© 1976 and 2000 by James Davies and Ogawa Tomoko

Elementary Go Series, Volume 6

The Endgame

by Tomoko Ogawa 4 dan & James Davies

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The endgame tends to be the neglected side of the game of Go. This is strange indeed, for it also tends to be where the outcome is decided, and frequently accounts for about half the stones played.

This volume, by a Japanese professional Go player and a strong American amateur, seeks to rectify this situation by setting forth the basic tactics, strategies, and counting techniques needed in the endgame.

Everything from the smallest local tesujis to the global macroendgame is covered with numerous examples and problems, many of them drawn from the Japanese author’s professional games. The reader is encouraged to think for himself and, by doing so, will certainly become stronger.

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About the Authors

Tomoko Ogawa

was born in 1951 in Nagoya. In 1965, at the age of fourteen, she won the Women’s Amateur Honinbo Tournament, which led the following year to her entrance into the Kitani Go School in Tokyo. There she became a professional go player. Her promotion record is:

Shodan 1970
2 dan 1971
3 dan 1974
4 dan 1975

In 1975 she scored an impressive 18 wins, 7 losses in professional competition and was named the outstanding woman player of the year by Kido magazine. She is also known abroad, having made go-playing visits to China and Europe.

James Davies

was born in 1945 in Philadelphia. He graduated from Oberlin College in 1967 and entered graduate school at the University of Washington, only to have a mathematics professor interest him in the game of go. In 1970 he came to Japan, where his go playing has advanced to the amateur 6-dan level.

Besides writing for the go books, he is a regular contributor to quarterly magazine Go World. He lives with his wife in Yokohama.

Copyright Page

Elementary Go Series, Volume 6

The Endgame

Tomoko Ogawa 4 dan & James Davies

Published by
Kiseido Publishing Company
Kagawa 4–48–32, Chigasaki-shi,
Kanagawa-ken
Japan 253–0082

© 1976 and 2000 by James Davies and Ogawa Tomoko

All rights reserved according to international law. No part of this book may be reproduced by any mechanical, photographic or electronic process, nor may it be stored in a retrieval system, transmitted or otherwise copied for public or private use without the written permission of the publisher.

ISBN of the printed version: 978–4–906574–15–5

Converted for SmartGo Books by John Mifsud.

Preface

In this book we have tried to do two things: to cover the basic moves and principles of the endgame; and to show how they are applied in actual game situations. Go is an intellectual pursuit, so we assume that you will want to try to think through as much as you can on your own, and not just take our word for it that such-and-such is a correct move. Accordingly, more than half of the following pages are given over to problems. Working them out may require some patience, but it should make you stronger in a very tangible way.

The primary responsibility for the five chapters is divided as follows.

Ogawa: Chapters 1, 4, and 5
Davies: Chapters 2 and 3

We consulted, however, throughout the book. One of us (Davies) drafted the entire text, and the other of us (Ogawa) passed judgement on all the diagrams.

Our thanks go to the Nihon Kiin for the use of their facilities while working on this book, and to James Kerwin, who proofread the manuscript and suggested a number of modifications.

Tomoko Ogawa
James Davies
Tokyo, Japan
June, 1976

Contents

The Endgame

About the Authors

Copyright Page

Preface

Chapter 1
Introducing the Endgame

The chapters in gray are included only in the full book.

Chapter 2
Counting

Chapter 3
Endgame Tesuji

Chapter 4
The Macroendgame

Chapter 5
Games

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About SmartGo Books

Chapter 1

Introducing the Endgame

The endgame could be called the small-scale stage of the game of go. During the opening and middle game the board is open and the fighting tends to range all up and down and across it. By the endgame the board has been more or less divided up into separate territories, and most of the fighting tends to affect only two of them, occurring at a mutual boundary. The opening and middle game are much like a single large battle between two armies; the endgame is like a number of smaller battles going on in different places simultaneously. In a way this makes the endgame easier, because the local engagements, being smaller, are easier to read out, but in a way it makes it harder because one’s attention must be focused on several areas simultaneously.

Whether you find it easy or hard, one thing can be said about the endgame: it is decisive because it comes last. True, there is sometimes no endgame – one player loses a large group of stones and resigns early – but in all other cases the endgame determines the victor. Reversals of the lead are frequent. Watch a professional game: you will see the players most tense and serious during the endgame. The endgame may be less exciting than the middle game, but there is a great amount of satisfaction to be gotten from playing it well, no small part of which comes from winning.

