The Game of Go/Chapter VII

by Arthur Smith

VII

THE END GAME

A work on the game of Go would not be complete without a chapter especially devoted to the subject of the end game.

On the average a game of Go consists of about two hundred and fifty moves, and we might say that about twenty of these moves belong to the opening, about one hundred and fifty to the main part of the game, and the remaining eighty to the end game. The moves which may be regarded as belonging to the end game are those which connect the various groups of stones with the margin, and which fill up the space between the opposing groups of stones. Of course, there is no sharp distinction between the main game and the end game. Long before the main game is finished moves occur which bear the characteristics of end game play, and as the game progresses moves of this kind become more and more frequent, until at last all of the moves are strictly part of the end game.

Toward the end of the game it becomes possible to calculate the value of a move with greater accuracy than in the middle of the game, and in many cases the number of points which may be gained by a certain move may be ascertained with absolute accuracy. Therefore, when the main game is nearing completion, the players survey the board in order to locate the most advantageous end plays; that is to say, positions where they can gain the greatest number of "Me." In calculating the value of an end position, a player must carefully consider whether on its completion he will retain or lose the "Sente." It is an advantage to retain the "Sente," and it is generally good play to choose an end position where the "Sente" is retained, in preference to an end position where it is lost, even if the latter would gain a few more "Me."

The player holding the "Sente" would, therefore, complete in rotation those end positions which allowed him to retain it, commencing, of course, with those involving the greatest number of "Me." He would at last come to a point, however, where it would be more advantageous to play some end position which gained for him quite a number of points, although on its completion the "Sente" would be lost. His adversary, thereupon gaining the "Sente," would, in turn, play his series of end positions until it became advantageous for him to relinquish it. By this process the value of the contested end positions would become smaller and smaller, until at last there would remain only the filling of isolated, vacant intersections between the opposing lines, the occupation of which results in no advantage for either player. These moves are called "Dame," as we have already seen.

This is the general scheme of an end game, but, of course, in actual play there would be many departures therefrom. Sometimes an advantage can be gained by making an unsound though dangerous move, in the hope that the adversary may make some error in replying thereto. Then again, in playing against a player who lacks initiative, it is not so necessary to consider the certainty of retaining the "Sente" as when opposed by a more aggressive adversary. Frequently also the players differ in their estimate of the value of the various end positions, and do not, therefore, respond to each other's attacks. In this way the possession of the "Sente" generally changes more frequently during the end game than is logically necessary.

The process of connecting the various groups with the edge of the board gives rise to end positions in which there is more or less similarity in all games, and most of the illustrations which are now given are examples of this class. The end positions which occur in the middle of the board may vary so much in every game that it is practically impossible to give typical illustrations of them.

Of course, in an introductory work of this character it is not practicable to give a great many examples of end positions, and I have prepared only twelve, which are selected from the work of Inouye Hoshin, and which are annotated so that the reasons for the moves may be understood by beginners. The number of "Me" gained in each case is stated, and also whether the "Sente" is lost or retained. To these twelve examples I have added eight positions from Korschelt's work.

I

Plate 35 (A)

The following stones are on the board: White, S 15, R 14, P 14, L 17; Black, R 16, Q 16, N 15, N 17.

If White has the "Sente," he gains eight "Me," counting together what he wins and Black loses.

White

Black

1. S 17. This is White's only good move; S 16 does not take advantage of the opportunity, and he cannot risk S 18.

2. S 16. If Black had had the move or "Sente," he could have avoided White's invasion by playing here.

Plate 35

3. T 16. An instance of "Watari."

4. R 17.

5. S 18. White cannot venture to play at R 18.

6. R 18. If Black neglects this, White would jump to Q 18.

White retains the "Sente."

II

Plate 35 (B)

The following stones are on the board: White, R 9, O 5, O 3; Black, P 7, Q 3, Q 4, R 7.

If White has the first move, it makes a difference of six "Me."

White

Black

1. P 2.

2. Q 2.

3. Q 1.

4. R 1.

5. P 1.

6. S 2. Black cannot neglect this move.

White retains the "Sente."

If Black had had the first move, the play would have been as follows:

Black

White

1. P 2.

2. O 2.

3. O 1.

4. N 1.

5. P 1.

6. M 2.

And Black has the "Sente."

III

Plate 35 (C)

The following stones are on the board: White, B 16, C 14, E 15; Black, C 17, D 16, E 16, G 17.

If White has the move, it makes a difference of seven "Me."

White

Black

1. B 17. White dare not go to B 18 because he would be cut off eventually at B 15.

2. B 18.

3. A 18.

4. C 18.

White retains the "Sente."

