Improve Fast in Go

Table Of Contents Introduction Chapter 1 - The Role Of Fighting In Go Chapter 2 - Important Stones Chapter 3 - Strong/Weak Stones Chapter 4 - Peeps And Cuts Chapter 5 - Sector Lines, Enclosure & Connectivity Chapter 6 - S.W.O.T. Analysis Chapter 7 - A Sampling Of Major Fighting Scenarios Epilogue Glossary Of Japanese Go Term

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Improve Fast In Go

© Milton N. Bradley 2008, 2010

Introduction

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About This Book​s On-Line Publication The on line publication of this book provides two quite extraordinary assets: - It​s FREE. - It​s perfectable! A printed book is fixed in form and content, and remains essentially immutable from the moment of its publication. So except for the inclusion of a separate list of errata or the subsequent issue of a second edition, any errors of omission or commission it contains remain unchanged forever. In sharp contrast, whatever flaws this on line publication possesses can be readily corrected, if only you, the reader, are kind enough to communicate your perceptions to me. If anything substantive has been omitted, it can be added. If anything is unworthy of inclusion, it can be excised. If I got anything wrong, including typos and diagrammatic and/or commentary errors, it can be corrected. If more or better examples are needed, they can be provided. And if anything is insufficiently clear, it can be clarified. All that​s necessary to achieve a ​perfect​ presentation is for the reader to provide me with the appropriate positive feedback. Just click the link below or at the end of any chapter, and send me an email detailing the problems you perceive, and - this is most important - specifics of exactly what you 5

suggest as their correction. This is not quite like Wikipedia, where the reader can directly modify the presentation, but it​s close. In order for this process to be successful, when you provide your feedback it​s essential that you include your rating (AGA or other), so that I can properly evaluate the perspective from which your caveat has originated. Obviously, if a high Dan tells me that I​ve got something wrong it will carry more weight than if a double digit Kyu player makes the same claim, but all positive comments will be treated with the respect they deserve. Finally, if you like the book, and especially if you​re in its target audience and agree that it has significantly improved your understanding (and rating!), I​d much appreciate your communicating that to me. It​s really the only thing that will make the vast amount of time and effort that went into its creation worthwhile. Introduction This book is not a Go primer nor even a second book, so it presumes that the reader intending to profit from it already has a firm grasp (if perhaps not yet complete mastery) of the basic rules of Go, as well as the fundamentals of life and death, Joseki, and Fuseki. When deciding whether or not it will be worth the time and effort necessary to profit from a Go tutorial 6

such as this, the most relevant criterion employed will almost necessarily be the amount and rapidity of improvement in your rating that you can expect in return. Although it​s manifestly impossible to correctly assess this without an in-depth appraisal of your individual intellect and countless other factors, some highly relevant insight into this matter can nevertheless be gained from considering the author​s own experience. As originally conceived, this book​s objective was to provide players from double digit to perhaps 5 Kyu with crucial insights into the key issues of deciding what, where, and why to play next. But as a result of my own experience, I​ve just come to realize that the range of players who can find in it the insights that can and will lead to significant improvement in their Go skill (and rating) extends at least to 1D AGA! How and why I​ve come to that startling conclusion is related next. With the possible rare exception of a few geniuses at the very top of the Go professional ratings, every Go player throughout its extensive history has eventually reached a skill and rating plateau which they never thereafter exceed. For many players, intermediate plateaus also often hold sway for a number of months or even years, but ultimately a final, highest level is reached and then continues until age induced decline takes over, if the player is fortunate enough to live that long. As I​ve observed during the 60 years of my own Go playing 7

experience, depending on the player these final plateaus range all the way from high double digit Kyu for the least apt (most of whom drop out in frustration), to high ranked 9P. But the one seemingly invariant factor characterizing them all is that once a certain amount of time has elapsed (typically 10 years or more), or age has been reached (typically 60-65), the player​s then operative plateau is final, and is never thereafter transcended! But what has just happened in my own Go playing life violates both of those seemingly impenetrable time barriers! I​m now 83, suffering from the incurable, invariably fatal Acute Amyloid Leukemia, and have been at a 1D AGA plateau for over 20 years. But despite that, my latest results definitively demonstrate that I​m now no weaker than 3D AGA, and most probably 4D, and, perhaps most startling of all, am unquestionably still improving! When I watch games on IGS between players rated 4D* (= 7D AGA) and above, I now quickly and easily find their exact moves a vast majority of the time! The key that the reader should be aware of is that this ability didn​t develop immediately after I had organized the key ideas and translated that into this book, but only reached its current state of fruition after another couple of years of integration of those ideas into my thinking. But as noted, I​m quite old by any standard and consequently undoubtedly more fixed in my thinking than the average player who 8

will read this book, so I have every confidence that those of you who put forth the requisite effort can, as I​ve done, reap rewards of Go rating beyond your fondest expectations! Now about the book itself. At its most fundamental level, playing Go is heavily dependent upon pattern recognition. As a result, an essential factor in progressing from beginner to intermediate and beyond is perfecting knowledge of the key recurrent local patterns, especially as embodied in Tesuji and Joseki. This knowledge constitutes the tactical bedrock upon which Go skill is built, but even its mastery is insufficient to make one a strong player! What​s missing is the ability to visualize and then act appropriately on those patterns in actual global board contexts, and that latter capability can only be realized in the service of key strategic ideas like those developed in this book. Preeminent among these key ideas is that fighting is the heart and soul of Go, to the degree that the final outcome of a high proportion of well played games is decided directly or indirectly by big battles. For that reason, mastering the art of fighting is one of the most productive of the essential steps in becoming a strong player. There are two quite different but equally essential aspects of fighting: 9

1. Deciding where, when and why it​s appropriate to fight. 2. Knowing how to fight. This book focuses on the former. Its basic premise is that a fully developed skill arsenal is unquestionably essential to becoming a strong player, but is insufficient because the full value of that skill can only be realized in the service of deep strategic understanding. It​s much like driving a car technical driving skill is essential for maneuvering safely and efficiently in traffic, but useless for getting where you want to go without an adequate road map! So the focus in this book is on how to identify which fights are necessary and/or productive and which should be avoided, rather than on how to conduct a fight once it​s begun. It attempts to do what many believe impossible - to explain this essential aspect of Go to beginners and intermediates so clearly and concisely that they will thereafter think much like strong players, even if they​re still far from being able to consistently translate that understanding into fully accurate and incisive play. Of necessity, we do discuss the details of some fights, because it can be very helpful to the reader to see the sort of complications that may result from the implementation of the ideas being studied. But even in those cases, our emphasis is on identifying plausible moves which fulfill the position​s overall 10

strategic objectives, rather than on finding those that are absolutely best. Finally, it must be understood that although this book provides a valuable road map for Go fighting in the form of a set of simple but important strategic ideas which are generally (but certainly not always) applicable, those protocols must be viewed as neither absolute prescriptions that must be slavishly followed, nor unerring guides to the absolutely best moves! Despite that important caveat, the book​s premise is that mere exposure to these key ideas will provide the greatest increase in any beginner/intermediate​s playing strength for the least effort expended! But, as desirable as that is, it​s only a good first step. Completing the transformation into a strong player will also take much study and practice of the detailed techniques of Go, as well as lots of over-the-board playing experience - all things well beyond our present purposes, and which are therefore left for your independent effort. The Use Of Ratings In This Book Except as otherwise noted, all of the illustrations in this book were taken from actual Dan level games played on leading on-line Go servers, and that means that the stated ranks are all really equivalent to 1- 3 stones stronger on the AGA scale! So although 5D may not seem all that impressive, when you realize 11

that it​s really equivalent to from 6D-8D AGA and therefore among its highest rated players, that player​s judgment about where to play becomes much easier to accept as valid. Acknowledgement I hereby pay my respects and acknowledge my debt to all of the many wonderful Go teachers and authors who have preceded me. Thanks are hereby offered to the vetters of this book​s original incarnation, Ray Kukol 4D, Lisa Maloney, Michael Quintero, Dale Blann, Masaaki Hamaguchi, and my son Randy, who were kind enough to review the manuscript, find errors, and offer some insights into places in which it needed clarification and/or modification. Thanks are also offered to Joanne Phipps 3D and Louis Abronson 5D, who vetted the revised manuscript, found some significant errors, and made key suggestions that helped me reedit it yet again. But in the end, because I​m a Beethoven and not a Mozart, I once more rethought and completely recast everything, so that although much of the book​s content is essentially the same as in the earlier versions, the presentation is now completely different. As a consequence, responsibility for what appears here, including any errors, remains uniquely mine . Finally, special thanks are offered to Jakob Meulengracht for his invaluable assistance in preparing the HTML coding of the manuscript that 12

allowed its on line publication. Milt Bradley, July 2008

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Improve Fast In Go

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© Milton N. Bradley 2008

Chapter 1 - The Role Of Fighting In Go

The financial investment model is an appropriate, if rather grossly simplified, way to grasp the essence of a Go game. Think of the stones you play as your investment capital, and the resulting territory you acquire as the return on that investment. It​s well established that a prudent financial strategy invariably requires a judicious balance between long and short term investments. It​s much the same in a Go game, where the balance that must be struck is between profit (short term) and such relative intangibles as thickness and attack (long term). In this balancing process, it​s often feasible to cede even a large temporary lead in solid profit to the opponent, in the expectation of later recouping. But whatever the chosen strategic mix in any given game, at game​s end the sole determinant of victory or defeat is the amount of empty board space controlled by each side. Capturing more stones than the opponent, or even capturing any opposing stones at all, is essentially irrelevant except as it contributes toward that goal. Given that fact, it might seem that victory should be achievable through the simple walling off of areas by both sides. But that​s not true! Even if that primitive strategy (pejoratively termed ​ground gaining Go​) could be successfully followed initially, the finite size of the Go board coupled with the fact that both sides are seeking to gain control of the same limited amount of space means that conflict is ultimately inevitable. And that​s especially true when one side or the other realizes it has fallen behind in acquiring territory and can only recoup by ​stealing​ a portion of what the opponent has claimed. So in well played Go games the confrontations usually begin early, and then are almost invariably crucial in determining the final outcome. 15

As a result, perhaps the major key to making appropriate strategic decisions lies in understanding that:

Go Is A Fighting Game

This should distinctly not be interpreted as implying that fighting is all there is to Go, because nothing could be further from the truth. Rather, fighting is perhaps best understood as the essence around which all of the many subtleties and complexities of Go tactics and strategy coalesce to produce the wonderful game which has intrigued humanity for millennia. The Basic Principles Of Fighting

The Life Or Death Of Groups Is The Central Issue In Fighting

Although most high level Go games are decided as a result of fights, those fights are anything but random, mindless conflict for its own sake! Quite the contrary. Fights between competent opponents occur only because both sides are unavoidably competing for control of the limited assets of space, shape and connectivity available on the 361 intersection Go board.

Only Fights Involving Important Groups Are Likely To Be Productive

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How to identify important groups is the subject of Chapter 2.

Only Fights Against Weak Groups Are Likely To Be Successful

How to identify weak groups and determine when and why they are vulnerable is the subject of Chapters 3 and 4. When attacking vulnerable groups is most likely to be successful is the subject of Chapters 5 - 7. Rather

Gratuitous Fights For Their Own Sake Are Almost Always A Mistake

Fight Only In Pursuit Of Strategically Important Objectives And Only When And To The Extent Absolutely Necessary

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Diagram 1 In this game between a 5D and a 7D, the atari of B1 on the marked White stone has forced the connection of W2, with (small) advantage to Black because B1 not only separates White and is potentially useful, but also because W2 only adds insignificantly to White​s already thick formation. The key question now is how Black should best continue.

Diagram 2 The exchange of the atari of B1 for W2 on the left has created useful Aji for Black to exploit 18

at the proper moment, but continuing there immediately to support/utilize the 2 Black stones would only prematurely start a fight that would almost certainly be to Black​s detriment! As things stand, Black​s absolutely essential play is B3! This begins to sketch out a Black corner in the lower right while partially neutralizing the White thickness, and also prevents the excellent extension/kakari of W​a​, and leaves the decision regarding what to do with the 2 Black stones on the left for later. (In the actual game, the proper moment to support those stones never 19

arrived!)

Diagram 3 In this game between two 7 D​s, White has retained Sente, so it​s his choice as to how to proceed from this point forward. Invading the wide extension between B1 and B21 seems inviting. But is it really? And if it​s not, what would be better? And why?

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Diagram 4 This is the sort of position in which it​s tempting to start a fight by invading with W2! Although that might conceivably succeed, the 7D who played White in this game thought better of it. He instead opted for this calm development, which had the advantage of taking no unnecessary risks. Its detriment is that it yielded him only a minuscule overall plus. Caution! There is 21

sometimes no reasonable alternative to initiating a fight when you​ve fallen behind, and less aggressive play is unlikely to reverse the game​s losing trend! But other than in such exceptional circumstances, avoiding gratuitous and/or potentially dangerous fights is usually sound policy. How to Distinguish between vital fights and those that aren​t is one of the major subjects of this book, so, hopefully, that important distinction will be much 22

clearer after you​ve read it all.

Fighting Guidelines: In a fencing bout, every legal touch has the same value. So when the opponent thrusts, a fencer​s first response must be to parry! Only then does it become feasible to initiate an aggressive counter action. In a boxing match, every legal blow has the same point value to the judges, but more effective blows can not only steal the initiative from the opponent but can also serve to wear him down so that both his attack and defense become less effective. Equally important, they can also serve to instantly end the bout via a knockout! And it​s much the same in Go. A move by the opponent which intends to seize Sente by making a threat that you can​t afford to ignore may be defended against as expected, but it also may be ignored in favor of a threat of one​s own which is in fact more serious. In each case, deciding what​s appropriate strategically and then achieving their desires requires accurate positional appraisal followed by precise execution by both sides, so in the final analysis a player​s arsenal of tactical skills is the foundation upon which his strategy is both built and realized. The crucial factor in the conduct of any fight is the realization that each separate group of both White and Black stones must somehow form at least two separate and distinct eyes by the end of the game, to both remain alive and garner the territory that will count toward a win. So the more separate groups you can force your opponent to establish, the more ​free​ moves you gain with which to pursue your own objectives. This is generally true because most moves made by the opponent to secure his own eyes won​t also expand his space or attack your positions! Because it​s easy for a beginner or intermediate in a handicap game to be intimidated by White​s superior skill, it​s also important to remember that

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The White Stones Have No Special Powers, And Share The Same Need For Eyeshape, Space, and Connectivity As Black​s

So Black must carefully appraise and then seek to exploit any weaknesses in White​s positions, rather than reflexively playing purely defensively as though the White stones were somehow invulnerable! The following principles provide excellent guidance in most situations. Why they​re generally valid will become clearer when we discuss strong and weak stones in Chapter 3.

