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© 2003 Richard Hunter

Counting Liberties and Winning Capturing Races

Richard Hunter

Buy the full book at gobooks.com

Every game involves counting liberties in capturing races, from huge game-deciding battles to small scale questions of whether a cut works or a defensive move is necessary. How many times have you been surprised to end up one liberty short? Did you miscount or somehow misplay the fight? Shouldn’t you have won instead? Every go player has had this experience. Losing a capturing race can be disheartening, but winning one can be exhilarating.

Counting liberties and winning capturing races are part of the fundamental knowledge that you need to understand thoroughly. This book provides a systematic coverage of how to count liberties in the different types of fight. The first chapter guides you through numerous simple examples and presents general principles that you can apply in your games. The level is suitable for beginners, who should have no trouble following this clear and methodical explanation, but even dan players will find something new and important here. The following chapters present applications of these principles to more complicated capturing races, several games with detailed comments, and numerous problems for practice. Study this book carefully and you will find yourself winning more capturing races and savoring the joy of killing your opponent’s stones rather than dying.

Copyright Page

© 2003 Richard Hunter

All rights reserved. Reproduction in whole or in part is strictly prohibited.

Based on material originally published in the British Go Journal and in The Second Book of Go.

Cover design by Laurie M. Crammond

Photograph of Richard Hunter by Louise Bremner

SmartGo Books edition converted and edited by Richard Hunter

Print edition edited by William Cobb and Richard Hunter

ISBN of print edition:
1–932001–04–2

Preface to Printed Book

Counting liberties and reading out capturing races are important basic skills that you need to learn. Many players, even quite strong ones, have a poor grasp of these fundamentals. One reason is that they have never before been clearly and systematically explained in any book in English. Books on tesuji assume you already know the fundamentals and only review them briefly. Books for beginners give a simplified introduction, leaving out important details. Here for the first time is a thorough explanation of the principles of counting liberties and their application to practical situations that are likely to occur in your games. Once you have mastered the material presented here, you may find yourself out-fighting stronger players who previously exploited your lack of knowledge. The reason players miscount liberties is that they don’t really understand what constitutes a liberty and what doesn’t. For example, when there are vacant points shared by both sides, do these count for both sides or only one side, and in that case which side?

Chapter One analyzes the six different types of fight involving no eyes at all, one eye for one side, and one eye each. It clearly explains what counts as a liberty and what doesn’t. Unlike other books that try to cover the subject in half a dozen diagrams, this chapter uses hundreds of diagrams. Some of them, not only ones showing the starting position, but also ones showing the end results of different variations, have no moves in them at all. This makes it easy for you to judge the status. The moves leading to those results are shown in separate diagrams. There are no clever moves to find in this chapter. The challenge is merely to count liberties. Chapter Four extends the analysis to capturing races that involve ko. Chapter Five discusses fighting techniques for gaining liberties for yourself and efficiently stealing your opponent’s liberties. Chapter Seven presents four exciting games involving capturing races, with detailed comments given by professionals. Chapter Nine discusses capturing races involving an L group. How many liberties does this well known shape have? Interspersed among these chapters are numerous problems to review what you have learned and to challenge you.

The contents are based on my series of articles published in the British Go Journal nos. 102–120 from 1996 to 2000, and reprinted here with permission from the British Go Association. This long time span was sufficient to give readers time to absorb the concepts gradually. The coverage was exhaustive, but also exhausting, so don’t expect to grasp everything in this book in one pass. Read Part One quickly first to get an overall impression, then study it a section at a time and take a break before studying the next section. Apply what you learn in your games and come back and reread the chapters. You should see a dramatic improvement and will also find yourself enjoying your games much more. Winning capturing races and killing enemy groups is fun.

While the journal is read by some people in other countries, the readership is undeniably limited. I’m delighted to have this opportunity to make this material available to a wider audience. I’d like to thank Brian Timmins, who was the editor of the British Go Journal for most of this series, and his team of helpers for putting my ideas onto paper. I’d also like to thank David Woodnutt, who took over as BGJ editor for the final two issues of this series and is continuing to edit my current series of articles. I’m indebted to Simon Goss for permission to include his BGJ article on counting liberties in bamboo joints. I’m extremely grateful to Matthew Macfadyen for technical advice and encouragement while I was writing the original articles and the extra material for this book. Many thanks to John Power for reading an early draft and offering numerous suggestions for improving the English. This book includes the complete contents of the BGJ series plus a considerable amount of additional material, notably a large chapter covering capturing races involving ko. I’ve corrected one or two minor errors and the material has been completely reformatted. The BGJ series was appreciated by readers of the British Go Journal and a few of the early parts were reprinted in Dutch by the Belgian Go Journal. I’m grateful to everyone who provided feedback and encouragement. Some of the BGJ content also appeared in the second edition (Kiseido, Jan. 1998) of The Second Book of Go by Richard Bozulich, which was published about halfway through the BGJ series.

I have changed one term (fake eye) that appeared in the BGJ series and The Second Book of Go. In this book, it’s called a "weak eye“. It first appears on page 28 and is used several times thereafter. It’s an important concept, but I haven’t seen an English term for it anywhere else. I think ”weak eye" expresses the concept more clearly. I hope this change does not cause any confusion.

(The link to sgf files that was given here in the printed book has been deleted.)

