When we first began this new course three weeks ago, we started out with the "capturing game," a simplified version of go in which capturing one single stone won the game. After both players have more or less understood this concept, the rules can be changed so that the first to capture three stones (or five, or 10, for that matter) wins the game-set the number of stones that need to be captured before starting the game. If one person consistently loses, he should be given a handicap. A handicap can be given in three ways :

1. By taking Black. Remember, Black plays first.
2. By placing two or more stones on the board as the first move for Black.
3. By requiring White to capture more stones than Black.

Once we are ready for a game in which more than one stone can be captured, we will encounter new types of moves.

Ko

Ko is a situation where a position threatens to be repeated eternally. There doesn't seem to be a way out. Fortunately there is a rule that puts this local situation into perspective, and allows the surroundings to shape the solution to this local problem. It is like finding yourself stuck in a rut. How do you get out of it ? By focusing on something else and then going back to that situation later.

Diagram 1 : In this situation, the marked black stone is in atari-he has only one liberty left. What happens next if it is White's turn ?

Diagram 2 : White can capture the marked stone by playing at 1.

Diagram 3 : This is the situation after White captures the black stone. And as you can see, the marked white stone is in danger as it has only one liberty left. If Black were allowed to recapture the white stone right away, this would lead to a repetitive situation from which there would be no escape. This situation is known as ko. The word ko can be written as a character meaning 'eternity' or 'to threaten.'

The second technical rule :

A scenario cannot be immediately repeated
Since the situation locally does not provide a solution, a remedy has to be found elsewhere. How would you solve this problem ? I've asked this questions of many beginners, once they discovered the possibility for ko. At first they were confused, but once they started thinking about a solution, these novices usually found some kind of rule that would prevent either side from continuing this kind of situation. And, of course, that is part of the answer. When there is a ko, you can only recapture after first having played elsewhere.

In practice :

Diagram 4 : There is a ko in the upper left corner and it is White's move.

Diagram 5 : White can now capture the marked black stone with 1. Black is not allowed to capture that white stone immediately. Instead he is free to play anywhere else, but if White responds to his move, Black can then recapture white 1. So if it is advantageous to win the ko, he should make a move that White needs to answer. Black 2 is such a move: it threatens to capture either one of the marked white stones. Therefore, White may want to answer with 3.

Diagram 6 : At this point, the board situation has changed and therefore, Black can capture the marked white stone. In an attempt to make Black answer, white 5 attacks the marked black stone.

Diagram 7 : Black 6 may not be the best move now, but it stops the ko. White 7 gets a good grip of the adjacent black stone and black 8 and 10 pull out the lonely three black stones in the lower right. White decided to answer once before taking the upper right corner. Black 12 is a tricky move and White is forced to defend with 13 (see Reference 1). Next, black 14 puts a white stone in atari.

Reference 1 : After black 1 (12 in diagram 7), if White inadvertently resists with 2, black 3 puts the white marked stone in atari, forcing white 4. Next black 5 is a nice tesuji (locally good move), capturing three white stones. Note that even if White plays at A, Black B will take away the last liberty of the white stones, killing them.

Diagram 8 : Instead of answering passively, White decides to attack with 15. Granted, black 16 captures a stone, but white 17 and 19 also take one stone. With 18, Black found an interesting way to resist. White captures with 19 and Black secures atari again with 20.

Diagram 9 : White 21 overdoes things. He should have just connected at 22, but he starts another ko. However, Black captures the ko first with 22. To his great embarrassment, White realizes he has no moves that Black needs to answer-such moves are appropriately called ko threats. To make the best of the situation. He gives atari with 23. Black 24 is not shown in the diagram, but is played at the points where the marked white stone used to be. Preventing Black from cutting there, White defends at 25. Black then captures one more stone with 26 and 28, White saves one with 29. Let's now tot up the score.

Black captured four stones (when playing 4, 16, 22, and 28) White captured three stones (when playing 1, 19, and the marked black stone, which has not been captured yet, but cannot escape-verify this for yourself).

So, Black won the capturing race by one stone, if counting only the total number of stones caught.

Next week, however, we will look at a completely different aspect of the game, namely the real objective of the game and how to count.

Solutions to last week's problems

Solution 1 : Black 1 frees the marked black stones while capturing the marked white stone. Resisting with moves like 2 and A is futile.

Solution 2 : Black 1 captures the three marked stones while setting free the three marked black stones.

Solution 3 : Black 1 puts the two marked white stones in atari. If White saves one stone with A, Black captures with B, and vice versa.

Solution 4 : After white A, black 1 captures three white stones. In other words, white A was reckless.

New problems

Problem 1 : The marked white stones seem hopelessly lost. Playing with White, can you find a way out ?

Problem 2 : The white stones in the upper left are completely surrounded. Try to get White out of trouble.