To Attack, Play Away. (Keep a discreet distance, inhibiting the opponent​s ability to expand and/or form eyes.)

The Nature Of Attack An attack uses threats against weak stones to create gains, either locally or elsewhere, which typically take the form of territory (profit), the creation of power/influence, or an attack on another group. Attacking plays will usually elicit a response, but won​t necessarily result in an immediate fight. Attacking scenarios are of almost transcendent importance in playing Go and among the most satisfying to implement, so it will be worth our while to briefly examine their structure and implications here, deferring fuller discussion for later. 24

In a 2008 article in the AGA e-journal, well known American Go teacher Jim Kerwin, 1P, said the following: ​The key to attacking is to start by choosing where and what you want to gain. You will find it difficult at first to see a possible gain and how to use attack to get it. The good news is that if you can​t see how to use the weak group to get what you want, you can afford to wait. The worst case is that the opponent will eventually spend a move to reinforce the group allowing you to play a profit move, so you​re guaranteed something.​ This is splendid advice, as might be expected from a Go professional, but I believe that it​s still amenable to modest refinement for the beginners/intermediates who are endeavoring to learn from this book. The relevant issue is the player​s meta-strategy for playing Go in any particular game. When engaged in competition in which winning and rating are the motivation, Kerwin​s conservative strategy of staying within the confines of the player​s current knowledge/skill base except in desperate circumstances is clearly appropriate. But in playing ​casual​ Go, especially when expanding your experience base is the dominant motivation, a far more adventurous and aggressive strategy will usually be more appropriate! Given that such ​casual​ games will almost necessarily constitute by far the majority of your early playing experience, rather than holding back unless you​re reasonably certain of success as Kerwin suggests, in those games your preferred strategy should be to assess as best you can, and then, if in your best judgment it seems at all feasible, attack! Then, especially if you later review what happened (or use a service like The Go Teaching Ladder to have a much stronger player point out your errors), by learning from your mistakes you can maximize your rate of progress.

To Defend, Play Close (Make contact as a method for creating eyeshape and/or sealing off eyespace.)

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Contact plays will almost invariably result in an immediate fight. In any event

Before You Play Defensively, Always Seek An Offensive Move That Also Satisfies Your Objectives

FIGHTING CONTINUES UNTIL BOTH SIDES ARE (at least temporarily) STABLE

This may mean that both sides are safe, that one side​s stones are either unequivocally dead or temporarily abandoned, or that both are still incompletely settled. In the latter cases, the fight will often resume later, when the appearance of other stones nearby makes it profitable for one side or the other. To see how these principles work in practice, let​s examine a situation that frequently arises in both even and handicap games.

Diagram 5 The ​Knight​s Move​ approach of W1 (or the symmetrical point on the upper side) is the most common way for White to begin operations against the Black 4-4 point stone.

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Because it​s an attack, it doesn​t make contact with the object of that attack, but instead stays a discreet distance away! When Black is in a position to respond aggressively, the one point squeeze play of B2 is the strongest counterattack, also playing at a discreet distance from its target, and inhibiting W1's ability to expand down the side to make a base there. Feasible but milder squeeze plays instead of B2 which may be globally preferable in some situations are ​a​ thru ​d​, while ​e​ is sometimes chosen when Black feels the top and/or center are more important than the left side. After B2, White has the choice of defending W1 immediately or playing elsewhere. (If he tenukis he will suffer a fairly serious local detriment if Black is first to play locally again, but even then W1 can​t be killed.) How each of White​s feasible responses to B2 can play out is shown next.

Diagram 6 In response to the pincer attack of B2, one common (but rather passive) continuation is for W3 to dive into the corner. After the Joseki sequence thru W11 (B​a​ in place of B10 is sometimes preferable), White is not only alive with profit in the corner, but is also unconfined. In return, W1 is at least temporarily abandoned 27

and Black has thickness. This dynamic ​equality​ is a fair allocation of assets for both sides for the moment, but not a fully adequate characterization of the situation. The important aspect of this position unaddressed by that assessment is that White​s profit of about 10 points in the corner is almost (but not quite) already assured, but Black​s thickness on the outside must still be sooner or later converted into an approximately equivalent gain either locally or elsewhere for this trade to be ultimately fair.

Diagram 7 ​Abandoning​ W1 as in Dia 6 isn​t always globally desirable, and in that case the one point center skip of W3 here is often a good alternative to entering the corner. After that, the calmest sequence is as shown, with White getting strong center influence in return for Black​s sketching out corner territory. (The contact play of B6 helps defend the corner territory in Sente by threatening to connect underneath to B2 by continuing at 7, thereby inducing W7 to prevent that.) After this, with the 3-3 point (​a​) in the corner and ​b​, ​c​, and ​d​ all still available for White if and when circumstances make them appropriate, and with the skirt at ​e​ also still open, the big corner territory is as yet far from securely Black​s!

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Diagram 8 It​s also feasible for White to switch W5 in Dia 7 to the ​shoulder hit​ on B2 shown here, with this common result. B14 prevents a White enclosure, and at least tentatively assures life for the B2-14 group. Then, depending on what​s going on elsewhere, White may play ​a​ immediately to assure his connectivity (the best way to do that), or tenuki and hope that he​ll be able to get back to consolidate his position here before Black can play to cut him apart. Instead of the aggressive squeeze play of B2 in Dia 5 - 8, Black might feel it preferable to play defensively, so let​s examine next just how differently that will play out.

Diagram 9 Especially when Black already has the marked stone or one near it in place, instead of squeezing, the attachment of B2 is feasible. As earlier noted, this is not an attack! A contact play like this B2 is actually a defensive move which is intended to 29

enable Black to both ​make shape​ and take some corner/side territory. Its main detriment is that it also induces White to make shape and territory as shown, thus simplifying the position while also reducing both side​s later options. (There are a number of other feasible Joseki variants beyond these few which give somewhat different results, but those details are outside our present interest and so will not be discussed here.)

Diagram 10 Relevant to this discussion is the ​bang against​ attachment of B2 here, which, as earlier noted and despite its appearance, is primarily an attack and not a defensive move! Since this is something that seems inconsistent and therefore may be confusing, understanding its rationale is important. The attachment of B2 is most appropriate when the triangled Black stone (or one at ​a​) is already in place on the upper side, and is even more effective when (as here) the marked left side star-point stone is also present (as is true in high handicap games). The aim of B2 is to make infeasible an 30

immediate White switch to the 3-3 point in the corner at ​b​, as in Dia 8. It does this because if W3 at ​b​to ​steal​ the corner territory, B4 at 3 would give Black excellent eyeshape while severely damaging W1. So most often W3 is considered necessary.

Then B4 works perfectly, in conjunction with the triangled upper side star point stone, toward building a large Black territory in the upper left corner and adjacent upper side. (Although as noted in Dia 7, that territory is still far from completely secure, especially with W​b​ still available.) After B4 White needs eyespace for his 2 stones, but the marked Black left side star point stone stands in the way of an ideal extension, leaving only the very short one point skip to W5 as really feasible. Next, B6 prevents a White slide to either ​c​ or ​d​ to expand his eyespace, after which W7 is necessary to create the beginnings of some eyespace and shape while fleeing toward the center. B8 is then often best, building Black​s strength and looking toward the lower side. What​s really important here is to recognize the fundamental difference between the almost entirely defensive attachment of B2 in Dia 9 and that of Dia 10, which is primarily (but not entirely) offensive. Once that critical difference is clearly understood, it should then be far easier for you to make the proper decisions and appropriate followup in similar situations that arise in your own games.

Whatever the situation

Don​t Act On 31

The First Plausible Move That Solves Your Major Problem.

Always Look Further For A Better Move, Especially One Which Also Accomplishes Other Desirable Goals.

Diagram 11 This is a fairly common type of position, in which the central area to the left of the Black stones is still quite open. In most cases, when the marked White stone probes his one point skip Black will want to maintain his connection, and the first step in finding the best way to do this is to identify the feasible alternatives. Please decide on your own candidates before looking at the following diagrams.

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Diagram 12 Black​s available connection options are marked from ​a​ to ​d​. But which is best? There is no one universally correct answer because the preferred option will depend upon other stones already in place (not shown here) or deemed likely to appear in subsequent play.

Diagram 13 The simplistic choice is the hard connection of B1. Although this is the only absolutely secure, unbreakable connection, it​s also the one that creates no shape at all while offering the fewest followup alternatives. Despite these detriments there are situations in which it​s the most desirable option, so it can​t simply be dismissed out of hand. But absent special circumstances that make the other options infeasible and/or Black​s ultra-solid thickness here particularly useful, this is usually the worst choice. So an alert Black will look further.

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Diagram 14 A slightly better alternative, which in certain circumstances may be preferable to the others, is the extension of B1 here. This maintains the connection because if W​a​, B​b​, and if then W​c​ cuts, the atari of B​d​answers. And if W​e​ then extends, B​f​ is a Geta that traps the two White cutting stones. But instead of pushing at ​a​, which obviously doesn​t work, if the position to the left is suitable an alert White might continue with something like W​d​, to induce B​c​, and then follow with something like W​f​, to leave the entire Black group ​floating​ without either eyes or shape.br> And that possibility is one of the reasons that this B1 as the way to maintain Black​s connection is not often best.

Diagram 15 A bit more stylish and versatile is B1 here. After this if W ​a​ pushes into the gap in the Black formation, depending on surrounding 34

B1 doesn​t reach far enough out from his wall.

Diagram 16 So after further reflection, the one point skip of B1 here is revealed as the move that best accomplishes all of Black​s objectives! After this, if White makes the shape-killing placement at ​a​, B ​b​ connects efficiently because W​a​ is now almost trapped. After that, playing immediately (as at ​c​) to rescue W​a​ would only help Black. Not only would he then have a larger White group to attack, but (assuming the relatively open center we noted at the outset) that newly formed White group will probably not seriously threaten Black because those White stones will almost certainly be weaker than the Blacks they are supposedly attacking. If after B1, instead of W​a​ White pushes at ​b​, with B​a​ the position reverts to Dia 15 after W​a​, B​d​ there. 35

certainly yielding Black one eye.

Enclosure In the big fights that decide the majority of well played games it​s important that each side retain as many options as possible, and key among those options is finding support for both attack and defense from nearby friendly stones. Groups which are enclosed not only can​t simply run away from an attack, but are also unable to connect with other friendly stones which might offer help, either to win the fight outright or to at least survive it. It​s also true that if one side is enclosed it​s almost necessarily disconnected from other friendly groups, and in many (but not all) cases that also means that the opponent is connected. The result is that when looking at the final position of games which are close enough to count, it will much more often than not be true that the side which has the fewest number of groups (= is best connected!) is the winner! Perhaps most important of all is the fact that

Only Enclosed Groups Can Be Killed

Therefore

To The Extent Feasible

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To The Extent Feasible Avoid Becoming Enclosed

Becoming enclosed almost necessarily imposes a burden that is not infrequently sufficient to swing the balance of the entire game in the opponent​s favor. The converse perspective is equally valid, so under most circumstances enclosing the opponent is an excellent strategy. For that reason, understanding the principles governing enclosure constitute a major factor in becoming a strong player.

To Counter An Enclosure Threat "If In Doubt, Run Out"

The rationale is simple. Enclosed stones: - Have no interface with or influence on subsequent play elsewhere on the board. - Must be able to make 2 eyes, or die. Caution! As the board fills up throughout the game, every group will ultimately become enclosed! So the guidelines we discuss here apply primarily during the Fuseki and early middle game. It​s also true that all such ​rules​ of behavior represent simplifications of often quite complex situations, but they are nevertheless quite valuable because in surprisingly many cases they also provide the clues that can allow even beginning players to find excellent moves they might otherwise miss.

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high handicap games, this is a fairly common position, in which White has made a double kakari against a star point stone. In the absence of special circumstances Black should without fail play to prevent White​s enclosure! For this purpose, B1 as shown is usually best, but sometimes the attachment at either ​a​ or ​b​ is preferable. Dia 18 If Black doesn​t respond to the double attack and allows White to play the marked enclosing move on his key point before answering, he can still (just barely) achieve life in gote as shown, but with even a slight 38

shown, but with even a slight inaccuracy he will almost surely die! And even if he does live, White​s advantage is considerable. So, on balance, Black would be well advised not to allow himself to be forced into this kind of situation!

The principle of searching beyond the obvious for the best move stated earlier generally applies, but it​s especially relevant in the enclosure context, where the sense of relief that almost necessarily accompanies a successful escape may readily blind you to the fact that a superior global result might have been obtained if only you​d looked further for a better move. Here​s a fairly ​typical​ situation which beautifully illustrates this scenario.

Dia 19 In this game between two 5 D​s, the 39

enclosed, with no sure eyes yet! (Although one can be easily made.) So if they don​t get out immediately they will almost certainly be in big trouble, possibly even resulting in a loss sufficient to cost White the game! So what​s the best way for White to break out?

Diagram 20 Beginning with the atari of W1 and then continuing 40

atari of W1 and then continuing with the forcing plays thru W9 succeeds in allowing White to escape, and in some situations would be the best way to play, but not here! The problem with it is that Black becomes too strong on both sides. So finding a better way to get out is highly desirable.

Diagram 21 Beginning with the atari on the other side is clearly better, because now Black has only been strengthened on the left, but it​s still inferior! Although many players might be satisfied with this, the 5D who played White in this game looked further, and found something better! Do you see it? Try to find it for yourself before looking at the next diagram.

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Diagram 22 With the stylish ​dog​s neck​ extension of W1 here, White not only gets out as smoothly as before, but now is one step ahead in his race into the open center - a major difference in enabling a later connection to friendly stones or forming eyes. (W1 works because ​a​ and ​b​ are miai for it to remain connected to his group below!) Perhaps equally important, playing this way doesn​t induce Black to strengthen himself on either side! White escapes in each case, but the seemingly small difference between Dia 22 and either Dia 20 or Dia 21 can easily change the balance between victory and defeat in a close game!

