Endgame Problem 24 / Solution

Tedomari problem 1  

The value of the plays:

Move a has a miai value of 1 1/2. The local count is -1 1/2 (negative count for White). Whoever plays at a gains 1 1/2 points.

Move b has a miai value of 2. The local count is -2.

Move c has a miai value of 1 3/4. The local count is 1/4. Black can play to a local score of 2, while White can play to a local count of -1 1/2. (Mistake?) ^[1]

The current overall count:

Black has 3 points of solid territory in the top left plus 8 points in the bottom right. The area around c is worth 1/4 point, for a total of 11 1/4 points.

White has 8 points of solid territory plus 2 points around b and 1 1/2 points around a, for at total of 11 1/2 points.

The current overall count is -1/4.

Optimal play:

Normally the correct play is b, the largest one, but Black should make a small sacrifice to get tedomari.

Black mistake  

Black mistake:

takes the largest play. takes the largest remaining play. Now 3 and 4 are miai.

Each player has 11 points of territory, for jigo.

Black gets tedomari  

Optimal play for Black:

The starting count is -1/4. gains 1 3/4 points, for a count of 1 1/2. gains 2 points, for a count of -1/2. And now Black gets tedomari. gains 1 1/2 points, for a final score of +1. Black has 13 points and White has 12.

White plays first  

Optimal play when White plays first:

After White takes the largest play, Black's optimal play is again to make the second largest remaining play to get tedomari. Black has 11 points of territory and White has 12. White wins by 1 point.

{0|-3}  

This is worth 3 points for white.

{0|-4}  

This is worth 4 points for white.

2  

This is worth 2 points for black. White fills at e and black at d, in either order.