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

Improve Fast In Go

© Milton N. Bradley 2008, 2010

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

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

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

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

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:

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

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

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

allowed its on line publication.

© 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.

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

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

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

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

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?

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

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

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

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

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.)

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.

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.

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!

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

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).

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

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.

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.

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

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.

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 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.

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

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

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 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.

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,

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

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.

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

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

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 eye-killing 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

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,

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?

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

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

© 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:

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​

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

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.

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.

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 ....

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

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.

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

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

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 multi-purpose move because it: - Provides

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

Diagram 10 B1

is an ideal multi-purpose 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

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.

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.

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

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

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

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

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.

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

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

on the lower edge.

W2 counter-squeezed 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

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.

© 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

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:

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-by-move.

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!)

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,

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

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.

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

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

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

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.

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

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

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.

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

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 5-Liberty Criterion provides the