Fighting Against Unenclosed Groups

Because Only Enclosed Groups Can Be killed, 42

There​s Little Value In Playing ​Inside​ Moves Against An Unenclosed Group

It​s Usually Better To Play Outside Moves, And Force Your Opponent To Make Eyes And ​Live Small​

Caution! This principle is not absolute! There are circumstances in which the global position makes it more advisable to strike first at the opponent​s key shape point(s) to prevent an easy two eyes, and then profitably harass the fleeing group as it struggles to either connect or secure its eyes in the center. The following shows a situation in which attacking an unenclosed group from the inside was counterproductive.

Diagram 23 This is the position a few moves after what we will 43

discuss later as Dia 7, Chapter 2, with Black​s attention focused on the White group in the lower right center. This White group is not yet enclosed, so it​s in no immediate danger of dying no matter what happens next. But Black evidently reasoned that if he could prevent its ability to easily make two eyes that would both force it to run and make it vulnerable to later profitable harassment. 44

So....

Diagram 24 B1 invaded to occupy the key shape point of the White formation, hoping to either cut it apart or prevent its making eyes. Allowing B2 next would enable B1 to connect out to the Black corner stones, shattering the White group​s viability and forcing it to run 45

into the center eyeless. W2 was the best way to prevent that. Then B3 aimed at either connecting B1 to the left or allowing it to escape.

But White neatly avoided that by extending with the simple but effective W4, assuring the capture of B1 and creating one eye, with good prospects for another and/or easy escape into the center. So the result of this premature invasion by B1 was not only a tactical failure but also an important strategic mistake, because it made the White group almost invulnerable!

Diagram 25 Instead of the invasion of B1 in Dia 24, Black should 46

simply have played on the outside like this, expanding and strengthening his own formation and aiming to seal White in, while biding his time to when an eyekilling sacrifice attack at the point of ​a​ might have a reasonable chance of success.

Fighting Against Large Groups

DIRECT THREATS TO KILL LARGE GROUPS ARE RARELY SUCCESSFUL

Because of the need for efficiency, the enclosure of a large group will often be more or less incomplete. So as the battle progresses and the group 47

continues to grow, those imperfections will typically provide a number of opportunities either to break out directly or to make eyes in place by capturing some of the surrounding attackers. Consequently

THE BEST PLAN USUALLY IS TO USE SUCH THREATS INDIRECTLY, AS THE MEANS OF ACHIEVING OTHER IMPORTANT OBJECTIVES

Here​s a ​typical​ example.

Diagram 26 In this game between a 7D and 6D, Black has secured the upper right corner and a small life on the lower right side. In return, 48

White has secured the lower right corner, as well as eyespace on the upper right edge for his large incompletely settled but not yet enclosed group there. But it​s Black​s turn, and although there​s little chance that he can kill this White group, if possible he​d like to keep the pressure on and gain profit elsewhere by attacking it. But how to do that?

Dia 27 49

Knight​s Move of B1 is the strongest way to proceed! Although White can then readily live on the edge if he acts immediately, allowing himself to become enclosed is bad strategy! So instead White tried to escape. Dia 28 this sequence, Black deliberately didn​t go all out to try to prevent White​s escape! Instead, he cleverly parlayed enclosure threats to build center strength (note the 50

almost captured W6 and 8), resulting in a global advantage that ultimately enabled him to win the game.

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© Milton N. Bradley 2008

Chapter 2 - Important Stones In Go

At each turn, the player​s primary task is to find the globally best move in the current position! In doing this, appropriate tradeoffs must be made between many diverse yet complementary factors (e.g. territory vs. influence, attack vs. defense, etc.) if a good result is to be achieved. But those essential factors are really useful only after you have successfully identified: - Which stones are globally important and which are not, and - Whether the important stones are strong or weak

Important Stones Require Attention/Action! Unimportant Stones May Often Be safely Ignored.

But what makes stones important? Safe stones which enclose territory are valuable, of course, but in the sense relevant to our focus on fighting: 52

Stones Are Important Only To The Extent That They Significantly Influence Further Play

There are seven (7) ways in which this importance is manifested. Stones are important if they significantly affect: 1. Contesting /controlling a key board area.

Diagram 1 In this early middle game between two 5D players, the only areas now fully controlled are A (Black) and B (White). They are somewhat different because although the Black ​A​ 53

group is alive and takes about 8 points of territory, it​s almost completely contained and is therefore unimportant to the future course of play! The White ​B​ stones are somewhat important because they impact the adjacent still unsettled marked Black stones. Although Black almost has control of the C and D areas, both are still open to a White invasion so these stones are at least moderately 54

important. The game​s main focus from this point on will center on the fact that each side has a large (marked), still unsettled group in the lower center. Black​s group has much better eyeshape, but White has more open space available, so there​s no real advantage on that score at the moment to either side.

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Diagram 2 In this early middle game between two 1D players, the marked weak White and Black one point skips in the lower center and the two not yet settled Black and White groups to their left are not only important, but will form the focus of future action until their respective fates are resolved.

2. Deciding which side wins or loses an important fight. 56

Diagram 3 In this game between a 9D and 7D, W80 completed the enclosure of the huge Black center group, thereby making it vulnerable to attack. With Sente, Black can easily secure his group, but unfortunately he missed the potential of the marked White stone and mistakenly believed that he was safe. So .... 57

Diagram 4 When B81 made the territorially large move on the right side, W82 92 shocked him by developing the marked White stone to cut the big Black center group apart, leaving it with portions already dead and the remainder with only one sure eye. So Black resigned. Instead of B81, if Black 58

had recognized that he was so vulnerable to being cut apart, the simple play at 83 would have trapped the marked White stone, not only creating a sure eye for Black but also essentially unifying all his local forces. After that, given his solid positions in all 4 corners, the game would have favored him.

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more customary B7 was a slightly atypical conclusion to the popular Joseki in the upper left corner. br> After this, if W6 at ​a​ to approach the upper right corner stone, B​b​ would happily squeeze while creating an ideal Black formation in the upper left. So if White wants to prevent Black from getting too much territory locally that way, he has little choice but to invade with W6 as shown.

Although this is a reasonable strategy for White, the price he must pay for it is allowing the blocking attachment of B7. This threatens to continue at 8 to make perfect shape for Black while seriously damaging W6, so it induces W8 to prevent that. But that gives Black the opportunity of making a large knight​s extension from the upper right corner stone with B9, which does double duty by also preventing White from creating his own base via the ideal 3 point skip third line extension to ​a​ from the 2-stone base of W6-8.

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Although this is a reasonable strategy for White, the price he must pay for it is allowing the blocking attachment of B7. This threatens to continue at 8 to make perfect shape for Black while seriously damaging W6, so it induces W8 to prevent that. But that gives Black the opportunity of making a large knight​s extension from the upper right corner stone with B9, which does double duty by also preventing White from creating his own base via the ideal 3 point skip third line extension to ​a​ from the 2-stone base of W6-8. The result as shown is a newly created W6-8 group that must flee baseless into the open center, and this is a large part of the reason that the somewhat ​unconventional​ B5 was such a strong move! Although W10 was the move actually chosen next to flee into the center, any of W ​c​, ​d​, ​e​ or ​f​ might in some circumstances be preferable alternatives, the choice between them depending on the location of other nearby stones of both colors, and White​s strategy. Here​s another excellent example.

Dia 7 When B1 sealed off some eyespace and territory in the corner, a Black followup at 2 would have created a powerful pon nuki eye shape, 61

That in turn allowed B5 to occupy White​s key shape point, making W6 necessary to provide the White stones on the right with their own base.

4. Expand/enclose your own territory/eyespace and/or reduce the opponent​s.

Dia 8 In this position, a few moves after that of Dia 7, whoever plays first locally has an enormous advantage! Dia 9 If it was White​s turn, W1 would provide eyespace, stabilize his stones, and also greatly diminish both the territorial and eyemaking potential of the 4 Black stones to its left. But it was actually Black​s turn, so ...

Diagram 10 B1 is an ideal multipurpose move because it: - Provides 62

of the 4 Black stones to its left. But it was actually Black​s turn, so ...

Diagram 10 B1 is an ideal multipurpose move because it: - Provides eyespace for the Black stones to its left - Prevents the excellent W​a​ (as just discussed). - Threatens to follow with B​c​, to seriously undercut (and attack) the still unsettled White 2-stone group to its right. B​b​ instead would be a mistake because it would induce W​c​. Then if B 2, White would have Sente for W​a​and that would be bad for Black (as already noted). 63

the corner at an appropriate later moment. 5. Ensure your own and/or prevent the opponent​s shape and/or connection.

Diagram 11 Both sides share the same key point here, although its implications are quite different for each. It would provide both shape and connectivity for Black if he can seize it, and make Black​s shape impossible if White can play there instead.

Diagram 12 If it​s Black​s turn, B1 would provide both ideal shape and connectivity, making Black very strong locally. But it was White​s turn, so 64

Diagram 12 If it​s Black​s turn, B1 would provide both ideal shape and connectivity, making Black very strong locally. But it was White​s turn, so ...

Diagram 13 After W1 on the key point destroys Black​s shape, it​s necessary for him to defend in order to assure the connection between the two marked stones and his main force, to prevent White from capturing them to make a big lower side territory. White​s threat is to cut via W​a​, B​b​, W​c​, or W​a​, B​c​, W​b​, so let​s see how Black should best play now to ensure his connection and prevent White​s big local gain.

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ensuring that Black stays confined. Then B3 makes a ​bamboo joint​, assuring a virtual connection, but in Gote. The problem with this for Black is that, if later B​a​, depending on what​s going on elsewhere on the board White may not feel constrained to answer at ​b​ in order to ensure Black​s confinement! So instead ...

Diagram 15 Best for Black is to begin with the Knight​s Move of B1 here, because now W2 is forced, else B2 connects out. Then after W4 and B5, this position is identical with Dia 14 except for the addition of B1 and W2. But that exchange favors Black, because B1 is a cutting stone which may later either cause White 66

Then after W4 and B5, this position is identical with Dia 14 except for the addition of B1 and W2. But that exchange favors Black, because B1 is a cutting stone which may later either cause White problems or force him to expend resources to ensure its capture, while W2 merely adds an insignificant amount of extra strength to an already very solid White formation! The difference between Dia 14 and 15 may be small and subtle, but it​s the kind of thing that not only wins close games, but also distinguishes really strong players from ordinary ones!

6. Keep your own stones strong and/or the opponent​s weak.

Diagram 16 At the moment, 67

opponent​s. So this is a key point for both sides which takes priority, and must not be missed!

7. The group contains too many stones or occupies too vital a position to afford to give up. The basic principle to be followed is:

Urgent Moves Before Big Moves

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and/or connectivity of your own important weak groups (or attack the opponent​s) before even considering making moves with ​mere​ territorial implications, almost no matter how large! This is a principle that strong players invariably follow almost instinctively, but which weaker ones often have yet to learn.

Diagram 17 In this game between two mid-single digit Kyu players, when B1 was played White should have answered with W​a​ to secure some eyespace as well as his center connection for his 4 stones at the top. Instead, he foolishly ignored the safety of this weak group to play the territorially big W2 on the right 69

the right side.

Diagram 18 After the mistaken W2, B3-7 severely punished White​s failure to secure his center connection by cutting his formation apart and winning 5 stones with enormous profit, forcing White​s resignation only a few moves later.

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The Relative Strength And Importance Of Stones Constantly Changes, And Therefore Must Be Reappraised Before Every Move!

To better understand the meaning and implementation of this important concept, let​s look at an example from an early middle game position contested between two 5D players.

Diagram 19 As things stand now, the marked 3 stone White wall seems not only strong (it has 6 liberties and a large adjacent open area), but it​s also unquestionably considered very important by both players because it sketches out the 71

sketches out the beginnings of a huge White moyo on the lower side, in conjunction with the two Whites on the right. But watch how that appraisal changes in what follows, as both sides evaluated the evolving dynamics as they continued from this position.

Diagram 20 Black concluded that, despite appearances, the 3 marked White stones were vulnerable, so he attacked very aggressively with B1 to prevent them from readily making a base and too much 72

on the lower edge. W2 countersqueezed B1, because at the moment that lone Black stone is weaker than the 3 stone White group! His objective was to prevent Black​s easily making a base for that lone stone, while beginning to sketch out a substantial White territory between W2 and the lower right corner stones.

Then, after the brief sequence of B3 thru B7 that followed, White apparently realized that the influence the 3 stone wall had formerly been providing had essentially ceased to exist, with the result that his evaluation of those 3 stones had suddenly changed, not just from an important valuable asset to one that was relatively unimportant, but to an actual potential detriment! So White concluded that running out to save those 3 stones in the current global position would be counterproductive. Instead, it would be better to change strategy, and rather than trying to save those 3 stones to use them as sacrifices in order to help consolidate as much of his lower right territory as possible! So ...

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Diagram 21 The result: The formerly important 3 White stones have become Black prisoners, but in return White has consolidated about 30 points of territory in the lower right corner!

The key idea to grasp is that White didn​t view his 3-stone wall as a fixed asset, but rather as just another potential bargaining chip, which he was prepared to trade in at any time if sufficient compensation was available to make that transaction profitable for him. If you proceed with that kind of flexible attitude, as your skills advance with experience you won​t be confronted with the need to change your mental perspective in order to realize the rating improvement that should rightly be your due! Now let​s try a few problems to see how well you not only understand these concepts, but can recognize them as they occur in real game situations.

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© Milton N. Bradley 2008

Chapter 3 - Strong/Weak Stones

Strong Stones Are An Advantage

Strong stones require little or no defense, so they allow you to attack or play aggressively.

Weak Stones Are A Disadvantage

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Weak stones require defense, so they also require more cautious play. In many real game situations, beginning or intermediate players may find it quite difficult to correctly determine, in advance of its being played through to a conclusion, whether a fully or only partially enclosed group is going to end up alive (= very strong) or dead (= maximally weak)! That in turn means that the assessment of such a group​s viability upon which the player will have to base his strategy will often be more of a ​guesstimate​ than a fully reasoned and reliable judgment. The only long term solution to this problem is to develop your assessment ability via the study of Tesuji and Joseki, solving many, many life-and-death problems, and watching and/or playing a lot against the strongest players you can find. Since, as earlier noted, all of that is part of the ​standard​ protocol for progressing in Go, it will not be further discussed in this book. Instead, our focus will be on identifying the factors that determine the strength or weakness of stones.

