In his book The Seven Principles of Success,

By Rob Van Zeijst

In his book The Seven Principles of Success, Stephen Covey says one should think with the end in mind. For the past 10 weeks or so, we have looked at what the end might look like in go. You now have the means to more or less calculate what territory you can expect from a certain position in the endgame. You do not have to wait until the last move is played to know the result of a game. Professionals often know the final score within a range of one to two points more than 100 moves before the last move is played. In fact, in his book Positional Judgment High-Speed Game Analysis, Cho Chikun shows one game that he says hangs by one-half point at move 41. However, Hideo Otake, who was Black, eventually beat Cho in this game by 4! points.

Positional judgment

Pros tend to make a detailed analysis from a very early point and compare different outcomes and scores for almost every move.

Diagram 1: This is the Cho-Otake game, with Black 1 representing move 41 in the game. Black 1 defends against two threats (see References 1 through 3). As all groups are more or less safe after this move, we can look at the score at this point (see Diagram 2). This is called positional judgment.

Reference 1: If Black plays elsewhere than at 1, White can slip into this spot, followed by black 2 and white 3. Black is now forced to connect at 4, and White captures most of the corner with 5 while freeing his own stones. This is a disaster for Black.

Reference 2: Instead of this sequence, what if Black exchanged 1 for 2, then played elsewhere, i.e. at 3? White would immediately strike at 4 and 6. What then?

Reference 3: To avoid a huge ko in the corner, Black will probably connect with 7, but 8 threatens to connect underneath (along the edge). If Black stops that threat with 9, White ensures he will live in the sequence through 16. What is more, Black's base and eyes are gone, while White's marked stones have become stronger, as a white move at A threatens to link up with his stone at 12.

Diagram 2: Cho says the borders of Black's territory are broadly defined by the crosses, while White's territory falls within the triangles. Accordingly, Black's territory is 46 points, while White's territory is 40 points, plus 5.5 points komi (number of compensation points for playing the first move), for a total of 45.5 points. The difference is then one-half point in favor of Black, but he has played an extra move.

Diagram 3: On the other hand, if it is Black's turn, usually attaching at 1 is the best move. This is called the hit-under tesuji. In general, White will block at 2, and the exchange 3 for 4 follows. Of course, Black can defend his stone at 1 by playing A or B. But even if he does not, he has already profited.

Solutions to last week's problems

Solution 1: Black can reduce White's territory by attaching at 1. The moves through 8 will likely follow. So Black makes two points (triangles) and White's territory is nine points, assuming white A and black B.

Solution 2: Black 1 is the correct move to enlarge his territory in the corner. After white 2, Black can either pull back with 3 or descend to A.

Reference 4: On the other hand, White may want to attach at 1. If Black answers with 2, the moves through 4 will follow. This situation would make White happy.

Reference 5: However, Black may put up resistance with 2 through 6. White's best defense is 7 through 11 to keep his corner alive, but black 8 and 12 put a huge dent in White's territory. However, as the result is unclear, Black may want to stick with the sequence in Solution 2.

Problems

Problem: What is the value of a white move at B or a black one at A from a territorial perspective?