The last rule--ko

Last week, I discussed how to teach go and the need for simplicity when explaining the rules. After the students have played the "Capturing Three Stones" game for a while, they will encounter a seemingly paradoxical situation.

In Diagram 1, Black captures a stone with 1. The result is shown in Diagram 2. It now appears as if White can capture the black stone with 1 in Diagram 3, but the position in Diagram 4 is the same as Diagram 1. If this were allowed there would be an endless capturing game. This situation is called a ko.

To prevent this from happening, the following special rule was created: If one side captures a stone in a ko, the other side cannot capture a stone in that ko on the next move. In short, no move is allowed that re-creates a previous board position.

Diagram 5 shows an example of a ko fight. The game continues to white 10, after which White captures the stone at 4 with 11, starting a ko fight.

In Diagram 6, because of the ko rule, White plays elsewhere at 12, attacking the black stone at 1. Black answers the threat with 13, and now White can capture black stone in the ko with 14. Next, it is Black's turn to make a ko threat. With 15, he threatens to split White's stones on the top left in two. White defends at 16.

Now as he is allowed to take the ko again, Black captures at 17 in Diagram 7. White makes a threat with 18 and Black answers aggressively by cutting. He has a special plan.

In Diagram 8, White 20 captures the ko. But instead of making a threat, Black plays 21, allowing White to end the ko, which White is happy to do with 22. Black now plays 23 and also is satisfied as he built a strong formation on the left side while capturing White 12. Regardless of the merits of the individual moves made, these figures illustrate how a ko is fought.

Living Groups

Diagram 9 shows 5 examples of groups that can never be captured. This is because White can never play a move to take away Black's last liberty. If White tries to play at A, Black still has an extra liberty at B.

Problem 1 shows 4 problems in which White can kill a black group. The answers will appear in next week's column.

Tactics as part of Strategy

Go players often find themselves in lost positions. When this happens, the favorite strategy of the stronger player is the deployment of a ko. This is measure that is not for the faint-hearted and calls either for pure recklessness or for managing calculated risk--a bit like investing. The difference in Go is that you will only lose the game (and a bit of pride, for some), but not your shirt.

Many games have been turned around through a ko. Diagram 10 is a game between Koichi Kobayashi on Black and Norimoto Yoda on White in their fifth and decisive clash for the Gosei title played on Aug. 26. Until White 54 the game is in balance, but Black 55 is a little too greedy. Black wants to exchange 55 for 56 and 57 for 59. However, refusing to go along with Black's plans, White 58 takes the key point, both attacking the black group (29 and 31) and defending his corner. After White 72, Black is behind in territory.

Black first plays some forcing moves, then starts a long tactical maneuver with 1 in Diagram 11. Finally, he sets up a ko with the combination of 11 and 19. By sacrificing the group in the upper left corner, Black succeeds in destroying White's territory at the lower edge. Note that White 24 and 26 are the biggest ko threats, worth roughly 30 points.

Kobayashi reverses the flow of the game by winning the ko. White is still slightly ahead, but the psychological factor grinds him down. You should note that by killing the stones in the upper left hand corner, White's marked stones have not gotten any stronger. But by winning the ko, Black has significantly weakened the marked white stones marked and strengthened his own marked stones.

A weak group is said to have a value of minus 30 points. In other words, if you weaken a group of your opponent or strengthen one of your own weak groups, you gain 30 points. This can often decide the game. In this game, Kobayashi, who is playing black, goes on to win the game by 1.5 points, snatching the title from Yoda.