Strength of stones comes in two disparate incarnations: - Intrinsic Strength tends to remain largely invariant 77

as the position changes. - Relative Strength is always influenced by and is frequently extremely sensitive to even small changes in the proximity and configuration of nearby stones, so it must be continuously and carefully reevaluated move-bymove.

A. Characteristics of Intrinsically Strong Stones: 1. Already Have 2 Eyes, or can make them despite any opponent attack. (Very Strong)

Diagram 1Although the White corner stones are almost completely enclosed, they​re safe and strong because there is no way that Black can directly prevent them from making two eyes! The problem with White​s strength here is that, except for the territory enclosed it​s essentially wasted, because these stones are almost completely cut off from any interaction with the remainder of the board. (So in the sense of the last chapter, these stones are unimportant!)

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2. Have Good Eyeshape. (Strong)

Diagram 2When W2 is distantly squeezed by B3, making contact via W4 on the 3-3 point begins several popular Joseki variants. In this variant, after the W8, B9 exchange White​s shape is good and he may safely play elsewhere, because either W​a​ or ​b​ will assure his two eyes!

3. Enclose Sufficient Space For Eye Formation, Even Under Attack. (Strong)

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and configured well enough that it​s virtually as strong as if it already had eyeshape. As things stand, with even minimally correct play White is assured of being able to make 2 eyes despite any Black attack.

Diagram 4 The upper left corner of this Fuseki, contested in the 2006 North American Masters tournament between Ming Jiu Jiang 7P (Black) and Z Chen 6D (White), shows a not uncommon 80

type of local resolution, in which Black has created superb thickness (and a burgeoning left side moyo in conjunction with his B5-11 stones below), in return for White​s large profit in both the upper and lower left corners.

B. Characteristics of Relatively Strong Stones: 1. Are effectively connected to a very strong group. (Strong)

Diagram 5 At the moment, the virtual connection between White​s three marked stones and his two-eyed corner group is safe because if B​a​, W​b​, B​c​, W​d​ connects. But this connection is not absolutely 81

Diagram 5 At the moment, the virtual connection between White​s three marked stones and his two-eyed corner group is safe because if B​a​, W​b​, B​c​, W​d​ connects. But this connection is not absolutely secure, because, if played as a Ko threat that White can​t afford to answer, any of B​a​, ​b​, ​c​ or ​d​ will set up a cut. So this situation will have to be carefully watched by both sides until it​s definitively resolved.

2. Are in an open area, with no significant problems for the opponent to exploit. (Moderately strong)

Diagram 6 The marked White stones have the beginnings of both shape and 82

until the local situation is definitively resolved, White must be wary of their being later undercut, separated, and/or enclosed.

3. Any Significant Nearby Opposing Stones Are Weaker. (Moderately Strong)

Diagram 7 The Black stones both above and below the 3 Whites are relatively strong because they have reasonable eyemaking potential at the edge. The Whites are somewhat weaker because it​s somewhat harder to make eyes in the center. But the White stones are far from being completely without resources, because they aren​t anywhere near being enclosed. They have lots of room to run (to ​a​), or to make eyespace and shape if necessary, beginning with either ​b​, ​c​,​d​, ​e​, or ​f​as appropriate to the overall 83

But the White stones are far from being completely without resources, because they aren​t anywhere near being enclosed. They have lots of room to run (to ​a​), or to make eyespace and shape if necessary, beginning with either ​b​, ​c​,​d​, ​e​, or ​f​as appropriate to the overall global position. Because these stones are currently far from being settled, White must continue to monitor this situation very carefully, especially if B​a​ is played.

C. Characteristics of Weak Stones: Stones are weak because they exhibit serious deficiencies in one or more of three major areas: 1. Enclosing eyespace and/or making shape. 2. Connectivity. 3. Liberty count. The relative weakness of a group exhibiting one or more of these deficiencies is a function of the seriousness of the deficiencies, how many of them it exhibits, whether or not the group is enclosed, and whether or not it​s involved in a fight with an equivalently weak opposing 84

who can best defend his own.

Dia 8 The Black group lacks both eyespace and shape, so ... Dia 9 If White can play at 1, it would effectively rob Black of his base, leaving this key group floating and vulnerable! Because that would be disastrous for Black ... Dia 10 With Sente, the simplest and most solid way for Black to play is with B1 on that same key point, as shown here. 85

Dia 8 The Black group lacks both eyespace and shape, so ... Dia 9 If White can play at 1, it would effectively rob Black of his base, leaving this key group floating and vulnerable! Because that would be disastrous for Black ... Dia 10 With Sente, the simplest and most solid way for Black to play is with B1 on that same key point, as shown here. This not only provides Black with excellent shape, but does so without inducing White to strengthen the 2 stones below, which may now be potentially vulnerable. 2. Connectivity Deficiency Dia 11 The two point skip between the W2 and W4 is weak because it can easily be cut if Black 86

2. Connectivity Deficiency Dia 11 The two point skip between the W2 and W4 is weak because it can easily be cut if Black moves first! But it​s still joseki because doing so will not necessarily be profitable.

Dia 12 is the correct way to begin, and after the strong hane of W2 the drawbacks of B3 and W4 87

11 is Joseki!

3. Shortage Of Liberties ​The Five Liberty Criterion​ There is one simple but almost transcendentally important idea that governs fights between opposing groups:

WHEN OPPOSING STONES ARE IN CONTACT, AN UNENCLOSED UNIT IS STABLE, AND A PLAY ELSEWHERE IS FEASIBLE, IF THE UNIT HAS 5 OR MORE LIBERTIES.

This is generally an excellent guideline. But as with all other such criteria it has exceptions, so every position must be judged on its individual merits. Understanding this one simple idea can completely transform your ability to properly conduct many of the fights which arise. The beauty and power of this elegant criterion is that in 88

indication (but also not a proof) that it isn​t likely to die immediately or easily. Failure to obey this simple precept is a prime cause of many of the tactical debacles which surprise and plague beginning and intermediate players, as the following examples demonstrate.

Dia 13 This is the beginning of a ​the main line​ of a popular Joseki which frequently arises in both handicap and even games. When B2 squeezes W1, diving into the corner with W3 is one feasible 89

Joseki which frequently arises in both handicap and even games. When B2 squeezes W1, diving into the corner with W3 is one feasible (and common) way to proceed. After B4 and W5 the relevant question to our present interest is what Black should play next, and the 5Liberty Criterion provides the 90

the relevant question to our present interest is what Black should play next, and the 5Liberty Criterion provides the answer!

Dia 14 The extension of B6 is necessary, and when it​s correctly played as shown the 3 stone unit that it completes then has 5 liberties, and so is ​contact stable​ i.e. able to fight successfully. After W11, White has secured the corner territory plus egress along the right side. In return W1 is temporarily abandoned, while Black has 6 liberties, thickness, plus some territorial potential along the bottom. Now let​s see what bad things can happen if B6 is played differently.

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underneath of W7, followed by B8 and the two forced connections of W9 and B10. Then when W11 cuts, not only is B6 isolated, but (more important) the B4 -10 4-stone unit has only 3 liberties, and is in serious trouble!

Some feasible continuations are shown next, to give you some idea of just how badly Black can fare after this error.

Dia 16 this variation White gets an enormous corner by capturing the 5 B1420 stones, and B​a​to trap the 3 White stones doesn​t work! So B​b​ to escape is necessary. But this allows 92

is somewhat better for Black, although White is not only alive in the corner with the sequence B​a​, W​b​, B​c​, W​d​, but also has tremendous thickness in the center, while Black​s position is low on both sides.

There are also many other possible continuations after the cut of W11 in Dia 15, some better than those shown and some worse, but all are inferior for Black because of his violation of the 5-Liberty Criterion!

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There are also many other possible continuations after the cut of W11 in Dia 15, some better than those shown and some worse, but all are inferior for Black because of his violation of the 5-Liberty Criterion!

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© Milton N. Bradley 2008

Chapter 4 - Peeps and Cuts

Peeps and cuts are among the most common mechanisms by which weak stones arise. The primary differences between a peep and a cut are: - A peep​s value is often almost fully realized at the moment it succeeds in forcing the opponent​s connection, so that in many cases it may then profitably be (at least temporarily) ​abandoned​, to thereafter serve primarily as Aji. - Most cuts result in the formation of a new (often weak) group, which thereafter must be watched and defended. Although there is no single simplistic ​rule of thumb​ that can provide unerring guidance in deciding whether it​s best to cut or peep in any given position, in general, and 95

considering only the local situation:

DON​T PEEP IF A CUT SUCCEEDS

The problem confronting the double digit Kyu player is that (s)he​s typically uncertain of whether or not any given cut should succeed ! And considering that their own play is probably going to be less than perfect, in games in which the main objective is learning and improvement rather than just victory, the best strategy is to cut, and then learn from experience both how to correctly appraise that decision in advance and how to conduct the resulting fight once you​re embroiled in it.

Peeps

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Dia 3 Next, the peep of W13 is a Kikashi which is answered by the connection of B14, and this is followed by the similar W15 peep, B16 connection exchange. After this, the White corner has the miai of ​a​ and ​b​ for its life so it​s safe! And, in the absence of other nearby friendly stones to help, there is no reasonable attack that White can currently expect to successfully mount against Black​s solid enclosing wall. So local action often ends for the moment, leaving this situation as is until later events make it clear what each side needs to do next locally.

IMPORTANT! Just because a peep has been played (and answered), it distinctly does not imply that direct use must be made of that peep stone either immediately or ever! That may in fact occur, but at least as often a peep stone will be used indirectly to attain some other desirable goal (most often as a ladder breaker), or may even simply be temporarily ​abandoned​as Aji, for possible later use. With that in mind, let​s now look again at the situation of Dia 3 and appraise 97

responses. The first thing that we notice is that W13 is a completely isolated lone stone pressed against a solid Black position, and W15 is only a bit stronger because of its assist from W3. So both of these peep stones are, by definition, more or less weak! In response to these peeps, we see that Black has not only been forced to add two stones of his own, but also has been forced into a position which, although thick, not only has absolutely no shape, but is also already partially enclosed and inhibited from expanding readily. The overall assessment of the position in Dia 3 is therefore: - On balance, Black is clearly the stronger on the outside. - If White correctly views W13 and 15 as expendable potential sacrifices rather than as essential assets which must be maintained even at cost, for the moment White stands at least equal overall because of their presence. Whether this Joseki integrates better into the global strategy of one side or the other depends on the position on the remainder of the board and is an issue beyond our present focus, so it will not be discussed here.

Figure 1 In this early middle game between two 4D players, the key issue at the moment is the fight in the upper right 98

between two 4D players, the key issue at the moment is the fight in the upper right that has just begun between the enclosed and still unsettled B47-55 group and the enclosing W10-54 stones, which are still lacking shape and which therefore must be strengthened before he can safely attack Black. The solution to this dilemma that White conjured up was W56, peeping into the cutting point at ​a​ in Black​s lower right group. Because the B1- 43 stones would be 99

possibly disastrous) fight if cut off, that gave Black essentially no choice but to connect at ​a​. Having thus helped stabilize his own weak stones in Sente, White was then able to turn his attention back to the desired attack on the weak Black group in the upper right corner. So in this position the peep was the perfect move!

Cuts

The Typical Intention Of A Cut Is To Permanently Separate 100

and that almost invariably means that the cutting stone(s) will subsequently have to be reinforced/supported as required. A cut therefore typically initiates an important long term commitment.

Diagram 4 In this position from a game between a 9D and a 7D, the hane of B1 is a typical continuation of the Joseki in the corner. After the exchange of W2, B3, the necessary continuation thru B7 resulted in the creation of a weak Black group, in return for which White​s thickness has been effectively neutralized. Whether or not this turns out to have been good strategy by Black will depend on the followup by both sides.

Cuts Are Also Commonly Used To Make Shape Or To Facilitate Escape 101

Diagram 5 The cut of B8 followed by the forced sequence thru B12 sets up the capture of the marked White stone, resulting in White​s superb thickness in return for Black​s securing a large corner. Now let​s look at a position in a game between two 5 D​s in which making a judicious cut was the best way for a nearly trapped group to escape.

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Diagram 7 Cutting with W1 is the way to begin.! That makes W3, 5, 7, 9 and 11 all forcing moves, sacrificing 2 stones (W1 and 5), and then moving smoothly out with W13., and leaving behind the potential for an almost certain eye at the top. Beginning instead with 103

either W3 or W7 would allow either the connection of B1 or the extension of B10, and then White will have to flee eyeless! The outcome of a cut will frequently not only be decisive (as in these examples), but sometimes unpredictable, at least among players at less than a very high level, with the result that:

Making A Judicious Cut Is Often The Most Powerful Way To Play, And Sometimes The Only Possible Route To Victory

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Diagram 8 This is a not uncommon position, especially in high handicap games. At first glance, it appears that a White cut at ​a​ will be big, so that it​s necessary for Black to protect against it. But that​s only an illusion! On deeper analysis, it becomes apparent that a White cut at ​a​is actually infeasible!

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Diagram 11 After the atari of B10 forces the connection of W11 (with simply awful shape), the exchange of W13 for B14 is necessary to allow W15 to be an atari, which then forces B16 and gives White time for W17 to move out.

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Diagram 11 After the atari of B10 forces the connection of W11 (with simply awful shape), the exchange of W13 for B14 is necessary to allow W15 to be an atari, which then forces B16 and gives White time for W17 to move out. This diagram shows one continuation after the plausible diagonal move of W17. Unfortunately for White, it fails. But there are lots of chances for Black to go wrong in the resulting fight, so White may well live instead if Black plays weakly.