Richard Hunter
Tokyo, Japan
February 2003

Slate & Shell
1425 Westshire Lane
Richmond, VA 23238
www.slateandshell.com

Preface to SmartGo Book

In converting the paper version into the SmartGo Book version, I have taken the opportunity to make several enhancements: I have added extra diagrams and inline diagrams, the table that appeared in the British Go Journal, the full game records of all of the professional games discussed in this book, a glossary of technical terms, an index of the problem diagrams, and an index of the summaries and bullet points. I have slightly adapted the text to suit the SmartGo Book layout and features, re-edited and slightly improved the text, and corrected a few minor errors.

The SmartGo Book format lets you play out moves in the diagrams. This is especially useful for a book like this one: in the printed book, the move sequences in many of the diagrams were hard to grasp without being played out on the board. The problems in Chapters 3, 6, 8, and 9 are presented in interactive problem diagrams where you can check your solutions. These problem diagrams confirm the correct line(s) and explicitly refute many incorrect lines. The following pages present detailed explanations of the best solution, alternatives, and the most instructive failures in interactive diagrams where you can play through the book moves or try out your own moves. Inline diagrams (tap the brown colored text) illustrate some explanations written in the text or present earlier diagrams mentioned in the discussion in the text to save you turning back several pages. Internal navigation links (tap the blue text) will take you to relevant locations in the book such as diagrams being discussed or to an Appendix, the Contents, etc. Returning is easy: just tap in the navigation bar at the bottom of the screen.

The professional game records are given in the Appendix. They are also included in the game database bundled with SmartGo One.

Richard Hunter
Bristol, UK
July 2013

Table of Contents

Counting Liberties and Winning Capturing Races

Introduction

Copyright Page

Preface to Printed Book

Preface to SmartGo Book

Part One: Basic Principles

Chapter 1: Counting Liberties

What are Liberties?

Type 1 Fights: Zero or One Inside Liberty

Type 1A Fights: One Inside liberty

Type 2 Fights: Two or More Inside Liberties

Liberties Redefined

This sample provides selections from several chapters. The chapters in gray are included only in the full book.

Type 3 Fights: One Eye Versus No Eye

Type 4 Fights: Big Eye Versus Same Size Big Eye

Type 5 Fights: Big Eye Versus Smaller Eye

Type 6 Fights: Small Eye Versus Small Eye

Summary of Types of Fights

Chapter 2: It’s All Relative

Chapter 3: Simple Counting Practice

Chapter 4: Capturing Races Involving Ko

Summary of Capturing Races with Ko

Part Two: Applications

Chapter 5: Fighting Tactics

The Throw-in

Making an Eye

The Bigger the Better

Avoiding and Contriving Ko

Bamboo Joints (by Simon Goss)

The Art of Strategic Sacrifice

Chapter 6: Problems

Chapter 7: Commented Games

Chapter 8: Additional Problems

Chapter 9: The L Group

Appendix 1: Game Records

Appendix 2: Glossary of Technical Terms

Appendix 3: Supplementary Diagrams

Appendix 4: Index of Problems

Appendix 5: Index of Summaries and Bullet Points

About the Author

Buy This Book

About SmartGo Books

Part One: Basic Principles

Chapter 1: Counting Liberties

Reading out capturing races is easy. It’s usually just a matter of comparing two single-digit numbers. However, in practice, even dan players have trouble with numbers greater than three. What’s the problem? In a word: fundamentals. Most players only half understand a great body of knowledge and have fatal holes in their understanding.

Counting liberties is a topic that is usually dealt with rather superficially and not systematically explained. Books on life and death usually deal with one weak group pitted against strong walls, and books on tesuji cover only how to increase your own liberties or decrease your opponent’s.

This book focuses on counting to see who is winning a fight. It starts off at the double-digit kyu level, but dan players would do well to start from the beginning lest they skip over something they have failed to grasp in the past.

Using terminology introduced by James Davies, I shall describe positions as either settled or unsettled. In a settled position, it doesn’t matter who plays first; the result is already determined. An unsettled position is one where the side that plays first gains.

What are Liberties?

Liberties, also known as breathing spaces, are the unoccupied points directly adjacent to stones. They are the points you must play on to capture the stones. Only the points on the horizontal and vertical lines are relevant, not the ones on diagonals.

A single stone in the center of the board has four liberties, a stone on the side has three, and one in the corner has two.

Black must play on all four liberties to capture the single white stone in the center of the board. Since he can play only one move at a time, it takes him four moves to do this. Similarly, Black must play on all three liberties to capture the white stone on the side and on both liberties to capture the stone in the corner.

If White plays on one of his own liberties with 1 on the left, he forms a group of two connected stones. These have six liberties. So, with one move, White has increased his liberties by two. With 1 on the right, Black plays on one of White’s liberties, reducing the total to three, but with 2 White plays on one of his own liberties forming a group of two stones having five liberties. White gains more liberties than Black takes away: this makes it hard to capture stones by attacking them directly.

If White is surrounded, however, he may not be able to increase his liberty count. And if he bumps up against enemy stones, he may even reduce his liberty count.

Part One of this book examines fights where neither side can increase their liberty count. We will count to see how many liberties a group has and whether it has more or fewer than an opponent’s attacking group. This way of looking at liberties is actually a simplification. It’s sufficient for the moment, but later I shall extend it to cover more complicated positions.

