HERO posts small blind $10 VILLAIN 2 posts big blind $20 Dealt to HERO AcTs VILLAIN 3 raises $60.00 VILLAIN 1 folds HERO calls $50.00 VILLAIN 2 calls $40.00 Flop: Jd7d9c HERO bets $140 VILLAIN 2 calls $140 VILLAIN 3 calls $140

On the flop, this is a good board for us to represent a strong range of hands and also one that our opponent's may both check back a lot of the time so we lead with a gut-shot and an over-card, with decent equity, but not enough to make us comfortable getting stacks in on the flop. This hand is a great example of the options to consider in the section on leading

Turn: 4s HERO bets $420 VILLAIN 2 calls $420 VILLAIN 3 calls $420

On the turn, we can make a few assumptions given the play of our opponents on the flop. The first caller is very unlikely to have a hand like JJ+ because of pre-flop and unlikely to have other strong hands of the strong likelihood that we'd give him more action with the hands in our range if he did raise the flop. We can also apply similar logic to the pre-flop-raiser and therefore imagine their ranges as fairly weak the majority of the time. They both have to worry about a lot of scary turn cards killing their action if they do have good hands. Therefore, we can cap both of their ranges reasonably well at around AJ, and so we lead again, predicting that weaker straight draws like KQ will be forced to fold, we stop them from bluffing us off of ace-high if we do decide to stop betting, and hands like JT and 98 will begin to feel the heat of our aggression and be

concerned about the threat of a large river bet. Whether or not they fold on the turn is player dependent, but the most important part of this hand is that the more action each player gives us on our increasingly strong looking bets, the tighter the range that they should assume that we are bluffing. They know that we know our bluffs shouldn't work against strong made hands often and so we shouldn't too often continue with a bluff, especially now that the turn doesn't improve any of our semibluffing range.

River: 3s HERO bets $2559 VILLAIN 2 folds VILLAIN 3 folds Returned un called bet $2559 to HERO HERO wins $1858 from the main pot VILLAIN2 "so sick, 999?"

Finally, by the river, we are using our same logic from the turn combined with the fact that the pot is so big that both people would likely shove any hand on the turn with which they were reasonably comfortable,

especially the second player to act. At the time of the hand, I was also fairly confident that the pre-flop-raiser was drawing, given his actions and timing, especially on the turn. We go all-in for a slight over-bet, basically only worried about making the non-pre-flop-raiser fold. Because he knows that we have to consider the pre-flopraiser's range as tighter and slightly less capped, he then has to give our third barrel more credit, knowing that we should assume bluffs to be called more often. Also, because our range probably included some air on both the flop and on the turn, it's become increasingly unlikely that we are still bluffing on the river, and more likely that we are expecting one of the two players, especially the second to make a call. As we predicted, the first player tank folded and the second player folding instantly, making a missed draw, as predicted, most likely. This hand shows how the perceptions of other players' ranges within a hand can change the perception of our range.

CHAPTER 11: MOVING THROUGH THE LIMITS Some things you'll likely be confronted with after learning and experimenting with everything in this book are the problems associated with moving up through the limits. While it's a good problem to have, there are certainly adjustments to be made and misconceptions that could stunt your growth or cut into your win rate upon entering into regular play in a new limit. There are a few different mentalities that you may adapt, sometimes wrongfully, and that your opponents may assume that you adapt if they assume you're scared

money and over-adjusting to the players in the new limit.

Shot taking When taking shots at a limit, sometimes underrolled, it's important to realize that other regulars who know you may think that you are a mark for some high variance abuse. This thought process is because the better players will realize that you should be variance adverse when a higher percentage of your bankroll is on the line. For this reason, I recommend a slightly snugger style than your normal style of play, both to avoid the variance when you cannot stand it and to avoid making mistakes by making some incorrect assumptions about your opposition. Playing w ith tighter ranges pre-flop will also hurt your opponent's chances to make you fold as often as they assume you will if they are trying to reraise you often as a bluff. Playing extremely tight in this situation may even be more profitable than your normal

game plan because of how often some people will be bluffing you. especially pre-flop when it is cheaper. Be careful, those same assumptions about players bluffing you more often may lead you to make mistakes based on the idea that people are always making moves against you or that all your bluffs will get much more credit, since you're a new player to the limit. These possible mistakes lead us into our next topic:

Fancy-play-syndrome (FPS) A tempting over-adjustment many players make when entenng a new limit is to think automatically that everyone is omniscient and capable of seeing into your soul and, therefore, what used to be your standard play in a spot is going to be the wrong play or that the value of the play is drastically diminished. Think about this idea for a moment. Those plays are a large part of how you made it this far to begin with, so why would you abandon them now? If you're well-balanced in all the

spots we've been discussing, your value bets and bluffs will still do well. They may not do quite as well, but this is something that comes w ith mov ing into a more challenging game. Your opponents will be more skilled hand readers and your ranges will become more apparent to them quicker than they will become evident to worse players. Therefore, they are less likely to pay you off with worse hands when you value bet and less likely to fold to your bluffs when they have hands better than your hand. Another way to say this is that they will be less likely to make mistakes against your ranges in spots they've already seen you play. Even though their reasoning might be sounder, haphazardly debunking your game plan is more often than not going to be a one-way ticket back to the next lower limit.

Making it as a Poker Player Once you are beating 1/2 online and are able to make $4000 a month for about 8 hours of work per week, you may feel tempted to feel like you have made it.

If you want to be the best, then you should avoid complacency. It simply cannot exist for you. 1 know I've spent parts of an organic chemistry class calculating how much I can make a year by playing 6 hours of 400nl a day. That was a few years ago now, but the great feeling that washed over me when I saw that huge number at the bottom of my chemistry notes still upsets me a bit. That feeling will make you complacent and ambivalent to the competition's efforts to improve. When this happens, forget about being the best, you should be thinking about winning at your regular limit! Poker is an ever evolving game and as more training tools become available to the masses such as video

producing sites, private coaching, and amazingly written books, people will get better. Make sure you do not fall by the wayside. I have never been one to be content with mediocrity in a subject for which I have passion and you will see that this is the one thing that the top players have in common. Stylistically, some will differ from others Away from the tables, some may spend more frivolously than others. I will guarantee you that no matter who they are away from the table, the best players have been obsessed with the game and have put in the work alone or with a close group of poker friends

Challenge yourself to realize that you should never really "make it" as a poker player. To believe you have made it is to accept your current set of standards for your win rate, your game, and yourself and I believe it is to fail. Put in the hours and keep working or you will get passed by the pople who will not stop working in order to better themselves.