Sub-page of BeginnersEndgameExercise9

In this position it is not intuitive which move to start with, for both, or whether it matters. Let's evaluate the miai value of A first. To make things easy we're going to score White positive here, against common CGT practice.

If responds, there's 1/2 point left. The count is 1 1/2 and the value of the next move is 1/2.

Hence the count of "Black first" is 3/4 and the value of here (or in the previous diagram) is 3/4.

If responds, then we can evaluate the position from White's successive ignores. turns the score into 0 again, hence after the count is 1/2 and is worth 1/2. Hence after the count is 1 1/4 and the value of is 3/4. Hence after the count of "White first" is 2 1/8 and the value of is 7/8

The count of "B first" being 3/4 and "W first" being 2 1/8, the count in this diagram, assuming A is the better move, is 1 7/16 and the value is 11/16

Game tree for A (read minus sign for all the counts)

1 7/16 (11/16) / \ 3/4 (3/4) 2 1/8 (7/8) / \ / \ 0 1 1/2 (1/2) 1 1/4 (3/4) 3 / \ / \ 1 2 1/2 2 / \ 0 1

There's a problem in the tree: in the second branch the temperature increases, which means Black's move after is sente. We need to reduce the tree accordingly

11/8 (5/8) / \ 3/4 (3/4) 2 (1) / \ / \ 0 1 1/2 (1/2) 2 3 / \ 1 2

After , like previously, and make the score 0 again, so after the count is 1/2 (value 1/2), after the count is 1 1/4 (value 3/4)

Hence the count after is 5/8 (value 5/8)

Since the first exercise, we're on our guard. Indeed 3/4 > 5/8 so is sente. The actual count after is then 1 (value 1) and the count after is 1/2 (value 1/2). But this in turn means is sente, so the count after is 1 and both and are sente.