Type 1 Fights: Simple Fights

Diagram 1

Diagram 1 shows a position with two white groups and two black groups. The groups on the outside are alive, but the groups on the inside (the marked stones) are not. Neither side has two eyes, neither group can escape, and neither group can increase its liberty count. It’s a fight to the death. Who will live and who will die? The answer is simple.

Diagram 2

Diagram 3

Hereafter, I will simplify the outside groups in the diagrams and focus on the fight. As Diagram 2 shows, it takes White two moves to capture Black. And as Diagram 3 shows, it takes Black five moves to capture White. Thus, we can say that the black group has two liberties and the white group has five.

Diagram 4

Diagram 5
2, 4, 6: elsewhere

In practice, Black and White play alternately, of course, and White has more liberties, so he is likely to win. Even if Black plays first, White can capture the black stones, as shown in Diagram 4. This is the basic principle of reading fights—comparing the number of liberties on each side. Note that we assume both players try to win. You can’t expect your opponent to let you get several moves in a row, as happens in Diagram 5.

Five against two is a very unfair fight. The position in Diagram 1 is settled: It doesn’t matter who plays first and it’s pretty obvious who will win. In most practical cases, we will be comparing two numbers that are equal or nearly equal.

Diagram 6

In Diagram 6, Black and White have the same number of liberties.

Diagram 7

Diagram 8

If White plays first, he wins, as shown in Diagram 7. If Black plays first, he wins, as shown in Diagram 8.

Diagram 9

Note that all these liberties are equivalent; it doesn’t matter which order you play them in, as Diagram 9 shows. It’s only the number of liberties that is important.

In a simple fight, if the number of liberties is equal, the position is unsettled: whoever plays first wins. In an unsettled position, the winner captures in gote and the loser gets sente to play elsewhere. Throughout Part One, the moves in the diagrams are intended to facilitate counting to see who is winning. They don’t represent the actual moves that should be played in a game.

For example, Diagram 6 is unsettled. White 1 in Diagram 7 settles the situation. There is no point in Black answering at 2 and 4 and losing the capturing race. Black should read out in his head that the fight is lost and play elsewhere with 2, preserving moves 2 and 4 in Diagram 7 as ko threats, and leaving his dead stones with some liberties. If the stones are removed from the board, they have no potential. As long as they remain on the board, dead stones often do have some potential.

Nothing difficult so far, and if you take it step by step, there is nothing difficult anywhere in this chapter. Unfortunately, most people are impatient and skip several steps somewhere along the way. If you avoid doing that, you will be out-fighting stronger players before long.

Type 1A Fights: One Inside Liberty

Diagram 10

Diagram 11

In Diagram 10, both groups have four liberties. Black’s liberties are A, B, B, and B. White’s are A, C, C, and C. As Diagram 11 shows, it takes Black four moves to capture the white stones. (And, similarly, it takes White four moves to capture the black stones.) In Diagram 10, A is a liberty for both the black and white groups. I shall call this an “inside liberty”. The points marked B belong exclusively to Black and the points marked C belong exclusively to White. I shall call these “outside liberties”. Later, we shall see that there are two kinds of exclusive liberties: outside liberties and eye liberties.

Diagram 12

Diagram 13

In Diagram 12, Black plays first and wins. Note that the order in which Black plays on White’s liberties is important in this case. He must start with White’s outside liberties first (all the outside liberties are equivalent and they can be played in any order) and only fill the inside liberty last, since this also reduces his own liberties. Likewise, if White plays first, he wins, as shown in Diagram 13.

Diagram 14

Diagram 15

What happens if White starts by playing on the inside liberty? As Diagram 14 shows, both sides have three liberties after 1, but now it’s Black’s turn. Playing on the inside liberty reduces White’s own liberty count as well as Black’s, so it’s equivalent to giving Black an extra move. Even though White plays first, he loses, as is shown in Diagram 15. You do have to play the inside liberty to capture the stones, but you must play it last when it’s too late for it to count against you.

Diagram 16

In Diagram 16, Black has an extra outside liberty. The count is: Black five (4 outside + 1 inside); White four (3 outside + 1 inside). Even if White plays first, Black can win. And if it’s Black’s turn, he can play elsewhere and still win. The position is settled: White is dead.

Diagram 17

Diagram 17 shows a more complicated fight that might easily occur in a real game. This is no more difficult to count if you understand the principles. Some people like to count the sequence of moves: Black here, White there, Black here, White there, and so on. I cannot recommend this method. It’s too easy to skip a liberty or count the same liberty twice if you are switching back and forth from one side of the board to the other. Instead, count the liberties around the edge of each group.

Diagram 18

Count the points labeled W: 1, 2, 3, …, 8. Add one for the inside liberty at A to make a total of nine. Count the Bs: 1, 2, 3, …, 8 plus one at A equals nine. Aha: nine to nine. The position is unsettled. That’s not hard, is it?

Diagram 19

Diagrams 19 and 20 show the moves in the capturing race when Black and White play first, respectively.

Diagram 20

Summary of Type 1 Fights: Zero or One Inside Liberty

When there are no inside liberties, count the outside liberties for each side. If the numbers are equal, then the position is unsettled and whoever plays first wins. If one side has more liberties, the position is settled: the side with more liberties is alive and can play elsewhere and still win; the side with fewer liberties is dead.

When there is one inside liberty, count the outside liberties and add the inside liberty to each side’s count. If the numbers are equal, the position is unsettled and whoever plays first wins. If one side has more liberties, the position is settled. Play on the outside liberties first and the inside liberty last.