White​s problem is that even if he escapes after W15, the outside strength that Black will build up while attacking his ever growing weak group should doom his overall game prospects! On the other hand, if Black isn​t a particularly strong fighter, or if this sequence is used by White as ko Aji, it might still be very dangerous for Black. So on balance, unless White is a particularly strong fighter or believes that Black is an especially weak one, W1 at ​b​ in Dia 9 instead of the cut is objectively the better way for White to play. The problem is that in most 107

global situations that move won​t be Sente, so it must be timed correctly! Cuts And Ladders Cuts frequently give rise to a ladder. In those cases, wherever feasible the ​rule​ is

Capture Any Cutting Stone(s) As Soon As Possible

Diagram 12 When B1 ataris the marked White cutting stone, it sets up a ladder which favors Black because it runs into the Black stones in the lower right corner. Then W2 is a 108

B3, removing its dangerous Aji, perfecting his thickness, and thereby strengthening his now nearly complete moyo on the upper side. That this allows the excellent W4 is regrettable, but unavoidable.

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© Milton N. Bradley 2008

Chapter 5 - Sector Lines, Enclosure & Connectivity

In the previous chapters we discussed the principles upon which fighting must be based if it​s to be productive, and then spelled out how to identify the weak, important stones which should be the objects of any attack. In this chapter we begin the discussion of the criteria for deciding whether and when to initiate or avoid such attacks. Among the key operative themes in attack/defense are the closely related factors of enclosure and connectivity. These often become significant almost from the very earliest moves in the game as both sides maneuver for advantage, especially but not exclusively in the complex local (usually, but not exclusively corner) confrontations called Joseki. Another important issue, closely related to enclosure, is how to act against an opponent​s moyo. Moyo situations are typically quite complex, so without some simplifying concept to provide guidance the average player would 111

find it virtually impossible to accurately assess their often subtle interactions, and then make the correct decisions. The ingenious concept known as a Sector Line efficiently satisfies the critical need for guidance in both the attack/defense and moyo situations. Although the Sector Line concept has been applied implicitly for centuries in the Orient, the first explicit description of it of which I​m aware was in a mid 1970's article by Bruce Wilcox in the American Go Journal. But just what is a Sector Line?

A Sector Line Is An Imaginary Straight Line Extending Across An Open Board Area Joining Two Stones Of The Same Color, Or Extending From A Single Stone To The Board Edge.

The Sector Line​s conceptual rationale is that a solid wall of stones of that color could theoretically be constructed along that line. The fact that such a wall will almost never be realized in practice does not affect the Sector Line​s value as a guide to making the appropriate strategic and tactical 112

decisions.

Diagram 1 When B2 approaches W1, the squeeze play of W3 is particularly effective because ... Diagram 2 Now the lone Black stone is enclosed within the indicated White Sector Lines, as both players would visualize them.

When To Use Sector Lines - Sector Lines are primarily (but not exclusively) useful in dealing with weak stones, which might be captured if they can​t make eyes or escape. - Sector Lines are most often applicable in the Fuseki and early middle game, because it is usually only then that enough of the board is still vacant to make them really meaningful. The seriousness of the situation for the enclosed stones is primarily a function of: - The proximity of the nearest Sector Line. - The spacing between the stones forming that Sector Line. In each case closer is more serious, with the effect diminishing rapidly with increasing distance. No exact criteria exist for determining this spacing/distance effect, so each situation must be individually evaluated using the player​s best judgment. How Sector Lines Function - Sector Lines act as a kind of ​e arly warning system​ to indicate which 113

weak stones are in danger of becoming fully enclosed (and thus before the necessity of fighting a life-or-death battle for survival is thrust upon them). - Sector Lines provide only generally appropriate action guidelines, and do not specifically identify: - the preferred strategy to be followed - the best move itself, or even an explicit identification of the set of feasible alternatives from which the best move should be selected. Caution! Although the Sector Line concept is both simple and extremely valuable, it​s not always determinative! A Sector Line is not valid if it: - Intersects an opposing stone.

Diagram 3 When B1 is played, it breaks the outer Sector Line and negates it, so that Black is no longer enclosed!

A Sector Line is not valid if it: - Intersects an opposing Sector Line.

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Diagram 4 Here we see that W72 is within Black Sector Lines, but Black​s 6977 group is similarly enclosed by White Sector Lines which intersect Black​s. The two B49, 59 stones are within White Sector Lines, but are also an anchor point of the Black Sector Lines which enclose W72. The result is that none of these Sector Lines are valid for determining the appropriate action to be taken in this area. This sort of situation is quite common when the board becomes relatively 115

crowded, but in no way detracts from the general utility of the Sector Line concept.

Despite these very real limitations, the information Sector Lines provide is invaluable: A. To The Attacker, Sector Lines indicate whether or not to try to either: 1. Steal the opponent​s eyespace, and therefore drive his weak group out into the center. Or 2. Cut off flight into the center, and so force the weak group to attempt to live, either by making eyes in place or by capturing some of the attacking stones. B. To The Defender, Sector Lines indicate whether it​s best to either: 1. Run into the center to escape. 2. Try to connect to nearby friendly stones. 3. Make eyes. 4. Abandon the threatened stones (at least temporarily). 5. Counterattack. Caution! In any given position not all of these alternatives may be feasible, and choosing among those that are is a matter of the player​s judgment - a subject on which the Sector Lines themselves offer no direct help! Now let​s examine each of these Sector Line characteristics in detail. A. The Attacker​s Uses Of Sector Lines 1. Steal the opponent​s eyespace The sequence shown in the following diagrams occurred in a championship 116

game between two 9 Dan professionals, who were then among the top 10 players in the world. Yet the simple Sector Line concept explains and helps predict their moves to a remarkable degree!

Diagram 5 The position in the lower right corner begins with the same popular 3-4 point Joseki we saw earlier in Dia 1, in which White has just squeezed the lone Black stone from above, enclosing it within the indicated Sector Lines. These Sector Lines are close enough to constitute a fairly serious threat, so under normal circumstances Black would respond immediately. But because this 9P Black calculated that he can still readily live locally even if White is first to play again here, he instead chose to take Sente elsewhere. Although this was a rational global strategic decision, it gave White the opportunity to maximize his local advantage, as we see in the following diagrams.

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Diagram 6 W1 takes advantage of Black​s failure to defend by blocking him from the corner, making territory for White while making it harder for Black to secure eyespace locally. If White were to be allowed to continue at 2 next , that would not only make perfect shape for his own stones but would also make it extremely hard for the Black stone to make life locally. So with little choice, B2 occupies the key shape point himself, while cutting the White Sector Line! (A strong clue that this is a desirable move!) A (slightly lesser) problem with B2 is that it also makes his unit ​heavy​. W3 With this stylish Knight​s move extension, White increases the scope of his control of the corner by extending to the left, at the same time creating a new Sector line which once again encloses Black.(thereby maintaining Sente!)

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Diagram 7 In order to escape that enclosure it​s necessary to break White​s new Sector Line, and in this position the stylish diagonal extension of B4 is the best way to achieve this end. An alert reader will have noticed that B4 not only broke the White Sector Line but also established Black​s own Sector Line enclosing the lone White stone on the right side. But because the Black star point stone anchoring the upper end of that Sector Line is so far away, the lone White stone is only mildly affected by this. So for the moment White can afford to ignore that Black Sector Line, to continue his own attack. White​s natural response to B4 is to extend once again on the bottom with the one point skip of W5, increasing his local territory while also initiating the new Sector Line shown, to once again enclose the 3 Black stones.

Diagram 8 When B6 breaks the latest White Sector Line, there is no further White move that will simultaneously enclose the Black stones within a new White Sector Line while also extending White​s lower side territory. 119

That means that, for the moment at least, it is no longer profitable for White to continue playing on the lower side, because it would be Gote. On the other hand, we see that Black has now established his own Sector Line enclosing White​s lone right side stone. But because the upper anchor stone of this Black Sector Line is so distant, this lone White stone has more than ample maneuvering room to either make a base or escape into the center if attacked further. So the Sector Line analysis tells us that White can now afford to play elsewhere if his evaluation of the global board position indicates that would be more productive and that in fact is what the 9 Dan pro playing White in this game actually did!

2. Cut off flight into the center.

Diagram 9 This is a situation that frequently arises in both even and handicap games when Black fails to respond locally to the kakari of W1. 120

W3 (which is also often played at ​a​) encloses the Black corner stone within White Sector Lines as shown. But Black can still easily break out safely via a play at any of ​a​, ​b​, or ​c​. But if he doesn​t ...

Diagram 10 Most often, White​s strongest continuation is with W1 here, to solidly enclose Black within his Sector Lines. Black can then cut these Sector Lines, but can​t forcibly break out through them. Now let​s examine why allowing W1 is usually bad for Black.

Diagram 11 Black can still live in the corner, if he either knows this sequence by heart or can find his way through its tactical complications unaided. 121

But it​s dangerous because even a slight error in the sequence can easily result in the entire corner​s death! And even if Black lives, as here, White​s thickness usually gives him the better position globally. So playing this way is usually only advisable in special circumstances.

B. Defender​s Uses Of Sector Lines 1. Run into the center to escape.

Diagram 12 Black will usually be best advised to break out of the White Sector Line, most often by occupying the key point himself via B1 as shown, but sometimes by attaching at ​a​ or ​b​instead. After B1, W2 to seize the corner is by far the most frequent continuation, and then Black will usually (sooner or later) block at either ​c​ or ​d​, the choice depending on the global board position.

2. Try to connect to nearby friendly stones. 122

Diagram 13 In this game between an 8D and 6D, the marked Black stone is completely enclosed by White Sector Lines, so it appears that all of this large territory is about to become White​s. Living in place is difficult, but Black saw an opportunity to save this stone and neutralize much of White​s potential territory in the surrounding area if he could somehow manage to connect to the Black stones below. The next diagram shows how he went about doing it.

Diagram 14 With this clever sequence, Black managed to connect underneath in the lower left and achieve life, thus neutralizing most of this formerly large White area. In return, White captured a part of Black​s former lower edge group, to sharply increase his 123

own territory there. So Black​s gain was not without cost, and that​s a fairly common result of such confrontations. But on balance Black has profited a bit more, at least in part because he has emerged from this fight with Sente.

3. Make eyes.

Dia 15 In this game between two 7D players, when the marked Black stone was played it not only prevented White​s damaging push through-andcut, but also completed the enclosure of the White 7-stone group on the right edge. In the absence of special circumstances Black should without fail play to enclose White as shown! Dia 16 If White 124

circumstances Black should without fail play to enclose White as shown! Dia 16 If White now desires, his 7 stones on the right edge can live easily via W1, because then if B​a​, W​b​ completes his two eyes. And if Black doesn​t play at ​a​, it​s possible that at an appropriate later time White will be able to follow with the profitable endgame sequence of W​a​, B​c​, W​b​, B​d​.

The problem with making life by playing W1 is that Black will then happily continue with B2 to connect his corner stones out while seriously weakening the important (and presently both shapeless and eyeless) 5-stone ​L​ shaped White center unit immediately below! Because that was a prospect that was unacceptable to White, what he played instead of this W1 is shown next. 4. Abandon the threatened stones (at least temporarily).

Diagram 17 Because the result of Dia 16 was 125

center White string! This not only undercut the Black corner while preventing Black​s connection underneath, but also isolated the lone Black stone on the upper edge. But the severe price that White had to pay for this was B2, which more or less assures the death of the White right edge group, because now White needs both ​a​ and ​b​ to secure his two eyes, and he can only manage that by making two successive moves here. (Only possible if played as a Ko threat which Black can​t afford to answer.) So after B2 White had no choice but to tenuki, and hope that circumstances would later enable him to rescue this ​abandoned​ 7 stone group on the right edge.

Here​s another example, arising in a position that​s not uncommon in both handicap and even games:

Diagram 18 W4 is a probe intended to induce Black to fix the shape of his stones, so that White will then know how to best proceed locally at the appropriate later time. But as things stand it was too early in the game to be sure after B5 whether White will prefer to continue below, on the right, or on the 3-3 point in the corner, and W4 is enclosed within the indicated close and very threatening Black Sector Lines. So for the moment W4 was correctly ​abandoned​, as White played 126

indicated close and very threatening Black Sector Lines. So for the moment W4 was correctly ​abandoned​, as White played elsewhere! (From that, it might reasonably be argued that W4 was premature and should better have been deferred until a later time. But that's an issue well beyond our present focus.)

5. Counterattack.

Diagram 19 In this game between a 4D and a 3D, when W1 was played it seemed that White had visualized the indicated Sector Lines and the huge potential moyo that they enclose. But, 127

reasoning is actually doubly flawed! Not only are there are two Black Sector Lines running from the upper right to the lower left that intersect (and therefore neutralize) several of White​s, but, far more significant, Black can counter-attack by establishing his own far more threatening Sector Lines!

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Diagram 20 A strong Black response would have been as shown, not only enclosing the 4 weak White stones within the indicated close (and therefore very threatening) Sector Lines of his own, but also simultaneously assuring that Black can move into the White moyo before it can be consolidated. (Note that the 8 marked Whites at the top are tightly enclosed with only 3 liberties, and are therefore effectively captured!) Although the 129

followed isn​t entirely clear, it would have offered Black his best chance to win. When he failed to make this key play, White moved smoothly on to an easy victory!

Sector Lines As Moyo Invasion/Reduction Indicators - Playing anywhere inside the opponent​s Sector Lines will constitute an invasion. - A play on or just outside an opponent​s Sector Line will initiate a reduction. The key clues to deciding whether a reduction or invasion of an opposing moyo is the more likely to produce a satisfactory result are whether or not one or more of the following is true: - There is at least one long Sector Line operative. - One or more of the enclosing Sector Lines have significant gaps for possible ingress or egress by opposing stones, especially if - There are friendly stones fairly close outside those Sector Lines. If any of these conditions exist, an invasion will often be feasible because there will be opportunities to either connect out or to live within the moyo by placing key eyemaking stones which also threaten to connect out.

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usually be feasible. But it​s important to remember that there are no absolutes! Although the use of Sector Lines will go a long way toward enabling you to make the right decision, your ultimate success or failure in the fighting that ensues will still depend upon your ability to find and correctly time the right threats, and on your opponent​s ability to meet them. The following example shows the kind of dangerous tactical complications that frequently result from invasions, and why application of the indications provided by Sector Lines must always be made with great caution and forethought.

Diagram 21 This is a not uncommon situation in which Black has made a 5 point skip from a 4-stone wall based on the third line to form a small moyo, against which White will often feel compelled to act. But how? And where?

