Endgame Problem 6 / Solution

White first  

White protects with . Later, is a 1 point sente. The result is a local count of -3. (By convention, White scores are negative.)

Black first  

Black throws in with . Through is Black's sente, reaching a three stage ko. If White wins the ko the result is -3; if Black wins, the result is +4 (next diagram).

Black wins ko  

Black has captured 2 more stones than he has lost.

It takes Black 4 net moves to win the ko and get 4 points. In 1 net move White can prevent or win the ko for -3 points. The miai value of a play is (4 - (-3))/(4 + 1) = 7/5 = 1.4 points.

The original count is -3 + 1.4 = -1.6 points.

Losing sente  

is a losing sente. After the local temperature has reduced to 1 1/6, a well-known yose (See Miai Values List / 1.00 to 1.99). Since results in a score of -3, the local count after is -3 + 1 1/6 = -1 5/6. Black has lost almost 1/4 point.

Black's original sacrifice is an endgame tesuji with a somewhat unusual point. Black gives up a stone to prevent White from playing her best play in response to ( in the Losing sente diagram). Capturing the sacrifice stone is not as good as the solid connection.

--Bill Spight