In the next section we look at fights with two or more inside liberties. Here the situation is rather different and people often make reading mistakes (dan players pay attention).

Type 2 Fights: Two or More Inside Liberties

Diagram 1

The left side of Diagram 1 shows a Type 1A fight, which we just studied. The right side shows a similar looking fight, but there are two inside liberties. What difference does that make? Think about it before reading the next page.

Diagram 1 repeated

On the left side, Black and White both have four liberties. Whoever plays first wins. When you consider groups with various numbers of inside liberties, the sequence: 0, 1, 2, 3, 4, … is not a smooth progression. There is a yawning chasm between 1 and 2. On one side are 0 and 1, while on the other side are 2, 3, and above. It’s like ice warming up degree by degree towards its melting point. The smooth progress is suddenly interrupted by a phase change as the ice turns into water, which has completely different properties from ice. A fight where there are two or more inside liberties is completely different from one with one or zero. Let’s look at some examples.

On the right side, Black and White both have three outside liberties, and there are two inside liberties.

Diagram 2

Diagram 3

As Diagram 2 shows, Black could capture the white stones in five moves. But that’s not going to happen in a real game: White will resist. When Black plays 1–3–5 in Diagram 3, White plays 2–4–6. The result is a standoff, called seki.

Diagram 4

If Black next plays 1 in Diagram 4 to put White in atari, he puts himself in atari and White captures him. Seki is a position where neither side wants to continue playing because it would be suicidal. In a Type 1 fight, the outcome can never be a seki: one side or the other must die. Type 2 fights are completely different.

Diagram 5

If Black and White have the same number of outside liberties and there are two or more inside liberties, the result is a seki. In Diagram 5, however, Black has seven outside liberties, while White has only three.

Diagram 6

Diagram 7
2, 4, 6, 8: elsewhere

In this case, Black can play on all five of White’s liberties, including the inside ones, before White can catch up, as Diagram 6 shows.

On the other hand, if White plays first, as in Diagram 7, there is no way he can capture Black. Not only can Black win by playing as in Diagram 6, where he was three moves ahead, he can also ignore White and play elsewhere again and again and again and still live in seki. Of course, Black has to be careful not to ignore White too many times, otherwise he will look rather foolish.

Now we can formulate some guidelines for reading out Type 2 fights:

• In a Type 2 fight, the side with more outside liberties is unconditionally alive.

In this type of fight and in all the later types, I shall use the term “favorite” to describe the side that has an advantage. The other side is the “underdog”. He is at a disadvantage, but he might be lucky if he has a large number of outside liberties. The criterion for judging who is the favorite depends on the type of fight. Here, the favorite is the side with more outside liberties. In more complicated situations involving eyes the criterion is not so simple, as discussed later in this chapter.

Diagram 8

Diagram 9

Diagram 8: Black is the favorite; he is alive. Does Black have enough liberties to kill White or is White alive in seki? To kill White, Black must play on all White’s outside liberties and on the inside liberties. Diagram 9 shows that when Black plays first, he can capture White.

To determine whether the position is settled or unsettled, we simply compare the number of liberties on each side. If the numbers are equal, the position is unsettled and whoever plays first gains. The problem is deciding which points are liberties. In Diagram 8, White has five liberties because that is how many moves it takes Black to capture him. But White cannot capture Black unless Black plays elsewhere several times. So how many liberties does Black have? What we want is to find a useful number that indicates whether Black can capture White. Saying that Black has seven liberties is misleading. The obvious number to choose might seem to be the number of outside liberties that Black has. However, …

Diagram 10

In Diagram 10, Black has one outside liberty fewer than in Diagram 8. Black is still the favorite (four outside liberties to three). Black has four outside liberties against White’s total of five outside and inside liberties. So White should be safe, with the position being settled as a seki, right?

Diagram 11

Wrong. Diagram 11 may come as a rude shock to people who make facile assumptions like that. When Black plays first, White dies. To get the threshold for an unsettled position, we must count one inside liberty for the favorite. Note that this is not the case in fights that involve eyes, so it may explain some of the mistakes that people make.

Reading Type 2 Fights

Diagram 10 (repeated)

Returning to Diagram 10, here is the correct way to read the fight. Black is the favorite (four outside liberties to three). Black has five liberties (four outside liberties plus one inside). White has five liberties (three outside and both of the inside liberties). The number of liberties is equal, so the position is unsettled. The favorite (Black) is unconditionally alive. If he plays first, he can kill. If the underdog (White) plays first, he can live in seki.

It would be unkind to expect you to learn a mysterious rule, “count one inside liberty for the favorite in Type 2 fights,” so let’s investigate a little further.

Diagram 12

A useful way of analyzing the position is to cancel out equivalent liberties, as shown in Diagram 12. Here, we reduce the position to exactly two inside liberties (the minimum Type 2 fight) by adding an equal number of moves for each side.

Diagram 13

Now it should be easy to see that when Black plays first, as in Diagram 13, he wins. Black 1 fills an inside liberty that belongs to White. White 2 fills Black’s last outside liberty, but Black has one remaining liberty on his group: the final inside liberty. This is the one that Black, as favorite, counts for himself. By mentally canceling out liberties on both sides until there are only two inside liberties left, one can easily determine the status of the fight.

