Counting territory
Diagram 1: Here is the result of a game between two beginners. What territory does Black and White have? What is the fate of the marked black and white stones?
Diagram 2: This is the position after all of the dead stones--the marked stones in the previous diagram--have been removed. The stones that are marked here are in seki. In other words, there is a standoff in this corner. Actually, Black can play at A, followed by black B, white C and black D. As both players would capture two stones, there is no difference in the number of points.
Diagram 3: Next, the prisoners--the marked stones that were dead in Diagram 1 and removed in Diagram 2--are put in the territory of the other player. White's six captured stones and Black's nine captured stones are marked to show where they have been placed. This makes it easy to count the territories. There are seven points in White's territory compared to five in Black's, so White wins by two points.
Diagram 4: Last week, we looked at this position. To make the same number of points--nine--the black A group uses seven stones, the B group 11, and the C group 15. Using the same number of stones--seven--the White D, E, and F make five, eight and nine points, respectively. So stones make territory most efficiently in a corner as long as the stones are not too close to that corner, and least efficiently in the center or extremely close to the edges.
Diagram 5: Which of the stones 1 through 4 has been placed most efficiently to make territory? Black 1 is too close to the corner. White 2 is a lot better and might be the best move on the 9x9 board. Black 3 is good but on this format board, it might be too far from the corner. White 4 is a good move.
Solutions to last week's problem
Solution: The A group has no points because it is in seki with the marked white stones.
1. Black should play 1 and 3, while White follows with 4 and 6. Playing black 7 before defending with 9 is clever. White has to defend at 8, otherwise Black cuts at the marked spot to capture 2. This allows Black to defend with 9. Otherwise this situation becomes seki or ko.
2. The marked black stone is dead.
White has 6 points (around B) + 3 points (around D) + 4 points (around F) = 13 points.
Black has 8 points (around C) + 2 points (around E) = 10 points.
White wins by three points.
Reference 1: If Black plays first on the other side with 1, what happens then? White would get 14 points against Black 10, a difference of four points.
Reference 2: If Black played at 1 first, he would have to defend with 5 after white 2 to prevent this corner from becoming seki. In that case, White gets 14 points against Black's 9, a difference of five points.
Reference 3: If Black did not defend the corner, White could play at 1. After Black connects with 2, White forces 3 through 6 to bring about a seki situation. Black loses this corner.
Problems
Problem: As it is White's move, where should he play? What are the best moves after that? How many points will each player end up with? As Black moved first, White received two points compensation, called komi. Who will win this game?
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Van Zeijst is a four-time European go champion and European representative at the Fujitsu World Championship.