Sentestrat/example 1 solution

black to play  

Before white played , the top right was seki. The move at is sente, threatening to capture two black stones and break the seki.

If black plays a, putting seven white stones in atari, then white should recapture, and the top right is seki again, with a net one point to black for the extra prisoner. If black doesn't play in the top right, then white will play b, for 5 points in the corner (including two prisoners). So the miai value of a move at the top right is 6 points.

If black plays b, killing the bottom left corner, then black has 14 points in that corner. Or if white plays b, then white has 2 points. A move at b is gote for both sides, so the 16 point swing translates into a miai value of 8.

Therefore the thermostrat move is for black to play b, because it's the bigger move. But sentestrat says black should play a instead, responding to the threat of .

If black plays thermostrat, then the outcome is:

Mistake: white wins.  

By Japanese counting, black has 3 points in the centre and right side, and 14 in the bottom left, for a total of 17 points. White has 8 points at top left, 5 at top right, and 5 at bottom right, total 18. So white wins by one point. (Exercise for the reader: by Chinese counting, white also wins by one point.)

For sentestrat, it's:

Black wins; at  

By Japanese counting, black has 3 points in the centre and right side, 14 at bottom left and 1 at top right, total 18. White has 8 at top left, 5 at bottom right, total 13. So black wins by 5.

For completeness: what if white doesn't actually reply to ?

Even worse for white  

This way, black has 3 points in the centre and right side, and 18 at top right (including 9 prisoners), total 21 points. White has 8 at the top left, 5 at the bottom right and 2 at the bottom left, total 15 points. So black wins by 6.