IV

Plate 35 (D)

The following stones are on the board: White, B 8, C 7, C 8, D 6, E 2, E 6, F 3, F 5; Black, B 6, B 7, C 6, D 2, 3, 4, 5.

If White has the move, it makes a difference of four "Me."

White

Black

1. B 4. This stone is sacrificed, but there is no loss because it is so threatening that Black must play twice in order to make his position secure, meanwhile White advances on line A.

2. B 3. Black's best move because it defends the connection at C 5, and also prevents White from trying to connect at D 1.

3. A 7. White gains one "Me" by this move.

4. A 6.

5. A 8.

6. C 4. Necessary because the connection at C 5 is now in immediate danger, but Black thereby fills up another of his "Me," and White retains the "Sente."

V

Plate 36 (A)

The following stones are on the board: White, M 16, M 17, M 18, N 16, O 15, P 14, R 14; Black, N 17, N 18, O 16, P 16, Q 16, R 16.

If White has the "Sente," it makes a difference of six "Me."

White

Black

1. N 19.

2. O 18. Black cannot stop the invasion at O 19, as White would then play at O 18 and kill the black stones on line N.

3. O 19. White pushes his invasion farther.

4. P 19. Black can now arrest the advance.

5. M 19.

6. P 18.

White retains the "Sente."

VI

Plate 36 (B)

The following stones are on the board: Black, M 2, M 3, N 3, N 4, O 4, Q 4, R 4, S 4; White, L 3, N 2, O 2, O 3, P 3, R 2, S 3, R 6.

Plate 36

Black has the "Sente" and gains nine "Me."

Black

White

1. T 3.

2. Q 2. The obvious answer is at T 2, but if White plays there, Black replies at Q 2 and White loses all his stones unless he can win by "Ko." He plays at Q 2 in order to form the necessary two "Me."

3. S 2. Black proceeds with his invasion. White

4. P 1. If White tries to save his stone by playing at R 3, Black replies at P 1, and the white group is dead.

Black retains the "Sente.

VII

Plate 36 (C)

The following stones are on the board: Black, B 17, C 17, D 16, G 17; White, B 16, C 13.

Black

White

1. B 14. This move is really "Go te"; that is to say, White is not forced to reply to it, but it is very advantageous for Black, as it effectively separates White's two stones.

2. C 14. C 15 is not so good.

3. B 15. The white stone at B 16 is now hopeless.

Black has given up the "Sente," but has gained considerable ground.

VIII

Plate 36 (D)

The following stones are on the board: Black, C 4, D 4, E 4, C 7; White, C 3, D 3, E 3, F 3.

Black has the move.

Black

White

1. B3.

2. B2.

3. B4.

These moves seem obvious, but the importance of Black's opportunity is likely to be underestimated; Black gains about eleven "Me" by this play. If the opposing lines extend one space nearer the edge of the board, the territory gained by a similar attack is not nearly so great.

IX

Plate 37 (A)

The following stones are on the board: White, M 16, N 16, N 18, O 17, P 18, Q 17, 18; Black, N 15, O 15, 16, P 16, 17, Q 16, R 12, R 17.

White has the move.

White

Black

1. S 17.

2. S 16.

3. R 18.

4. R 16.

5. T 18.

White has given up the "Sente," but these moves make a difference in his favor of about fourteen "Me."

X

Plate 37 (B)

The following stones are on the board: White, M 3, O 3, P 2, Q 3, R 2; Black, N 4, O 4, Q 5, R 3, R 4.

White has the move.

White

Black

1. S 2.

This move is really "Go te," but if Black neglects to answer it, White can then jump to T 5. This jump is called by a special name "O zaru," or the "big monkey," and would gain about eight "Me" for White.

XI

Plate 37 (C)

The following stones are on the board: White, C 15, D 15, E 15, 16; Black, C 16, D 16, E 17, 18, F 16, G 17.

White has the move.

White

Black

1. B 16.

2. B 17.

3. B 15.

White has given up the "Sente" and has gained somewhat, but if Black now neglects to defend and plays elsewhere, White can jump to B 18, and gain about seventeen "Me" altogether.

XII

Plate 37 (D)

The following stones are on the board: White, B 8, C 7, 11, D 5, 6, 7, E 6; Black, B 7, C 5, 6, D 3, 4, E 4, 5.

Plate 37

White has the move.

White

Black

1. B6.

2. B5.

3. A 7. Takes.

White has given up the "Sente," but this method of play gains about fourteen "Me," as it is now no longer necessary to protect the connection at C 8.

We will now insert two plates from Korschelt's book. The notes at the foot of the illustrations are his.

Plate 38

Plate 39