Calculating Poker Probabilities With a Simple Excel Spreadsheet _ Poker Savvy
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3/20/2011
Calculating poker probabilities with a s…
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Poker is a game of probabilities. Every time when you put money into the pot, you have to ask yourself: what are my odds to scoop the pot? How much to call this bet? How much to bet so that my opponent can not profitably call with his draw? A lot of questions that are posted on poker forums are of the type: what is the chance THIS or THAT happens? Here are a couple of examples: 1) I have KK and my opponent calls my raise with an Ace. What is the chance that he pairs his ace on the flop?
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2) I have a couple of small suited cards. What is the chance that exactly three cards of that suit appear on the board (and not four, because that would mean trouble). 3) I have two unpaired cards. What is the chance that I flop two pair or trips? 4) My opponent raises and could have any tw o cards doing that. I have a small pair, what is the chance that I flop a set? 5) My opponent raises and I know he only does that w ith AA/KK/QQ or AK. I have a small pair, what is the chance I flop a set?
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6) I have QJ on a T62 flop. What is the chance I make a straight by the river? For those among you w ith little affinity for mathematics, these questions could be above your head. So I´m going to provide you with a simple tool that can make these calculations for you. Create an Excel spreadsheet like this: In cell H2: the number of unknow n cards remaining in the deck, In cell H3: the number of outs remaining in the deck,
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In cell H4: the number of cards to draw , In cell H5: the number of outs you want to draw in those cards, In cell H6: the probability that this happens. Paste into this cell the following formula: =FACT(H2H4)*FACT(H3)*FACT(H2
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H3)*FACT(H4)/FACT(H2)/FACT(H3H5)/FACT(H2H3
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Of course you can use other cells in the spreadsheet to store the data, but
H4+H5)/FACT(H5)/FACT(H4H5)
make sure you adjust the formula accordingly. Now lets tackle the problems. 1) I have KK and my opponent has Ax, so there are 48 cards remaining in the deck (H2=48). Three of these are aces (H3=3), we w ill draw three cards (the flop, H4=3) and we want to know the chance that one ace appears (H5=1). In H6 the probability appears: 0.1717 or 17.17%. 2) 50 cards remain in the deck (H2=50), 11 are of that suit (H3=11), draw 5 cards (H4=5) and draw exactly three of that suit (H5=3). The chance is 5.77% 3) We´re getting the hang of it. H2=50, H3=6, H4=3 and H5=2. The chance is 3.37%. This is a pretty important number for those among you that call raises w ith stuff like suited connectors. At least 1 in 30 times the flop will make you happy (add to this the flops that give you straights/flushes or a good draw).
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Calculating poker probabilities with a s… 4) I have a small pair and my opponent raises ATC. He could have the same hand as me and the chance to flop a set would be zero! If he has one of that card, the chance to flop a set will go dow n significantly. How do w e handle this problem? The correct way is to assume that his hole cards are still in the deck. 48 cards remain in the deck, but there are 50 unknown cards and we have to fill in H2=50. The rest is easy: H3=2, H4=3, H5=1. The chance is 11.51%. 5) This is slightly different. We know the opponent has a big hand and all our outs remain in the deck. Whether he has AA/KK/QQ or AK doesn´t matter for the chance to flop our set. H2=48, H3=2, H4=3 and H5=1. The chance is 11.97%. The chance goes up a little, due to your knowledge of your opponents play. 6) This one is pretty hard, but doable with a little logic. The turn has to give us a straight draw , so it has to be a 8, 9, K or A. That is 16 outs. Calculate the chance with H2=47, H3=16, H4=1, H5=1. The chance is 34.04%. You could have calculated this yourself w ithout the spreadsheet (=16/47). OK, so now w e have a straight draw , what do we do with the river? Well, we have an open ender (8 outs) if the turn is a 9 or K or a gutshot (4 outs) if the turn is an 8 or A. On average we have 6 outs. H2=46, H3=6, H4=1, H5=1. The probability is 13.04% (or 6/46). Combine the turn and river probabilities: multiply 16/47 with 6/46 and you have the answer for your backdoor straight draw: 4.44%. Better than you think, hey? These w ere a couple of examples that show the potency of the spreadsheet, combined with your ability of using it correctly. I hope the tool will prove useful for your postbeadbeat analysis!
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This should be a welcome help for many players who are in the process of mastering this game. Well written, concise stuff. Rating: by KingCur on November 27, 2007 (login to reply)
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This looks really cool. First off, I think the easiest thing to get going is to download the example spreadsheet. I'll assume you know very little about Excel. This is very great. excel development Rating: by ExcelT8 on July 11, 2010 (login to reply)
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Somethings wrong here, I tried to put in the following which would replicate having a four flush by the flop and catching the 5 card flush on either the turn OR the river of which the sum/formula is: Turn Number of unseen cards = (47) minus number of outs = (9) which totals to (38) then do 38/47 to = 0.808 or (80.8%) River Then the Number of unseen cards = (46) minus number of outs = ( which totals to (37) then do 37/46 to = 0.804 or (80.4%)
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Calculating poker probabilities with a s…
(80.4%) Final Equation Then Times 0.808 x 0.804 to equal = 0.649 or (64.9%) Chance of NOT hitting your flush meaning a 35.1% Chance of hitting your flush (There or there abouts) on either the turn OR the river. However your formula in a spreadsheet shows the following..... Unknown Cards  47 No. of Outs  9 Cards to Draw  2 Outs Needed  1 Answer  31.64% I tried to work it out but cant, any ideas whats wrong here??? As it shows 31.64% instead of 35.1% Rating: by martynardelli on September 23, 2010 (login to reply)
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marty, your calculation resulting in 35.1% includes those times when you hit your flush card on both the turn and river, whereas the spreadsheet calculation requires you must only hit one of your flush cards. Rating: by yekulrd on February 5, 2011 (login to reply)
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