In a zero-sum game like go, the two sides divide ...

By Rob Van Zeijst

In a zero-sum game like go, the two sides divide the proverbial pie. The more one party gets, the less the other gets. In other words, the less territory your opponent gets, the larger your share. Many players concentrate only on one thing, either increasing their own territory or reducing their opponent's. Keeping both of these elements in focus at the same time and remaining flexible will help you become a stronger player.

Meijin title

Challenger Cho U has scored an important win over titleholder Norimoto Yoda in the Meijin title match, to lead the best-of-seven series 3 to 2. Now let's continue with Game 4, which we started last week. Yoda is white.

Diagram 1: (black 25 captures white 22 by playing where the marked black stone was captured earlier) Yoda has just played the marked white stone, and we made the evaluation that White was about 3.5 points ahead.

Last week, I asked where Black should play next. The answer: somewhere to the right because this is the largest open area. Prime candidates are A and B. Since he is weak in the upper right, White cannot afford to invade (at D, for example), so this area will likely become Black's territory.

However, Cho invaded at 1. To take pressure off his marked stone, White played 2 through 8, but this also caused Black's group around 5 to become weaker. This is apparent after Black cuts with 13 through 17 and White plays 18 and 20. White succeeds in forcing a ko with 22 and then moves out to the center with 24 and 26. Black completes the ko with 27.

White now had a chance to decide the game, but Yoda played at 28, a move he deeply regretted. Instead, he should have played at C to use this thickness of his stones at 18, 20, 24 and 26. This would have allowed him to play at D later, so that he could attack the black stones in the upper right and turn the right side into territory while heading for an easy win. However, Black reclaimed the initiative with 29 and went on to win by 7.5 points.

Diagram 2: (White plays 2 elsewhere) For the past few weeks, we have been putting values on positions and frameworks. We determined that the minimum territory for Black's original corner position (called shimari or enclosure) was 8 points. However, he also wields influence in both directions, and can capitalize on this by extending to 1 and 3. This position is called a double-wing formation. What is the value of this formation? If we count the X's, we find it is 33 points. White may still invade around A, but then the area on the other side, i.e. B, will grow bigger, and vice versa.

Diagram 3: (White plays 2, 4 and 6 elsewhere) Starting with the double-wing formation of Diagram 2, Black can further expand with 1, 3, 5 and 7. After 1, 3 and 5, Black's territory would be 33 (for the X's)+20 (for the triangles)=53 points. Furthermore, with 7, Black can score an additional 17 points. Also, the stones around 1 and 3 exercise influence around the lower right and upper left to provide even more synergy.

Diagram 4: White obviously should invade before Black completes his territory grab while it is still safe to do so. White 1 is a standard move to do this. White should make this move before Black plays at A and/or B, otherwise he will be in danger.

Solution to last week's problem

Reference 1: This is the position from the final game of the 11th Agon-Kiriyama Cup Lightning Go Open Tournament between Naoki Hane (Black), Kisei titleholder, and Koichi Kobayashi. If it is Black's turn, by threatening to invade at A, he can force the sequence 1 through 8 in sente, then exchange 9 for 10, and wall off the left side with 11. If White defends at 12, Black builds a huge moyo with 13. Note, Black's marked stone is unimportant in the big scheme of things (White can cut with B, followed by black C and white D). But, it is White's turn. How can he rein in Black?

Solution 1: After black 1, White must break through Black's wall with 2 through 6. Black 7 through 14 is a good combination, and black 17 threatens to surround a huge area. Before Black closes off this area at A, White has to invade. White 16 is a good move for this purpose. White lays waste to Black's territory at the bottom while Black destroys White's on the left side and rescues his marked stone with 27.

Problem: Count the territories in Solution 1 and assess the position. Who is leading? Where are the weak and strong groups? Where should Black play next?

Want to find out more? Come to Ben's Cafe (03-3202-2445) in Takadanobaba, Tokyo, where the English speaking go community congregates every Sunday. You can enjoy free lessons, 11 a.m.-1 p.m. Ben's Cafe can be accessed at www.benscafe.com.

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