It is not surprising that strong professional players are generally strong in the endgame. Sakata, 9-dan, is a brilliant endgame player. Rin, 9-dan, is noted for his ability to squeeze the last drop of profit from an endgame situation. Ishida, 9-dan, considers his greatest strength to lie in the endgame. It would be hard to find any professional or strong amateur who was really weak in the endgame.

What makes for strength in the endgame? One’s reading ability and one’s eye for tesuji are important, just as they are in the middle game. Another factor is one’s ability to count and determine the relative sizes of different moves. These tactical matters, however, are not everything. More important than counting to find the biggest move, for example, is finding ways to make profit in sente, or to keep the enemy from doing so. A player who could not count at all, but understood the difference between sente and gote, would have the advantage over an opponent suffering from the reverse affliction. Knowing whether you are ahead or behind in the game and varying your strategy accordingly is also important. So is making sure that you are always looking at the whole board, not focusing your attention on one part of it and forgetting the rest, as so many amateurs seem to do.

Perhaps the best way to explain the kind of thinking that goes into the endgame is to take you through an actual game and show you directly, and that is what this chapter will do. The game is a professional one, so as we go through it you will see how professionals count, and get lots of glimpses of professional strategy, intuition, and reading in action. Unfortunately, we cannot avoid exposing you to the difficulties and messy details of the endgame, too, but perhaps that is just as well. It is by mastering such difficulties and details that one becomes stronger.

As you proceed through the chapter, you will find some material set aside in boxes. Most of these boxes contain analyses that support statements made in the text, and they can be skipped over without breaking the continuity of the chapter. We recommend that you do skip over them on your first reading and go back to them later, perhaps after finishing chapter 2. Several of the boxes show how the values of certain moves can be counted, and this general method of counting will be explained fully in chapter 2. [In this SmartGo Books edition, the boxes are replaced by indented text like this paragraph.]

The following game was my (Ogawa’s) third game in the 1971 Oteai (the professional ranking tournament). My opponent, who had the white stones, was Haruo Kamimura, and at the time we were both shodan. Both of us had our eyes on promotions that year, so as you will see, we played very hard. The conditions were six hours per player and no komi. Kamimura, who is now 5-dan, is quite strong. I had a rematch against him recently and lost.

Figure 1 (1–50)

＞＜ ▶︎

Figure 1 shows the first fifty moves, and as you can see, my opponent concentrated on building up a large territorial framework on the left side and in the center, giving me all four corners. By the end of the figure, the weakness of the white group on the lower side had become the important factor in the game.

Looking back at the upper left corner, I wonder if you would have been able to resist the temptation to capture at a, instead of playing White 24 or Black 25. This is precisely the sort of move that can and should be saved for the endgame.

Dia. 1

＞＜ ▶︎

Suppose Black plays 1 and 3 in Dia. 1, instead of 25 in the figure. Her two-stone capture is certainly big, but the corner was alive even without it and White 4, as compared with a black play in that direction, is big too. Moves like Black 1 and 3, that do not attack or defend but just take profit, are not very attractive during the opening and middle game.

Figure 2 (51–66)

＞＜ ▶︎

I attacked White’s weak group with 53, and he spent the next twenty moves or so defending it. White 66, to point out just one stone in this sequence, was a well-timed forcing play.

Dia. 2

＞＜ ▶︎

If I answered it by giving atari at 1 in Dia. 2, White would play 2, and if I lost this ko, I would stand to lose four more stones to White a.

Dia. 3

＞＜ ▶︎

If I played safe by answering at 1 in Dia. 3, however, then after forcing me with a in sente (as he does at 70 in the next figure), White could connect at 2 to get a living shape.

Figure 2a (66–77)

＞＜ ▶︎

I rejected these two diagrams and answered White 66 at 67, but that made 74 sente, so White was able to live by playing 74 and 76.

He was not absolutely alive, because I could still force a ko with a, but he had so many ko threats to escape, starting with b, that the ko was not practical yet. What I had to do now was invade his thin position on the right side with Black 77 and wait for a chance to start the ko later.

