# BeginnersEndgameExercise9/Solution

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

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

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
```

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

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.

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
```

BeginnersEndgameExercise9/Solution last edited by Dieter on June 19, 2023 - 00:04