BeginnersEndgameExercise9/Solution

Original position  

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.

Black first  

If and White ignores, we score this as 0 points locally.

Black first  

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.

White first  

If White first and Black ignores, the local score is 3.

White first  

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

Original position  

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

Move B - Black first  

We now start with here. If ignores, the score is 0. White has a ko threat now.

White responds  

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.

Move B - White first  

After it's easy to see is sente and the count is 2.

This means, assuming B is the better move, the count of the original position is 1 1/2 and the value of the move is 1/2.

Game tree for B

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