Figure 3 (78–93)

＞＜ ▶︎

Invading the right side with 77 to 85 was extremely large; a fair amount of what might have been white territory was now black territory. Moves like these, that transfer territory from one player to the other, are twice as valuable as moves that just reduce enemy territory or just enlarge friendly territory.

At Black 83 I could have linked up to the upper right with 1, 3, and 5 in Dia. 4.

Dia. 4

＞＜ ▶︎

It is hard to say which is better, Dia. 4 or the figure, but Dia. 4 would leave White a big move at 6. If White had answered Black 83 at a, then I would have carried out Dia. 4.

Figure 3a (94–104)

＞＜ ▶︎

After whittling down the lower left corner in sente White exchanged 94 for 95, advanced to 96, bent around me at 98, and cut at 100, forcing me to connect at 103. Black 95 and 103 occupied neutral points, while White 94 (not to mention White 98, 100, etc.) was in a useful position for making territory, but I had compensation in that White had lost most of his ko threats, so the ko on the lower side was now a serious matter.

Figure 4 (105–111)

＞＜ ▶︎

White could not afford to lose this ko, so he ignored my first ko threat and captured at 8. The exchange in this figure marked the close of the middle game, and while my opponent was thinking over the first move of the endgame, I surveyed the board and made a rough count of the territories to see who was ahead. This is something that professionals do again and again throughout the course of a game, even in the opening, and I would like to show you how we do it.

The black territory in the lower right was already pretty well settled, so I could get an exact figure for it. First I had to make some assumptions about what its final boundaries would be.

Dia. 5

＞＜ ▶︎

I had to assume that eventually White would be able to play 1 in Dia. 5 in sente; if I did not answer at 2, he could slide all the way in to a. Similarly, I had to assume White 3 and Black 4. To complete the boundary on the right edge I put in White and Black . Note that I mentally added equal numbers of black and white stones.

Dia. 6

Next I counted the amount of territory left. I can do this accurately in under five seconds by counting pairs of points, as in Dia. 6. There is a neat column of 8 pairs going down the right edge, two points for the white prisoner at 9, a pair at 10, four more pairs going across the bottom edge at 11 to 14, a pair above them at 15, and finally a pair left over at 16. That makes 32 points, and adding on a point for the stone I captured at ✕, I saw that I had 33 points here.

Taking the rest of my territories, I estimated the lower left corner at a glance as 5 points. I estimated the upper left corner pessimistically as 10 points, and the upper right corner optimistically as 15 points. That gave me 33+5+10+15=63 points of secure territory.

Now why don’t you try estimating White’s territory? Assume Black a and White b on the left side, and don’t count anything for him in the neutral area in the lower right center. See if you don’t agree with me that even with the next move, it is hard for White to get 60 points overall, and so my prospects in the game right now were good.

Speaking of White’s next move, can you guess what it was before you turn the page?

Figure 5 (112–113)

＞＜ ▶︎

White started the endgame with 12, the largest move since besides seizing the open space between the two marked stones on the upper side, it threatened to invade the upper right corner. I knew from experience that my three-stone formation was vulnerable at either a or b, so after recounting to make sure that it would preserve my lead, I defended with Black 13. White had thus kept sente and could proceed to the next largest point. Can you guess where it was?

The following six diagrams show what could have happened if I had not defended with Black 13.

Dia. 7

＞＜ ▶︎

Given the continuation shown, White 1 in Dia. 7 is the most damaging invasion.

Dia. 8

＞＜ ▶︎

It may be possible to kill this invasion by descending at 4 in Dia. 8, but Black runs a risk in trying to do so because of the cutting points at a and b.

Dia. 9

＞＜ ▶︎

Dia. 10

＞＜ ▶︎

In any case, if White is afraid of Black 4 in Dia. 8, he can fall back on White 1 in Dias. 9 to 12. That invasion is unstoppable.

Dia. 11

＞＜ ▶︎

Dia. 12

＞＜ ▶︎

With Black 13 on the board ( in the two diagrams below), White’s invasions no longer work.

Dia. 13

＞＜ ▶︎

Dia. 14

＞＜ ▶︎

He is unconditionally dead in Dia. 13 (a and b are miai), and also in Dia. 14, where Black makes Black 4 possible.

End of sample. In the full book, this game is analyzed to the end.