Diagram 14

As Diagram 14 shows, if Black is left with no outside liberties, the result is seki (settled). If he has one outside liberty, Black can win if he plays first (unsettled). And if he has two or more outside liberties, he can play elsewhere and still win (settled). Note the word “mentally” in the previous paragraph. Don’t play these moves in a real game in order to see what happens. Read the fight out in your head and only play it out if it works. Once your stones have been taken off the board they have no potential left, not even for ko threats.

Diagram 15

Another approach, shown in Diagram 15, is to cancel the liberties all the way down to where Black puts White in atari. Here again it should be easy to see that Black can capture White if he plays first. Feel free to use whichever approach you prefer. It’s the result that is important, not the method.

Diagram 16

Instead of counting one inside liberty for the favorite, can we subtract one from the underdog’s count? No, we cannot. It’s not the same. Consider Diagram 16.

Diagram 17

The underdog’s number of liberties is physically meaningful and should not be distorted. The favorite’s number of liberties is an arbitrary number chosen for our convenience. In Diagram 17, Black needs to capture the white stones at the top before his cutting stones in the middle get captured. The white stones at the top really do have five liberties, not four. Therefore, as Diagram 17 shows, Black loses by one move even if he plays first.

To summarize: In a Type 1 fight, if there is an inside liberty (Type 1A), the favorite counts one inside liberty and so does the underdog. In a Type 2 fight, the favorite counts one inside liberty, while the underdog counts all of them. Thus, in fights that do not involve any eyes, the favorite always counts exactly one inside liberty unless there are none at all; the underdog counts all the inside liberties.

Diagram 18

In Diagram 18, Black 1 is playing with fire; this is dangerous and should be avoided. You should usually play on the outside liberties first and the inside liberties last. Actually, Black 1 is not fatal in this case: Black still wins the fight. But it’s a very bad habit to get into. Reducing the number of inside liberties from two to one changes the type of fight. No longer is Black safely alive in seki. It’s now a fight to the death. This is like in the movies when the hero throws down his gun to make a fair fight against his unarmed opponent. There is no need to do this in go; use every advantage you have.

Diagram 19

In Diagram 19, Black 1 is bad but not fatal; Black 3, however, is suicidal. The reason is that in a Type 2 fight (where there are two or more inside liberties), although all the inside liberties count for the underdog (White here), one inside liberty also counts for the favorite. Therefore, when Black plays 3, he is playing on one of his own liberties.

Diagram 20

Reading practice. You should be able to read out this fight in seconds. If you can’t, check the following explanation and then go back and try again. All you have to do is identify the type of fight and count the liberties on each side. Simple.

The procedure goes like this: There are no eyes anywhere and there are at least two inside liberties, so it’s a Type 2 fight. Black has more outside liberties, so he is the favorite and unconditionally alive. Is White alive in seki or can Black kill him? Count Black’s liberties: seven outside liberties and one inside liberty making a total of eight. (Don’t forget to count one inside liberty for the favorite.) White has four outside liberties and four inside liberties making a total of eight. Eight against eight. The two numbers are equal, so the position is unsettled. Black is alive.

Diagram 21

If Black plays first, he can kill White.

Diagram 22

Alternatively, you can mentally cancel out an equal number of liberties on each side until there are only two inside liberties left; since Black has one outside liberty left, he has time to kill White (the position is unsettled).

Diagram 23

If White plays first, he can make a seki. Does that analysis take long? The only difficult bit is knowing to count one inside liberty for the favorite. After that, it’s just a matter of counting liberties accurately, without missing any or counting any twice. If you want to go back to the beginning of this section on Reading Type 2 Fights and read through it again, tap here.

Diagram 24

Diagram 24 shows one more example for practice. First, read it out quickly; then take your time to check your answer. Practice until you are confident you will get it right every time in an actual game, even under time pressure. You can check your answer here.

Approach Moves

Diagram 25

Can you read out the result of this capturing race? If Black plays A, White will capture at B.

Diagram 26

However, in this simple situation, Black can play on all the other liberties first and finally capture with 5.

Diagram 27

In Diagram 27, on the other hand, there are two inside liberties. Black can’t save two different places until last.

Diagram 28

Black has to connect at 5 before he can play 7, so the result is a seki.

Diagram 29

If he plays 5 and 7 on the inside liberties here, he is playing on one of his own liberties, so he kills himself.

Liberties Redefined

How many liberties?

At this point we need to move on to a more sophisticated definition of liberties. The marked white group has two liberties. But how many do the marked black stones have? The simple answer is two, because Black has two physical liberties or vacant points adjacent to his stones, but then we must consider that White can’t actually play on either of them. If White plays at either A or B, he puts himself in atari and Black will capture him. First, he must play at C. So, rather than saying, “Black has two liberties, but White must make an approach move at C,” let’s simply redefine the number of liberties as the number of moves it takes to capture the stones. Thus, we will say that Black has three liberties. This change in definition will make things much easier for us.

Diagram 30

White has no outside liberties, so Black is the favorite. White has to play four approach moves: He has to play A before B, C before D, E before F, and G before H. Black also has two other outside liberties marked ✕. Plus, as the favorite, Black counts one inside liberty. That makes eight (counting the four approach moves White must make) plus two (the ✕s) plus one inside liberty equals eleven liberties for Black. White also has eleven liberties (all inside), so the position is unsettled.

This gives us an easy way to deal with approach moves when counting out capturing races.

