The book Theory of Games ...

By Rob Van Zeijst

The book Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern is a classic work that introduced game theory as a new field of scientific inquiry. For the study of go, we will consider the two-person zero-sum theory the book takes up. In a game where only one person can win, the book points out that a loss by your opponent is a gain for yourself. This means it is equally as important for you to play effective moves as it is to have your opponent play ineffective moves. The kikashi is one example of this because it is a forcing move that must be answered, and the exchange will give you an advantage.

Now let's continue the game we started a few weeks ago between Masao Kato (Black) and Cho U, current Honinbo, in the semifinals of the 2003 Oza title.

Diagram 1 (1-21 represent moves 55-75): In the previous article, Black played the marked stone, which White bottled up with his marked stone after a few preparatory moves. Is this exchange a kikashi? Before the exchange, Black was unable to cut at 1, but now he grabs his chance. Following the kikashi 2 for 3, White strikes back with 4 and 6. After 9, the question is, can White cut at A?

Rather than cutting there himself, he wants Black to play there so he can capture Black's two stones around 1. Therefore, White cuts at 12, aiming at A, and later at B, followed by black C and white D. To prevent the cut at A, Black exchanges 13 for 14 (giving up two stones, a small sacrifice), allowing him to exchange 15 for 16 (potentially taking three stones, a large profit). This will defend against the cut at A and allow him to play elsewhere. Thus, Black can resume his attack with 17 and 19. While White defends his center stones with 18 and 20, Black builds up center influence to start a new attack with 21. This game offers excellent study material as it has plenty of interesting kikashi maneuvers and exchanges. White won the game by a small margin.

Hints for improving your game

In a kikashi exchange, the player who forces a move gains an advantage while the opponent does not. Since pros do not like to get nothing for something, a kikashi can result in an all-out battle. This is illustrated in the following game, the fourth and final game for the Kisei title in which challenger Keigo Yamashita defeated titleholder Naoki Hane 4-0 to take the title and the ¥42 million prize money.

Diagram 2: After 6, Black wants to force the kikashi 7 for A in order to pincer at B. However, White counters with 8 through 14. In a way, the exchange 15 (most important) for 16 (second most important) is a kikashi for Black. Black 17 and 19 are an attempt to avoid making a forced move (see Reference 1) and force a kikashi himself (see Reference 2). White 20 avoids that and uses a kikashi himself with 22 through 26. White then plays the kikashi exchange 28 through 33, before turning to the most important spot on the board at 34. We will resume this game next week.

Reference 1: The moves 1 through 9 are a common sequence. Black bottles up the two marked stones but White can still play a kikashi at A, followed by black B, white C and black D. However, Black has no choice but to play 5 through 9, or White captures him in a ladder by playing at 9 himself. Black is clearly worse off in this exchange.

Reference 2: Instead of Reference 1, Black could sacrifice one stone (the marked one) and the sequence 1 through 5 would give him an excellent result. After 5, Black can play at A to take away White's base and leave him with just one eye. This is a terrible situation for White.

Solutions to Feb. 16 problems

Solution 1: The question was, why is the marked white move a bad response to Black's marked stone? Black can now play a kikashi with 3 and 5, and then attack with 7. If White plays 10, 12 and 14 as in the Kato-Cho game, Black can kill these stones with 15 instead of connecting at A--a terrible result for White.

Solution 2: If Black exchanges 1 for 2 before clamping with 3, white 4 and 6 are good countermoves. Without the 1-2 exchange, Black can cut at A in sente, but if he plays here now, White will capture him. In other words, the 1-2 exchange is not kikashi but aji-keshi (spoiling possibilities).

New problem

Problem 1: If Black wants to invade White's corner, he can do so with 1 through 7. After 8, he needs to play at A to ensure that he will live. But before doing so, he can play kikashi. Where should Black play before defending his corner at A?

Want to find out more? Come to Ben's Cafe in Takadanobaba, Tokyo, (03) 3202-2445, where the English-speaking go community congregates every Sunday.

Van Zeijst is a four-time European go champion and European representative at the Fujitsu World Championship.