Diagram 22 The best try to make a live group within the Black space is to begin with this one point third line skip of W1 from the extension stone. In response, the diagonal extension of B2 131

with this one point third line skip of W1 from the extension stone. In response, the diagonal extension of B2 is the strongest way to prevent White​s escape to the outside, forcing him to try to live in place. This diagram shows one possible continuation, in which the invasion dies, and the next diagram shows another with the same result.

Diagram 23 The problem in this position with an invasion like this W1. is that there really isn​t room enough for the invaders to live if Black defends correctly! And if White does die, as here, that allows Black to consolidate a territory of over 30 points.

Diagram 24 This diagram shows that if Black errs, then White can escape, with a 132

disastrous reduction to what formerly seemed a large potential Black territory. But in at least partial compensation Black now is strong on both sides while the still eyeless Whites remain weak and vulnerable!

Diagram 25 From the foregoing, it​s likely that a prudent White won​t choose to invade but will instead opt for a reduction. For that purpose, W1 as shown here (just breaking the Black Sector Line) or ​a​ are usually the best moves, the choice between them depending upon the location of other nearby White and Black stones and the tactical considerations they engender.

Now let​s see how Sector Line principles were applied in a complex Moyo situation.

Diagram 26 In this position from a game between two 133

position from a game between two 5D players, White has created a large moyo in the upper center which Black must do something to reduce before it can be consolidated into a winning territory! As usual in such situations, the question to be answered is whether Black should invade the moyo and attempt to live within its confines, or try to reduce it by nibbling away at it from somewhere on its outer perimeter. This is the kind of situation in 134

the best clue as to which of these courses of action is likely to be the most productive. The major difficulty in this position is that a White Sector Line actually covers each of this moyo​s borders, so that only an invasion is really feasible if Black wants to prevent White from consolidating too much of this vast area. At the same time, we see that there are four places, marked ​A​, ​B​, ​C​, and ​D​ in which the White Sector Line is long enough and/or Black stones are near 135

enough to it to offer support to an invasion. Such potential places of ingress and/or egress are called ​doors​. Here, only doors A and B offer real potential for Black as things now stand.

A complication is that the White moyo is so large that only a player of professional strength seems likely to be able to even come close to accurately visualizing all of the invasion possibilities and their likely responses in advance. So ​mere mortals​, even fairly strong players like the 5D protagonists in this game, necessarily have to largely rely on their ​gut​ instinct plus confidence in their tactical skills to guide them in making difficult decisions like this. A detailed analysis of all of the complex tactics involved in the fighting that transpired next in this game is advanced material far beyond the scope of our interest in Sector Lines. So in the discussion of the actual game resolution provided below we will focus only on the main theme of the invasion.

Diagram 27 Because the main A and B doors capable 136

main A and B doors capable of exploitation are both on the left side of White​s moyo, it​s clear that Black​s best invasion point must be somewhere in that vicinity, but the choice of B81 as the starting point for Black​s invasion was a judgment call. W82 Rather than simply trying to limit Black​s incursion, White counterattacked by threatening to continue at 83, which would both restrict the expansion of Black​s upper left corner territory while making a sizeable territory of White​s own in that area in 137

with his stones below. In addition, it blocked Black​s access to door A. B83 Given that door B is still open. and because a White continuation at 83 would be too good to allow, Black felt that he had no choice but to block here himself to seal off his upper left territory. So White retained Sente. W84 similarly blocks off Black​s flight path to door B, leaving Black with the difficult problem of how to continue to achieve life. But now Black​s chances for success are somewhat 138

because he will be able to play a second stone inside White​s moyo before White can respond there. The details of the complex fighting that actually followed in this game are primarily tactical considerations that lie far beyond our focus on learning how to use Sector Lines, so are not presented here.

CAUTION!! As we​ve seen, with substantial amounts of maneuvering room available inside a substantial moyo, not only does the ultimate capture of any invaders become more uncertain, but the possibility of resulting external complications also increases exponentially. And even when the invaders are trapped and must be at least temporarily ​abandoned​(as in Dia 23), they typically still retain considerable Aji. This may either lead to their later rescue or to an advantage elsewhere for the invader, especially if a Ko fight erupts. So both sides will have to remain alert to this potential until the situation is finally completely resolved or the game ends.

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alert to this potential until the situation is finally completely resolved or the game ends. As earlier noted, detailed exploration of those complications is beyond our present interest, but you might find it productive to investigate them on your own. Now let​s look at a key portion of the Fuseki/early middle game between a 5D and 4D, to see how Sector Lines provide almost unerring guidance to strong (if not necessarily perfect!) moves.

Diagram 28 W1 encloses the Black lower right corner stone within White Sector Lines. Then, in the absence of any more urgent play elsewhere, it​s to Black​s advantage to respond by expanding/sealing off his eyespace to ensure his life. The defensive attachment of B2 is an excellent, time tested way for Black to achieve safety, and begins a popular Joseki.

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After the necessary connection of W5 Black remains enclosed, but his formation can now make eyes against any White attack! So it​s not strictly necessary (although often desirable!) to make a further submissive play like B​a​ immediately, because even if W​b​ is permitted the simple B​c​ gives Black an unassailable live shape. So after W5 Black can afford to tenuki with sente. But because White is now threatening to build a moyo on the lower side, it​s often globally incumbent on Black to try to prevent that from becoming a reality before it​s too solid to readily counter. Black​s problem is that, wherever he plays on the lower side now, his stone will already be within (somewhat distant) White Sector Lines! But because the end points of the upper Sector Line are so far apart, that​s not particularly dangerous. So with B6 Black makes a ​standard​ kakari against the White lower left corner star-point stone. Because that doesn​t enclose the White corner stone within Black Sector Lines, White need not defend but may instead counter-attack. He does that with maximum force via the squeeze play of W7, which does enclose B6 within close (and therefore very threatening) White Sector Lines, while also making a maximum strategic extension from his W3,5 wall on the right! This leaves Black with only two viable choices - either dive into the corner and at least temporarily ​abandon​ B6, or run out to break the White Sector Line. Given White​s thick position in the lower right, diving into the corner would concede White too much almost secure territory on the lower side, so Black has no real option but to break White​s Sector Line! His choice to do this is the ​standard​one point skip of B8, although in some global positions either ​d​ or ​e​ may be preferable. B8 is Sente because it encloses the White star-point stone within Black Sector Lines! So W9 (or ​f​) to break that Sector Line and sketch out some territory is also natural. Although this also establishes a new White Sector Line enclosing B6,8, in conjunction with W1 all the way across the board, once again its anchor points are so far apart that it has almost no effect. The result is that Black is free to take sente with the strong ​shoulder hit​ on W7 of B10, to once again establish close (and therefore very threatening) 141

position, but in this game the circumstances in the lower right impelled Black to deviate from the ​usual​ sequence would normally follow, as we see in the next diagram. Although the complex ramifications of this intensely tactical fight are well beyond our focus on the Sector Line concept itself, they​re shown below for the reader​s edification.

The following material may be glossed over at the reader​s discretion.

Diagram 29 Instead of continuing with the ​normal​ Joseki move of W11 at 14 to establish a live group along the edge, with this W11 a swap occurred, with Black destroying White​s potential at the bottom in return for White​s effectively killing the 3 Blacks on the left and almost (but not quite) securing the 142

(but not quite) securing the lower left corner!

End of material to be glossed.

The Limitations of Sector Lines The action guidelines provided by Sector Lines are necessarily incomplete because: 1. There may be several different groups affected by active Sector Lines at any given instant, so their presence alone doesn​t change the player​s overall problem of deciding which situation takes priority, and of handling any interactions between them. 2. Sector Lines only provide guidance to an appropriate local strategy! Global considerations involving a nearby corner, side, the center or even the entire board may dictate that a move other than that indicated by a Sector Line analysis is best overall. A. From the defender​s perspective, this may mean that a rescue attempt should be deferred, or that a threatened weak group should be abandoned for later use as Aji, despite the fact that it could be rescued! B. From the attacker​s perspective, it will frequently mean that pressure should be applied to weak opposing stones without any real intention or expectation of capturing them (although that outcome will be welcomed if it should present itself!), in order to build up strength for use in attaining some important objective elsewhere. 3. Sector Lines do not identify the specific move that works best in any 143

play. Correctly identifying the best global move requires a high level of tactical and strategic competence, most of whose development is outside our focus in this book. Despite these limitations it​s advisable in your own games to:

Look First At The Relative Strength Of The Opposing Groups And Any Sector Lines They Generate

and

Override Those Indications Only If There Is A Clear And Compelling Reason For Doing So

No single simplifying idea like Sector Lines can instantly transform a beginning or intermediate Go player into an expert, but in many situations it can go a long way toward suggesting reasonable lines of play that might otherwise be missed. Although the influence of Sector Lines is often easy to see after-the-fact, 144

Reacting appropriately after you​ve recognized that an opponent​s move has enclosed one of your key groups within a dangerous Sector Line is often essentially routine because there may only be a limited number of viable options, but correctly deciding what to do next when you have Sente with which to play anywhere is quite another matter! Not only is it necessary to decide whether and where you should take profit or attack, but in the latter case to also where you might create potentially profitable new Sector Lines. And even if that hurdle is successfully surmounted, the concept still offers no automatically applicable criteria for judging which of several possible alternative Sector Lines might prove the most profitable. And then the Sector Lines in and of themselves offer little help in resolving any of the inevitable tactical complications that will accompany their creation. The result is that although full understanding of the Sector Line concept may be necessary, it​s nevertheless an insufficient condition for becoming a strong player! Finding the best move in any given position still requires an entire complex of knowledge and tactical skills that can only be developed over time as a result of much play and study - all of which are outside the scope of this book. Despite these caveats, mastering the simple idea of Sector Lines offers perhaps the greatest ​bang per buck​ for the effort expended in any beginning/intermediate player​s quest for improvement! Finally, it​s also important to recognize that when implementing the Sector Line concept in your own games, you will almost necessarily make some strategic errors and even more tactical ones. And those errors will in turn result in some failures in either or both attack and defense, sometimes even resulting in last minute reversals of winning games in which a long series of excellent moves is completely offset by a single egregious blunder. But such occurrences, however difficult they may be to accept cheerfully, are a natural part of the learning process and should not be allowed to dissuade you from making the strongest moves of which you are capable! With application of the key concepts provided in this book and continued diligent study and practice, sooner or later the number and seriousness of such errors will diminish, and your playing strength will then make the quantum leap upward that your new found strategic insights justify.

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quantum leap upward that your new found strategic insights justify. Now let​s try some problems to see how well you​ve mastered the Sector Line concept.

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© Milton N. Bradley 2008

Chapter 6 - S.W.O.T. Analysis

The themes we​ve explored in this book thus far provided the what, where, when and why of fighting. This chapter integrates those ideas and reaches their logical culmination in a technique widely applied in business management, known by its acronym of SWOT analysis, which enables the establishment of a rational and appropriate action plan. In Go, SWOT analysis begins with a global board evaluation of the importance and relative strength of the opposing groups prior to each move, just as we​ve done in the preceding chapters. Then we add to that an appraisal of our own aggressive potential, together with the converse appraisal of where the opponent can do us damage. The result is a global evaluation of each side​s: S = Strengths W = Weaknesses O = Opportunities 147

T = Threats This basic analysis is then augmented with an appraisal of how each side stands in terms of: - Settled territory. - Territorial potential. The combination of these factors then allows the creation of an appropriate action plan, specifying (to the extent feasible): - The main focus of play in the current position. - The most urgent immediate task for the player with Sente. - What (s)he should do to achieve that goal. - The opponent​s expected response. When properly completed and updated move-by-move, this global assessment and action plan provides the road map that guides both sides throughout the game! CAUTION! Even if the SWOT analysis is perfectly performed (no mean feat in many positions for less than strong players), finding the best moves to exploit that appraisal will frequently require both tactical and strategic skill well beyond players at the level for which this book is intended. But please don​t be discouraged by this, because it​s only a technical detail which will eventually be self correcting as your knowledge and skill improve with increasing experience. 148

Until that high level of competence is finally attained, the result of applying a SWOT analysis may ​only​ be that you identify the right objectives, even if you don​t always find the very best moves to implement them! So, at worst, any resulting lack of success won​t be because you overlooked some important element of the position! Now let​s revisit the position we examined earlier in Chapter 2, Diagram 2, and see how the more comprehensive SWOT analysis enables sharpening focus beyond the simple (but essential!) identification of strong and weak stones to produce an appropriate action plan. Diagram 1 The SWOT analysis of this position is as follows: Black: Strengths: - The upper side is very strong, but the ​b​ stones don​t reach out very far into the vital center, so their overall impact is only modest. - The ​k​ stones already have one eye and potential 149

for another both on the edge and in the center, so they may be considered modestly strong. Weaknesses: - The ​i​ stones have no eyes and are pressed on both sides by Whites which are stronger. Opportunities: - The (modest) chance to exploit the weakness of the White ​h​ stones. - The (even more modest) possibility of rescuing the trapped ​e​ stone. - The chance to attack and possibly capture the White ​f​ stone. - The potential for attacking the White ​j​ stones which still 150

have only 1 eye. Threats: - The still unsettled status of the fairly large ​k​ group. - The weakness of the ​i​ group, sandwiched between the stronger White ​h​ and ​j​ groups. Settled Territory: - 10+ points in the upper left corner.

Territorial Potential: - Almost, but not yet complete control of the entire upper side (because of the gaps between the ​a​, ​b​, and ​c​ groups, and the still open 3-3 point in the upper right corner.) which could easily total 50+ points if fully realized. - 10+ points in the lower right corner. White: Strengths: - Because of the trapped Black ​e​ stone, the White ​d​ group is very strong, and has great influence in the vital open board center. - Because of the trapped Black ​m​and "n​ stones, the White ​l​/​o​ group is equally strong, and also has great influence in the vital open board center. - The presence of both of these strong groups on opposite sides of the still open center greatly improves the fighting prospects of White​s still somewhat weak ​h​ stones. Weaknesses: - The fairly large ​j​ group as yet has only 1 sure eye. - The White ​h​ stones as yet have no eyes are squeezed on both sides by Black. Opportunities: - There is good potential to invade and reduce the still porous big Black 151

upper side, either between the ​a​ and ​b​ stones, between the ​b​ and ​c​ stones, or on the 3-3 point in the upper right corner. - There is also good potential to make territory between the ​f​ stone and the ​d​ group. - There is also modest potential to expand the left and right side groups into the center. Threats: - Mainly that either of the still unsettled ​h​ and ​j​ stones will either be captured or will lead to disaster elsewhere if they are forced to run. Settled Territory: - Essentially none at present. Territorial potential: - 20+ points on the left side. - Perhaps 15+ or so points in the ​d​ group. Action Plan: - The current global focus is on the interplay between the weak ​h​,​i​, ​j​, and ​k​ groups. Now let​s see how this simple but surprisingly powerful SWOT protocol was applied in a game between two 4D players.