Summary of Type 2 Fights: Two or More Inside Liberties

When there are two or more inside liberties, the side with more outside liberties is the favorite. The favorite is unconditionally alive; the underdog either dies or lives in seki. Count the liberties on each side. The favorite counts all his outside liberties and one inside liberty. The underdog counts all his outside liberties and all the inside liberties. If the numbers are equal, the position is unsettled.

• Don’t forget to count one inside liberty for the favorite in a Type 2 fight.

General Principles for All Types of Fights

• If the number of liberties is equal, the position is unsettled. One problem is knowing who gets the inside liberties.

• If the position is one that can become a seki, the inside liberties protect the underdog. The favorite needs a lot of outside liberties to overcome the seki and kill.

• Play on the outside liberties first and the inside liberties last.

• In an unsettled position, the winner captures in gote and the loser gets sente to play elsewhere. There is no fate more ignominious than to die in gote (DIG).

Summary of Types of Fights

Type 1: Zero or One Inside Liberty

Type 1

Each side counts his outside liberties and the inside liberty if there is one. If the numbers are equal, then the position is unsettled and whoever plays first wins. Seki is not possible.

Type 2: Two or More Inside Liberties

Type 2

The side with more outside liberties (the favorite) counts all his outside liberties and one inside liberty. The underdog counts all his outside liberties and all the inside liberties. If the numbers are equal, the position is unsettled. The favorite can kill; the underdog can make a seki.

• Don’t forget to count one inside liberty for the favorite in a Type 2 fight.

Chapter 3: Simple Counting Practice

Here are some simple examples of capturing races for practice. You should be able to solve them at a glance. It’s just a matter of identifying the type of fight and counting liberties. Watch out for approach moves and sente moves, but apart from those there are no clever moves to find.

Positions

What is the status of each of these positions? Consider both Black and White to play: the pair of problem diagrams lets you try your moves. If you think that the position is settled and that the side to play should therefore play elsewhere in any of the positions, then tap on any stone in the problem diagram and from the popup menu, choose Pass.

Position 1

Black to play

White to play

Answer 1

Black wins.

White wins.

Both Black and White have three liberties. Whoever plays first wins. If Black plays first, he can capture the four white stones. If White plays first, he can capture the three black stones.

For simple counting purposes, all of the liberties are equivalent, so they can be played in any order. In an actual game, however, it’s best to play from the outside (living stones) to minimize the loss in case your opponent plays in this local position as ko threats for a ko fight elsewhere on the board and you choose to ignore his local move and lose this capturing race in order to resolve the ko.

Position 2

Black to play

White to play

Answer 2

Black wins.

White wins.

Both Black and White have four liberties. Whoever plays first wins.

Part Two: Applications

Chapter 5: Fighting Tactics

In the previous chapters we have studied the basic types of fights and read out the status of each fight to see who was winning. You didn’t have to find any clever moves, as you do in tesuji or life and death problems. In this part, you will build on the reading skills learned so far in order to consider where to play when fighting.

Many book problems and also real game positions are difficult because it is hard to evaluate the eventual result and see whether it is good. Therefore, instead of presenting problems in the “Black to play” style, I shall present various possible end results first, so you can work out for yourself which ones are desirable. Then it’s easier to find the path towards the target.

The Throw-in

Position 1

Diagram 1

Position 1 shows a very simple fight that you should be able to read out instantly. Diagram 1 shows the fight a few moves earlier. Black wants to play on the white liberties, but which one should he play first?

Diagram 1a

If Black plays 1 in Diagram 1a, White will play 2. Then, after Black 3 and White 4, the result is easy to read. Black is a move behind.

Diagram 1b

However, the throw-in at 1 in Diagram 1b is a powerful tesuji. After Black 1, if White fills in one of Black’s outside liberties, Black connects at 3 and the result is easy to read. Black is a move ahead.

Diagram 1c
4: connects

If White captures with 2 in Diagram 1c, Black plays atari at 3, forcing White to connect. Now, after Black 5, we get the result in Position 1, which you have already read out. Black wins.

You will find many examples of this technique in books such as Richard Bozulich’s Get Strong at Tesuji, the series Graded Go Problems for Beginners, Yilun Yang’s Go Puzzles, Volumes 1 and 2, and James Davies’s Tesuji. However, it is important to understand that there are positions where the throw-in is a bad move. You need to think of the tesuji, read out the continuation in your head, and evaluate the result. If it works, fine. But if it doesn’t work, do not play it; look for another move instead.

Position 2a

Position 2b

Positions 2a and 2b show two possible results of a fight. What is the status in each position? They are both Type 2 fights, where there are two or more inside liberties. Black has more outside liberties, so he is the favorite.

In Position 2a, the fight is unsettled: if Black plays first he can kill White, and if White plays first he can live in a seki. In Position 2b, there is one more inside liberty. This belongs to the underdog, which is White. This fight is settled. Even if Black plays first, he can’t kill White, who is alive in seki. Of these two figures, Position 2a is preferable for Black.

Diagram 2: Black to play

Diagram 2 shows the same fight a few moves earlier. Black to play.

Diagram 2a
4: connects

Diagram 2b

Once again, the throw-in, at 1 in Diagram 2a, is the tesuji. Black 3 is atari, forcing White to connect with 4. Now the fight is the same as Position 2a. It’s Black’s turn to play, so if he fills one of White’s outside liberties he can kill him. Playing Black 1 in Diagram 2b lets White take the vital point and connect at 2. This is the result shown in Position 2b. Even though it’s Black’s turn next, he cannot kill White. The fight is settled: it’s a seki.

