Practical Endgame Test 8 / Analysis

White to play and win.  

For background, see Chilling, Infinitesimals, Numbers, Tedomari, and MiaiCounting.

There are 3 1-point plays on the board, which chill to infinitesimals, and 2 3/4-point plays, which chill to numbers.

Star1  

The hane-tsugi in the top right chills to * (star). Whoever plays first picks up 1 point. (If Black plays first the play goes B 3 - W a, B 1).

Star2  

Taking or saving the single stone also chills to *.

Down  

This chills to v (down), also written { * | 0 }. W 1 - 3 gains 1 point, while B 1 plays to * (when chilled). White can get local tedomari regardless of who plays first.

3/4 (1)  

This chills to "3/4". (The local count is actually 1 1/4, but in referring to types of plays we ignore the integers.) After W 1 the local count is 1/2. (Whoever plays at a gains 1/2 point.) After B 1 the local score is 2. So the original count is 1 1/4, and a play gains 3/4 point.

3/4 (2)  

Here you have to realize that W 1 - B 2 reverses (like the hane-tsugi). Because of symmetry, you can think of 1 and 2 as miai.
With no kos, play in the chilled game is never wrong. One rule is to play numbers last. So we can eliminate the 3/4s. (Besides, they are miai). That leaves us with the game, * + * + v. Since * + * = 0 (they are miai), we are left with v. By taking it White gets tedomari.

White to play and win.  

White wins. The rest is miai.
The whole board count: Black has 10.25 points, White has 11.25 points, for a net count of -1.

--Bill