Some games have a clear goal, ...

By Rob Van Zeijst

Some games have a clear goal, such as capturing all of the opponent's pieces or at least the most important piece--the flag or king. Beginners can grasp this concept immediately, and it can give them instant gratification. This life-and-death struggle has a sense of urgency and movement and the game is exciting at a very basic level. Of course, go contains all of these elements, because stones, and sometimes huge groups, could be captured if they do not have two eyes, and this might bring an immediate end to a game. However, go is more like a full-scale war. In war, capturing a bridge or strategic spot may be vital for advancing troops, but if this is accompanied by too many tactical losses, another strategy might be better. In fact, go is basically a game of economics. You must make sure your stones work together more efficiently than your opponent's. Let's see how that works.

Problem 1: Already after a few moves, it becomes clear that Black is moving all around the board while White is just concentrating at top left. Who do you think will win? Imagine what the final positions of Black and White will look like with the shape of their respective territories. Then, make a guess at the scores.

Solution 1: The moves through 52 are a possible continuation of play. If you count the scores, you will find Black has 81 points while White has only 36 points. Instead of the moves shown here, White might have been able to play better ones, but even so, it is obvious Black would win by a large margin. Since no stones were captured, it is easy to understand that the white stones have been placed less efficiently than the black stones.

Diagram 1:Let us have another look at the first few moves. White's stones 2, 4 and 6 are concentrated at top left. On the other hand, Black plays his first move at top right, his next move at lower left, and third move at lower right. It becomes apparent after move 14 that Black has used all of his stones efficiently in the sense that they all play a role on the board. On the other hand, white 2 becomes worthless after white 4 and 8, and white 6 is not working optimally after white 10. The same can be said about white 8. After 14, in retrospect, it should have been played somewhere else. The triangles indicate the borders of the potential territories. So already at this stage, White's position has become so inefficient, he cannot hope to win.

Diagram 2: Here, after occupying the right side, Black suddenly starts developing the center with 15 through 19. Meanwhile, White solidifies the top and lower side and he defends the corner with 18. Who will win? What do you think?

Diagram 3: White first threatens to invade Black's center territory with 20, 22 and 24. In addition, these stones reinforce White's side, top and bottom positions. He then goes on to destroy the top right corner and threatens the lower right corner with 30. However, Black keeps expanding his center with 31, 35 and 37. Finally, he defends with 39 and so on. What do you think the outcome will be? Do not try to actually count at this stage. Just make an estimate based on your feelings.

Diagram 4: Looking at the end position, you can see Black has bottled up two stones (white 22 and 24) in the center, so it looks as if he has done very well for himself. Now, without counting, estimate how many points each side gained. Who do you think won? If you guessed correctly, you will have worked out that Black has 37 points in territory plus 2 prisoners = 39 points. White has 61 points. The difference is a full 22 points. How did this happen?

Diagram 5: This diagram, which we saw last week, gives you some idea. The most efficient way of placing your stones is close to the corner, while the least effective way is to make territory in the center. In diagram 4, Black used 36 stones to make 39 points, a bit over 1 point per move. White lost two stones (22 and 24) but even if we include them, he made 61 points with 35 stones, a little under 2 points per move. In other words, Black used too many stones to gain territory in the center.

Problem 2: Let us not get rusty with our life-and-death problems. In A, B and C, where should Black play in each case to kill the white groups? Killing means depriving the stones of two eyes, which we discussed in the past two weeks.

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