Position 3a

Position 3b

So far, it has been rather easy. Now we get to the tricky bit, where it’s easy to go wrong. First, read out the status of Position 3a and of Position 3b.

Diagram 3: Black to play

Next, look at Diagram 3, where it’s Black to play.

Diagram 3a
4: connects

The throw-in of Black 1 in Diagram 3a is the instinctive response of many players who have learned the throw-in tesuji without fully understanding it, but in this position it fails. After the throw-in and atari, White connects with 4 at 1 and the result is the same as Position 3a. Black needs to add another move at 5 in Diagram 3a in order to live in seki; otherwise, White can kill him. Do not be satisfied with that result and think that living in gote counts as a success.

Diagram 3b

Diagram 3a is a failure for Black. Instead of throwing in, he should simply fill an outside liberty with 1 in Diagram 3b, forcing White to connect at 2. This result is the same as Position 3b. The situation is settled. Black is already alive in seki and can take sente to play elsewhere.

The important point to understand about the throw-in tesuji is that, while it efficiently reduces liberties, it’s essential to know whose liberties you are reducing. In Diagram 3, Black is the underdog because he has fewer outside liberties. Therefore, the inside liberties belong to Black. If he throws in at 1 in Diagram 3a, he reduces his own liberties. This is a sharp contrast to the first two positions.

Position 4a

Position 4b

Positions 4a and 4b show two possible results of a Type 3 fight, where Black has an eye and White does not. Position 4a is a more desirable result for Black because he counts the inside liberties; the status is unsettled. In Position 4b, on the other hand, Black is dead.

Diagram 4: Black to play

Diagram 4 shows the fight a few moves earlier, where it is Black to play. Think about how Black should play before reading on.

Diagram 4a

Diagram 4b

If Black fills an outside liberty with 1 in Diagram 4a and White connects at 2, the result is easy to read out. The position is unsettled and Black will win because it’s his turn next. The throw-in at 1 in Diagram 4b is a mistake because in a Type 3 fight, the inside liberties belong to the side with the eye. So here Black is reducing his own liberties.

Diagram 4c

Diagram 4c shows the continuation, which becomes the same as Position 4b after White connects at 8. White 10 puts Black in atari and it’s all over.

Diagram 4d

White 2 in Diagram 4a simplifies the situation. Instead, White 2 in Diagram 4d offers Black more opportunity to make a mistake. Black must not try and take advantage of White’s failure to connect by making a throw-in. It’s essential for Black to refrain from making the throw-in right up until the end. White has no hope of winning a Type 3 fight unless he plays all the inside liberties, so Black must not make a throw-in on an inside liberty.

Guidelines for winning a fight:

• Reduce your opponent’s liberties, not your own. A throw-in is a tesuji for reducing liberties, but make sure they are not your own liberties.

Chapter 6: Problems

Here are some problems to test whether you can apply the principles we have studied in Part One. Which type of fight is involved? If the type is still unsettled, which type will give the best result? You need to mentally play a few moves and reach a position that is easy to count.

All of the problems in this chapter are Black to play. If you think that the position is settled and that Black should therefore play elsewhere in any of the positions, then tap on any stone in the problem diagram and from the popup menu, choose Pass.

Problem 1

Black to play

Answer 1

Correct

Black seems to have fewer liberties than White. However, Black 1 is sente because it threatens to connect out, so White must answer at 2.

Failure

Black 1 here is not good. White can answer 3 at 4, so Black loses.

Problem 5

Black to play

Answer 5

Correct

Black should make an eye in the corner. This forces White 2. Next, Black throws in at 3, preventing White from making an eye as well.

Failure

Black’s hane at 1 is a mistake. White 2 is the best move (the vital point for both sides).

Continued

The result is a ko.

Chapter 7: Commented Games

Let’s look at some examples of capturing races from professional games.

In games between beginners, one often sees capturing races that result in a large group of stones dying. This seldom happens in professional games. Why not? Because beginners play moves just to see what will happen. Professionals are very good at counting liberties and reading out capturing races. They know what the result will be, so they don’t play sequences that end in failure.

In professional game records, there are very few capturing races. But that doesn’t mean capturing races are unimportant. On the contrary, they are crucial to almost every game, but they lurk unseen in the unplayed variations. A game record is like the tip of an iceberg: the players consider far more sequences than actually appear on the board. The source of instructive material about capturing races in professional games is the commentary.

Game 1

Having said that, the first example is an exception in that most of the game consists of one huge fight that comes to a decisive conclusion. I like it because I think amateurs like us can relate to it. It’s a lightning game and the professionals didn’t have time to read everything out perfectly. So some of their play is intuitive and they did make mistakes.

Komatsu vs. Nakazawa

This game is from the 40th (1992–1993) NHK Cup between Komatsu Hideki then 8 dan (Black) and Nakazawa Ayako then Women’s Honinbo (White). The images are from the NHK TV broadcast.

Ogawa and Ishikura

The commentary was by Ishikura Noboru 8 dan with assistance from Ogawa Tomoko 5 dan. This was Ishikura’s first NHK tournament commentary, although he was the NHK lecturer not long before, and he did a fine job of explaining what was going on. Since the game finished quite early, there was an extensive post-game analysis in which the players (mostly Komatsu actually) added their comments.