Figure 1 The SWOT analysis of this position is as follows: Black: Strengths: - A still quite incomplete lower left corner enclosure. - Good shape in the upper left corner that should allow making two 152

eyes against any currently foreseeable attack. - A fairly thick and almost connected right side, with one almost abandoned embedded White stone (W14) and one weak White stone (W26), both within Black​s Sector Lines. Weaknesses: - The ​thin​Black lower left side position. Opportunities: - The chance to exploit the weakness of W6 on the left, and W14 and W26 on the right. - The possibility for invasion into the big gap between W12 and 24 on the 153

upper side. - The Aji of the gap between W18 and 24. - The potential for expansion from the lower left corner, especially along the lower side. Threats: - The potential inherent in White​s possible development of W6 on the left and W14 and 26 on the right.

Settled Territory: - Essentially none. Territorial Potential: - A few points in the upper left. - Ten to 15 points in the lower left. - Perhaps 30 or 40 points on the right side, if the problem of W14 and (especially) W26 can be solved. White: Strengths: - A solid, shapely position in the upper left corner. - Solid and well coordinated positions in the upper and lower right corners. 154

Weaknesses: - W6 is a lone White stone splitting two Black positions and within distant Black Sector Lines. But that​s not urgent at the moment, because the area is too open for a Black attack to seriously compromise the ability of the W6 to make a base and/or escape. - W14, which abuts a strong Black wall and is also nearly surrounded, so it​s clearly at least temporarily abandoned. - W26, although at the moment it​s easily able to escape. The problem with this stone is that it must be aided before Black can play again to block its easy egress to the still open center, and then capture it create a vast Black territory. - The gap between W18 and 24, and between W12 and 24. Opportunities: - Primarily to develop W26 to prevent a large local Black territory. - The chance to develop on the lower side. - The chance to consolidate the upper side by adding a stone between W12 and 24. Threats: - Mainly that W26 will be trapped and captured, and that Black will make too large a territory in that area as a result. Settled Territory: - Essentially none at present. Territorial potential: - Ten plus points in the lower right corner. - Probably 10 or so points on the upper left side, and in the upper right corner. Action Plan: - The current global focus is on the weak W26, and the way in which both sides handle that problem will shape much of the remainder of this game! - Because the center is still so open, White does not have to support W26 immediately, but he must watch the local situation carefully! So at the moment White can afford to improve his prospects elsewhere, with the lower left as the currently most fruitful target.

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The following material may be glossed over at the reader​s discretion.

The optimal implementation of a SWOT analysis is mainly a matter of technique, and is therefore outside the realm of our focus on the analysis itself. But briefly showing how the fairly strong protagonists in this game answered this challenge may prove illuminating to the reader, so we show that next, with minimal commentary.

Figure 2 W32 induced B33 to defend the corner territory, and then W34 not only made a base but threatened to more or less complete a large moyo on the lower side by continuing at ​a​ or thereabouts at an appropriate later time. When B35 strengthened Black​s upper border, it would 156

normally induce W​b​ in response to preclude Black​s strong pressing move there. But in this situation the threat it posed against W14 and 26 on the right side is far more serious, so White felt compelled to respond to that instead! W36 follows the maxim of attaching for defense (see Chapter 1), and after the natural Hane of B37 in response, the cross cut of W38 is a standard technique to ​make shape​. But after the atari of B39, W40, B41, 157

instead of playing W42 White might have been better advised to simply play W​c​, B45, and then skip out lightly (and relatively safely) into the center with W​d​. But because White was also looking at the weakness of the Black lower right side group ... The sequence shown followed through W52, after which Black has succeeded in the first stage of his strategy by inducing White to develop the weak and isolated W26 158

into a group too large to give up, but which is nevertheless still ripe for attack!

Figure 3 After W52 White was out of Black​s Sector Lines, so there was no good way for Black to immediately exploit that still unsettled White center group. So Black​s attention 159

that! Black​s clever idea is to use B53 et seq as diversionary mechanism for creating thickness that area, with which to then: - support any weaknesses in his own lower right side group, and - prevent a later flight to safety in that direction by the weak White center group! After accomplishing those objectives, Black also emerged with Sente because W78 was necessary to secure White​s eyespace and territory in the lower right corner. So Black was free to implement his plan with the cap of B79, blocking the flight of the now large and still eyeless right center White string, once again enclosing it in Black Sector Lines, and forcing it to seek safety above.

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Black also emerged with Sente because W78 was necessary to secure White​s eyespace and territory in the lower right corner. So Black was free to implement his plan with the cap of B79, blocking the flight of the now large and still eyeless right center White string, once again enclosing it in Black Sector Lines, and forcing it to seek safety above.

What happened after that was primarily tactical and therefore beyond our current interest, but suffice it to say that after a tense and incisive battle the embattled White center group was unable to either make 2 eyes or escape, so White resigned. This is an almost perfect illustration of the danger that often follows when the Sector Line indications are ignored and a weak group (W26) is belatedly added to in an attempt to save it! Black​s final favorable result in this game depended upon his ability to produce the precise tactics needed to counter White​s many serious escape and counterattacking threats, so it was by no means assured after B79. But whether or not it was, the key idea to remember is that it​s best to not become enclosed and forced into the kind of desperate situation White confronted here.

End of material to be glossed.

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© Milton N. Bradley 2008

Chapter 7 - A Sampling Of Major Fighting Scenarios

What we​ve done in this book thus far is to explain how to: - Identify the important weak groups which should be the focus of play. - Use the SWOT analysis technique to develop an appropriate action plan for exploiting those weak groups. In this chapter, we illustrate a select few of the more important of those action plans. As noted earlier, the first step in attacking a weak group will usually be a threat to enclose, because only enclosed groups can be killed. That threat will then typically elicit a response in which the target group attempts to flee, usually either into the open center or toward friendly stones. Our focus in this final chapter is on the methods for taking best advantage of that flight. In most cases the attacker​s only reasonable expectation 163

should be that the attacked stones will succeed in escaping, so that any profit resulting from the attack will typically be realized elsewhere (usually, but not always, nearby). Consequently, all-out attempts to surround and kill will usually not only prove futile but unproductive as well. (Of course if the defender errs and the opportunity for a kill or other major coup does present itself, it should be seized, with alacrity and thanks!) Capping This is the commonest and most basic attacking technique - most often appropriate, but (as we show below) not always!

Figure 1 In this 2004 AGA-Ing Pro Cup match between Huiren Yang 1P (White) and Mingjiu Jiang 7P (Black), B31 has capped White​s weak 3- stone 164

W12-20 group, blocking its easy path into the center. Although Black has no reasonable expectation of killing these stones, this is nevertheless the best way to exploit their weakness, aiming to profit elsewhere by harassing them.

Figure 2 This is how the game actually continued. (The 165

details of the complex tactics involved are far beyond our present interest, and so will not be discussed here.) White resigned after B159 because the impenetrable Black lower center moyo is just too large for White to overcome.

Figure 3 in this 2005 North American Masters match 166

Masters match between Jie Li 9D (White) and Thomas Hsiang 7D (Black), Black has just erred with B81. Instead, he should have secured his large weak group via the one point skip to ​a​. Now White can exploit this oversight - but how?

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Diagram 1 Capping with W1 seems like the logical move, but here it​s not best because it leads to a Ko which might involve dangerous complications. Instead, 9D Li thought through those complications, and came up with an even better idea.

Diagram 2 Instead of capping, the diagonal move of W1 here is even better, because it precludes that Ko possibility. Next, Black thought it prudent to strengthen (and expand) his corner with B2 before answering W1. Unfortunately that turned out badly because B2 induced W3, which then contributed importantly to White​s attack on the weak Black group below. After the B2, W3 exchange, Black 168

had time to attach with B4, and at that point he must have believed that he was going to survive White​s attack relatively unscathed. But that expectation was dashed when the peep of W13 and the following W15 set up the later cut of W21, trapping the 8 Blacks on the right and leaving the rest of the big weak Black group fleeing with only 1 eye. Only a few moves later Black was forced to resign.

Diagram 3 In this 2006 Paris Open Championship 169

(White) and Fan Hui 2P (Black), B79 (B1 here) was played to make it difficult for White​s two marked stones to safely connect to his friendly stones in the upper left. This put the onus on White to either break through Black​s encirclement highly unlikely in this position - or to make life in this immediate area in the face of Black​s surrounding strength.

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Diagram 4 As this game developed, instead of trying too hard to enclose and kill the weak White center group, Black instead wisely chose to make profit at the top without unduly strengthening the target group. This succeeded so well that White resigned before the weak group​s ultimate fate could even be decided! This was superb strategy, and exemplifies how such an exploitation should ideally be carried out.

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Diagram 5 In this game between a 2D and 3D, Black has suffered a huge loss of 8 stones in the lower left, so his only possible chance to win is if he can somehow mange to kill the large still eyeless marked White group in the upper center. Since this group​s only realistic chance to connect with friendly stones is with the Whites in the lower right, the attachment of B1 is a fine (and typical) 172

way for Black to try to prevent that connection. Although that strategy didn​t succeed in this game, it in no way detracts from the general principle involved.

Diagram 6 In this game between two 4D​s, when W1 invades Black​s thin lower right position, with White​s strength on both the bottom left and right 173

side to run to, it would seem that this stone is not only quite safe, but actually may be stronger than the lone Black to its left as well. But is it really? Black​s clever response gives the answer.

Diagram 7 174

Diagram 7 After the twin kikashis of B2 and 4 followed by the attachment of B6, the lone White stone has now become weak and can only run straight up into the center, where Black is already strong. The price that Black has had to pay for this is that W3 and 5 have given White a considerable profit on the right, but if Black​s following center attack succeeds (as it did in this game), his compensation there will more than make up for that loss. So this strategy is inherently dangerous, but 175

adequately followed up.

The Steering Attack Unlike the Cap, which typically offers the capped player several options in response, a properly placed steering attack stone essentially constrains the opponent to running in a single desired direction.

Diagram 8 In this game between two 4D​s, White​s large weak center group offers Black an ideal opportunity to begin the creation of a large Moyo in Sente by forcing White to move in a 176

Do you see how?

Diagram 9 B1 blocks White​s progress to the right, forcing his group to flee up into the open top, allowing B3 to begin sketching out a large moyo on the right side. Although this area is still much too large and open to all become territory, it does provide Black with 177

that potential territory can later be realized as solid territory is, of course, still to be determined in subsequent play, but it does provide Black with a significant winning chance.

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Diagram 10 In this position from a game between two 5D​s, Black has set White up for the devastating splitting attack of B1, which is also on the key shape point of the lower White group.

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Diagram 11 The choice and timing of the best splitting point and the ultimate outcome of the resulting fight are both a function of the opponents​ skills, but unless gross blunders occur the end result should more often than not be favorable to the attacking player.

The Running Battle Now let​s look at the early stages of a game contested between an 8D and a 180

(but hardly the only) way for White to play, making the fullest possible use of his upper left 4-4 point stone by making a long strategic extension from it. A squeeze play is the best way for Black to answer because Black is concerned with neutralizing White​s center thickness below, and B2 is the strongest and most aggressive pincer available. Perhaps most important, it encloses W1 tightly within Black Sector Lines, so it​s 181

Perhaps most important, it encloses W1 tightly within Black Sector Lines, so it​s Sente! If instead Black were to passively extend at ​a​ to coordinate with his strong position in the lower right, W​b​ would work much too well with both the White upper left star point stone and his thickness below for Black to allow.

Diagram 12 If W3 now dives into the 3-3 point to seize the corner as shown here, 182

Diagram 12 If W3 now dives into the 3-3 point to seize the corner as shown here, this Joseki will inevitably follow, and that would leave Black with both thickness which helps neutralize White​s thickness below, and Sente with which to play at either ​a​ or ​b​in the upper left corner, again with a result White felt was unfavorable to him. So instead ...

Diagram 13 The one point center 183

Diagram 13 The one point center skip of W3 to break the Black Sector Line was necessary if White didn​t want to become enclosed, and that was the first key move in his strategy. It also enclosed both the Black corner stone and B2 in White​s own fairly distant Sector Lines. Most important, it was Sente because a following move at 4 would force Black into a low, nearly enclosed position in the upper right corner. So...

B4 Prevents White​s good play at this same point and breaks the White Sector Line, while increasing Black​s space. But it​s Gote because it doesn​t establish a Sector Line of Black​s own. W5 Since Black has no enclosing move next, White is free to try to establish some eyespace, and this ​slide​ threatens to follow at 6 (the 3-3 point), to both steal the corner territory and provide the White stones with almost certain life. So it retains Sente.

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W7 This is the second key move in White​s strategy, so it​s important that you thoroughly understand its rationale! What he intends to do is to counter Black​s strategy of negating the value of White​s center thickness below by building a compensating White moyo in the upper left! At least equally important, this stone prevents B2 from extending to the left to make eyespace, retains Sente by enclosing B2 in a White Sector Line, and also threatens to capture it by continuing with W​c​! (Pretty good for a single move!) B8 This is close to being the only logical response because B2 has no base, and attaching to W7 at ​a​ would only induce W​b​, B​c​ to strengthen W7 in Sente and thus play into White​s moyo strategy. B​c​ instead would not only be too slow in moving out into the center, but would also not threaten White in any substantive way. In sharp contrast, B8 breaks White​s Sector Line and establishes one of Black​s own which encloses W1-5, while also threatening to follow with B​d​ to lock those White stones in. So B8 seizes Sente, and begins a classic running battle in which each side has a weak group in potential danger.

