BeginnersEndgameExercise11/Solution

[Diagram]

Solution

[Diagram]

White first

B2 elsewhere.

W1 is honte. Later, W3 is an ambiguous move. Both W3 and B4 gain 1 pt., so the count remains the same. The final local score is +1 (for Black).

[Diagram]

White first

B2, B4 elsewhere.

The score is -1 now, so the count after W3 is 0 and the miai value of W5 (or B4 in the previous diagram) is 1.

[Diagram]

White first

B2 answers. Now the score is 2, so the count after W1 is 1 and the miai value of B2 (or W3 in the previous diagram) is 1.

Since the successive moves have the same miai value, we call the first move ambiguous, in that it might be sente or gote.

[Diagram]

Black first

Black plays on the same point.

To evaluate this position we look at the follow-ups.

[Diagram]

White follow-up

White can follow up with W1 - W3. The final local score is +3.

[Diagram]

Black follow-up

Black can follow up with B1. Black has 4 pts. of territory, and threatens to capture white+circle in ko. We count 1/3 point for Black in the ko, since he is 1/3 of the way towards capturing the stone. So the count is 4 1/3.

[Diagram]

Black first

Since this is a gote position, we evaluate it as the average of its follow-ups, (3 + 4 1/3)/2 = 3 2/3. Each play from here gains 2/3 point.

[Diagram]

Original position

The original position is also a gote, and we evaluate it as (1 + 3 2/3)/2 = 2 1/3. Each play from it gains 1 1/3 pt.



Game tree

               2 1/3 (1 1/3)
              /            \
            3 2/3 (2/3)     1 (1)
            /   \          / \
         4 1/3   3        2   0 (1)
                             / \
                            1   -1

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