Moves 39–40

Skipping over the opening, the action starts at move 39. At this point Black would like to play in two places: on the left (for example, around A), to save his weak stones, and also at the top. When he chooses to defend the top, White naturally attacks on the left with 40. Next, a peaceful strategy would be for Black to abandon his stones on the left and sacrifice them on a small scale by pressing in the bottom left corner at B.

Moves 41–47

However, Black stubbornly sets his stones in motion with 41. This is the correct move locally: it creates cutting points and potential. White 44 was described as the proper move.

Diagram 1

White would of course like to shut Black in and capture him by playing at 3 in Diagram 1, after first exchanging 1 for 2, but unfortunately it doesn’t work. Although Black can’t make two eyes on the side, he has at least three liberties, while White has a cutting point in the center. In fact White is quickly caught in a net. This is where reading skills are essential; most reading covers variations that are not played out on the board.

Diagram 2

Diagram 2 shows another line, exchanging 3 for 4 before playing 5. No definite conclusion was reached on its outcome, but all the professionals felt uncomfortable with White’s position if Black pushes out at A.

Move 48

Instead of White 48, …

Diagram 3

… playing 1 in Diagram 3 is very bad. Expecting Black to connect is too optimistic. Black pushes through and cuts, delighted to be able to sacrifice a few of his heavy stones in exchange for playing 8 and 10.

Moves 49–57

Black 49 invites White to play atari at 51, because Black is happy to play atari below and start a ko; he has lots of local ko threats.

White 52 is necessary. Even if Black were only to get a ko in the corner, that would be unbearable for White. But in fact the post-game analysis concluded that Black can kill the corner unconditionally if White omits 52. Black 57 is probably an overplay.

Diagram 4

It’s not hard for Black to live at this stage, as Diagram 4 shows, and he will still have several cutting points in White’s position to aim at. But Black has been patient long enough and thinks it’s time to counterattack.

Move 58

White 58: Both Komatsu and Ishikura expected the descent at 1 in Diagram 5.

Diagram 5

Komatsu planned to answer White 1 with A. Ishikura looked at what happens if Black answers by pulling out the stone in the middle. First of all, White 3 is a bad move. There is no ladder with White 5 at 6, so Black can press with 4 and 6 in sente and then capture the white stones in a net.

Diagram 6

The proper move is the diagonal one at 3 in Diagram 6. The sequence to 14 seems unsuccessful for Black, but a stone around A would make all the difference.

Moves 59–62

Black might contrive to play such a move in sente while threatening the three white stones on the left. However, there is too much uncertainty at the moment, so Black presses on the left first with 59 to build up strength. The potential in the center remains lurking below the surface for the next several moves.

White 60: This is a good move that took Komatsu by surprise. He was expecting the usual good shape move of 62. The 60–61 exchange reduces Black’s liberties by one.

Diagram 7

While Black was thinking, Ishikura took another look at pulling the center stone out at 1 in Diagram 7 in response to 60. What effect does Black’s extra move at 59 () have?

White 2 reduces Black to only five liberties in sente, but does White have enough liberties in the center? The sequence to 15 is similar to Diagram 6, but in response to White 20, Black can wedge in at 21 and connect at 25 in sente. With 29, White is finally trapped. Presumably, therefore, White would resist in some way.

Diagram 8

For example, she might hane at 6 in Diagram 8. Although this allows Black to capture the two cutting stones and escape, White captures three stones in return, so all is not lost. At this stage, though, rather than merely trying to live, Black is out to kill White on a large scale. Going back to Diagram 7, White 10 there is essential.

Diagram 9

If White defends her stones at the bottom with 1 in Diagram 9 instead of 10 in Diagram 7, she gets caught in a snapback at the top.

Diagram 10
9 at

White could consider playing 6 in Diagram 7 at 1 in Diagram 10, before defending the bottom stones with 3. However, it’s necessary to read out the continuation, which doesn’t look good, as we will see later on in a more detailed analysis of a similar position.

Moves 62–64

Black 63 continues to lean on the left in order to gain leverage against the center. While Black was thinking about move 65, Ishikura had yet another look at the precarious position in the center. If Black answers White 64 by pulling the stone out, what happens this time? White’s stone at 62 neatly prevents Black’s wedge at 21 in Diagram 7.

In the full book, this game is commented to the end and three other games are also presented.

About the Author

Richard Hunter

Richard Hunter is a British go player currently living in the UK. He lived in Tokyo, Japan, from 1980 to 2008. He was introduced to the game by his elder brother, Derek (then British Go Association Secretary), and began playing at Birmingham University Go Club and then at Oxford University, where he served as club secretary and president. He attended the opening of the London Go Centre, where he met Iwamoto Kaoru 9 dan and Magari Reiki 9 dan and later lost a 9 stone game to Magari in Bristol. Hunter was a member of the BGA council in 1978.

Hunter’s relocation to Tokyo allowed him to take lessons from Iwamoto and some of his disciples, and he eventually managed to get to four stones against Iwamoto and three stones against Magari. He was a regular contributor to the British Go Journal from 1991 to 2006. He received a UK 4 dan certificate in 1991 but currently plays as 3 dan. He regularly plays in British tournaments and has in the past played in several European Go Congresses, most recently Dublin 2001, and one US Go Congress (Washington DC, 1994). While in Japan, Hunter enjoyed browsing through second-hand book stores in Tokyo looking for old go books.