Diagram 14 Becoming enclosed would force the White stones to either live small in Gote or die, so escaping is essential. This one point skip of W9 is the best way to do that, because it retains Sente by threatening to continue at 10, which would force Black into a low position on the right edge. B10 Prevents White​s good move at this same point and increases Black​s potential right side 185

he can further coordinate it with his strong lower right corner. But despite that it​s Gote because it makes no serious enclosure threat against the W1-9 group. (W9 already broke what would have been Black​s new Sector Line.)

W11 Because the W9 group can​t be enclosed immediately, White can afford to use his Sente to play here because it encloses B2-8 within a new White Sector Line, while threatening to continue with W​a​ to lock-in those two Black stones and almost certainly kill them. This is a fine double purpose move, because it also coordinates with White​s upper left corner stone, beginning to construct the large White moyo in that area White was aiming at when he played W7. B12 Black must break out of the new White Sector Line, and this is the best way to accomplish that because it in turn puts the W1-9 stones within Black​s own new Sector Line, and threatens to continue with B​b​ to enclose him. So Black once again has Sente. W13 Even if White allows B​b​, after W​c​ it would still be possible for his enclosed group to live, but that scenario would be bad for him. So he has no real choice but to skip out to break the Black Sector Line thus. Although W13 actually encloses the weak B2-12 group within a new White Sector Line, it​s one with a very distant (and therefore not very threatening) 186

follow and that would be bad (although not disastrous) for the weak Black 3 stone string of one point skips! So instead ... B14 offers the weak Black string the most future alternatives, so it​s safest. But either B​c​ or 15 is also feasible, with the choice between these options more a matter of the player​s judgment than of necessity. W15 was the key turning point in this part of the game! Unfortunately, it was somewhat overambitious, despite being the most consistent with White​s moyo strategy in playing W7 and 11. It mistakenly emphasized the creation of White​s potential upper left moyo over the safety of his weak stones on the right, and thereby violated the earlier noted key principle of: ​Urgent Moves Before Big Moves​.

Instead, W​a​, ​b​ or 16 to strengthen his weak group were preferable alternatives, and, as with B14, the choice between them would be a matter of the player​s best judgment rather than of necessity. Because W15 yielded Sente to Black in the running battle it was also the riskiest choice, although one it seems that White undertook willingly because he lusted after the big moyo he was trying to create on the left, and as an 8D he undoubtedly had absolute confidence that his tactical ability 187

alternatives, and, as with B14, the choice between them would be a matter of the player​s best judgment rather than of necessity. Because W15 yielded Sente to Black in the running battle it was also the riskiest choice, although one it seems that White undertook willingly because he lusted after the big moyo he was trying to create on the left, and as an 8D he undoubtedly had absolute confidence that his tactical ability would suffice to rescue him from any resulting difficulties on the right. But even as strong a player as he would almost certainly have been better advised to play one of the other, safer choices noted above. B16 Because the Black string isn​t enclosed or even nearly so, Black is now free to be aggressive. Seizing the opportunity offered by White​s failure to reinforce the weak White group, this important play once again encloses those stones within Black​s Sector Lines, and forces a response. W17 Breaks the new Black Sector Line, but still leaves the White group within a more distant Black Sector Line anchored in the lower right corner, and that​s a measure of the size of White​s error in playing W15. B18 Reestablishes the more dangerous close Sector Line, and continues to force White​s response. W19 Not only breaks both of Black sector Lines, but also gives White access to some badly needed potential eyespace on the right edge. Equally important, it also threatens to play at 20 next, occupying the key pivot point in the corner. That would not only increase White​s own eyespace while reducing Black​s, but would also actually threaten the life of the Black corner because of its weaknesses at ​d​ and ​e​. Because that would be too good to allow ... B20 This is now the key move, stabilizing the Black corner stones and destabilizing White​s, which are now no longer certain of making 2 eyes! What happened next to the weak White stones will not be shown because it​s entirely tactical and therefore outside the scope of our interest in the basic Sector Line/connectivity/enclosure themes we​re discussing. But it may be 188

achieve life or break out of Black​s enclosure he overstepped the time limit and lost the game! A classic example of the difficulties that can follow from ignoring the indications provided by Sector Lines!

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© Milton N. Bradley 2008 Epilogue

Applying What You've Learned If this book has successfully realized its design intent, a double digit Kyu reader who finishes it should have acquired a set of new ideas which provide a much improved understanding of how high level Go is played. That​s a necessary first step, but real, sustained improvement will only result when those ideas have been permanently embedded in your thinking processes, so that their application has become an automatic, almost instantaneous response, rather than requiring the conscious application of a mental checklist. To realize that goal, there is no adequate substitute for playing many, many games, getting practical experience in implementing those ideas in the face of determined and competent opposition.

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But that raises a serious problem for most beginners/intermediates, because they will typically be playing most of their games against ​equal​ or only somewhat stronger opposition. The difficulty this presents is that the caliber of those opponents is not likely to be sufficiently high to afford the opportunity to confront (and therefore learn to counter) the most incisive moves. The unfortunate consequence is that it will often be possible to get by and even prevail with inferior plays that the far stronger opponents you will encounter later in your Go career will almost certainly severely punish. And so, despite your best efforts, by playing against only equal or marginally stronger opponents you will almost necessarily be learning many ​things that ain​t so​, which will therefore later have to be unlearned if you are to make the much desired advance to the higher skill levels. Fortunately, it​s relatively easy to transcend this important difficulty by watching/studying the games of professionals and amateurs who are strong enough to make few egregious errors. In earlier, less technically sophisticated times, being able to watch such strong players on any kind of consistent basis was impossible for any but the relatively few fortunate individuals who lived in communities in which there was a large local Go club with sufficiently strong members. But today, being able to do this is feasible for everyone, 24/7, through the 191

advent of the internet! KGS And IGS are by far the largest internet Go communities in the world, and also the preferred home of many of the world​s top ranked professionals, a number of whom play there regularly, albeit mostly anonymously. For these reasons, they​re my preferred choice. But some of the ethnic Go servers (especially the Chinese and Korean) are perhaps even stronger, so for those for whom the language barrier isn​t a problem they form an excellent (or even superior) alternative. But watching the games of professionals or the very highest rated amateurs is IMHO not the best way to proceed, at least for the ​average​ double digit beginner/intermediate! The reason is that the highly refined technique and exquisite positional judgment of these ultra-strong players enables them to employ strategy that is often essentially incomprehensible to anyone not close to their own stratospheric skill level. So until you​ve reached at least low single digit Kyu rating you will be well advised to concentrate your watching on players in the 1d to 5d range, where the strategy employed will usually be more or less comprehensible to you, while the protagonists​ technique will still be sufficiently well developed to minimize most egregious errors. But even that isn​t sufficient, because in order to 192

really profit from your watching it must be an active rather than a merely passive experience! What this means is that move-by-move you must mentally assume the role of each player in turn, evaluating the whole board situation, performing your own SWOT Analysis, and deciding on what you believe should be the best next move. Then as the player actually makes his move you must compare that with your own idea, and, in the many cases in which they differ, try to figure out why the move actually played was preferable to your own choice. Since this process of analyzing the differences will typically take much more time than is available between moves in real time, in order to be able to adequately conduct this kind of analysis, it will usually be necessary to save the game and then replay it later at your own pace. Although that may seem to be a lot of extra work, the payoff for going through this exercise on a regular basis can be immense! The ultimate result will be that, perhaps slowly and possibly quickly but in any event surely, you will begin noticing that your own move choices and those of the strong players you are watching will become identical more and more of the time, as your playing strength soars as well! If ever there was a ​royal road​ to Go mastery, this is it! And it​s fun as well - ​the best of all possible worlds​. 193

Enjoy!

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© Milton N. Bradley 2008

Glossary of Japanese Terms

AJI (ah​-gee): Potentially exploitable threats remaining in a position. AJI KESHI (ah​-gee keshi): A bad move which needlessly neutralizes the potentially exploitable weaknesses in the opponent​s position. ATE (ah​-tay): A move that gives atari. ATARI (ah-tah'-ree): A condition in which one or more units has been reduced to only a single liberty, and is therefore subject to capture on the opponent's next play. ATSUMI (atsumi): Thickness. BOSHI (bo-shee): ​Cap​. Usually, a one point skip above an opposing stone. DAME (dah'-may): A neutral liberty shared by safe 195

White and Black groups. Does not count as a point for either side. DAN (dahn): "Step". The designation of playing strength for those of master level. Ranges from 1-Dan to 9-Dan, but professional ranks are separate and much stronger. DANGO (dan-go): ​Dumpling​ = A shapeless mass of stones with little eyemaking potential. DE (day): A move which pushes between two opposing stones. FUSEKI (fuh-say'-key): The full board Opening. GETA (gay-tah): A trap or snare which can effectively capture opposing stones even when they still have several liberties. GO (goh): The name of the game. (Called Wei Ch​i in Chinese, and Baduk in Korean.) GOTE (goh-tay'): The converse of Sente. A move which makes no significant threat, and which therefore doesn't require an immediate response by the opponent. GOTE NO SENTE (goh-tay no sen-tay): A Gote move which contains (often hidden) aggressive potential. HANE (hah'-nay): A Diagonal attachment against an 196

opposing stone. HASAMI (hah-sah​-mee): A pincer. HIKI (hee​-kee): ​Draw back​. HORIKOMI (hori-koh​-mee): A ​throw-in​ sacrifice which kills an eye and/or whose capture reduces the opponent​s liberty count. JOSEKI (joh-say'-key): An analyzed sequence of plays which theoretically leads to a dynamically equal local result for both sides. KAKARI (ka-kah​-ree): An approach move against a corner stone to prevent a Shimari. KATA (kah​-tah): ​Shoulder​. The point diagonally above a stone. KATACHI (kah-tah​-chee): ​Shape​. Usually, good shape. KATATSUGI (kah​-tah-tsoo​-gi): The solid connection. KATATSUKI (kah​-tah-tsoo​-kee): A shoulder attack. KEIMA (kay-mah): The ​Knight​s Move​. KESHI (keshi): "Reduction​, or "minimization​. When played to reduce an opponent's Moyo (Sphere of 197

Influence), Keshi consists of "light" moves, not too deep within the area of the opponent's strength. KIKASHI (ki-kah'-shee): A forcing move which must be answered, and which therefore necessarily retains Sente, but which is incidental to the main flow of play. Such stones are typically abandoned after they have served their purpose of forcing the opponent's response, serving only as Aji thereafter. KIRI (kiri): ​Cut​. KO (koh): "Eternity". An important, oft recurring tactical situation in which a single stone is captured and THE NO REPETITION RULE applies. KOMI (koh'-mee): The points added to White's final score in ​even​ (no handicap) games to compensate for Black's first move advantage. KOSUMI (ko-suh​-mee): The diagonal extension. KYU (kyu): Rank. The designator of playing strength for players of less than Dan (master) strength. For amateurs, ranges from 35 Kyu (beginner) to 1 Kyu (just below master strength) MIAI (mee-iy): Two complementary points of approximately equal importance in a given situation, such that whichever one a player occupies, the opponent can 198

(and usually must) occupy the other. MOYO (moh-yoh): A large Sphere Of Influence or Potential Territory. NAKADE (nah-kah-day): The placement of stones inside an opposing group to reduce the shape to one eye. NADARE (nah-dah​-ray): The ​Avalanche​ Joseki. NIDAN (nee​-dahn): ​Two Step​. NI-REN-SEI (Nee-Ren-Say): A Fuseki pattern in which a player occupies both 4-4 points on a single side. NOBI (noh​-bee): Extend. NOZOKI (noh-zoh​-kee): A peep which threatens to cut. NUKI (nookee): A capture. ONADARE (oh​-nah-dah​-ray): The ​Large Avalanche​ Joseki. OKI (oh-kee): A placement, usually intended to steal eyes. OSAE (oh​-sah-ay): A blocking move. OSHI (oh​-shee): ​Push​. Usually along a line atop (or 199

alongside) an opponent​s stone or line of stones. PONNUKI (pon-nuh​-kee): A powerful shape created when 4 stones capture a single opposing stone. SABAKI (Sah-bah'-kee): "Disposal". Light resilient shape which allows a group to be easily settled, or to be partly or totally sacrificed if necessary without significant penalty. SAN-REN-SEI (San-Ren-Say): A Fuseki pattern in which a player occupies all 3 handicap points on one side. SEMEAI (semi-eye): A life-or-death fight (= race to capture). SENTE (Sen'-tay): The initiative. A move central to the major strategic and/or tactical motifs of the game, which therefore requires the opponent's response, and which cannot be ignored without significant penalty! Such stones typically have long term implications, and must therefore be watched and defended. The converse of Gote. Closely related to Kikashi. SHICHO (shih'-cho): The Ladder. SHIMARI (shih-mah'-ree): A Corner Enclosure. SHINOGI (shih-noh’-gee): A sequence of moves to provide a weak group with either escape or good 200

eyemaking shape. SUBERI (soo-beh​-ree): ​Slide​. A Knight​s Move toward the edge, usually from the third line to the second line. SUJI (soo'-gee): "Style" or "skillfulness". Clever, artistic play. See Tesuji. TAISHA (tie-sha): The ​Great Slant​ Joseki. TENUKI (teh-nuh​-kee). ​Play elsewhere​. TESUJI (teh-soo'-gee): A Suji which raises the overall efficiency of the player's local (and sometimes global) stones to their highest possible level. TOBI (tobi): A jump (= skip). TSUGI (tsu​-gi): A connection. TSUKE (tsu​-kay): An attachment to an opposing stone. TSUME (tsu​-may): An extension which inhibits the opponent​s extension. TSUME GO (tsoo​-may GO): A life-or-death problem. UCHIKOMI (oo​-chee-ko-mi): An invasion. WARIKOMI (wah​-rih-koh​-mee): A placement between 201

two opposing stones intended to set up cutting points. WARIUCHI (wah​-rih-oo​-chee): A wedge (placement) which has room to expand on both sides. WATARI (wah-tah​-ree): A connection at board edge. YOSE (yoh'-say): The Endgame. YOSU-MI (yoh​-suh mih​), formerly Yosu-miru : ​Wait And See​. A probe intended to retain sente while inducing the opponent to fix the shape of the stones.

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Table des Matières Table Of Contents

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Introduction Chapter 1 - The Role Of Fighting In Go

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