Practical Endgame Test 1 / Solution 3

Can Black keep the margin to 3?  

When Arno posted this position, I became fascinated by the question can Black force a better result than W+4? It took me a long time to think that I found the answer... --DaveSigaty

Variation 1  

Black plays because otherwise White's play at b is too damaging. White then goes back to , giving Black the chance to capture at . If White now plays on the left, Black plays forcing . White can not ignore because Black at followed by descending to the edge is a very big play (even bigger than capturing the stones if White plays at d instead of ).

On the left side, Black at is the right way to play. When White cuts at it is worth 2 points for Black to ensure an eye on the left side. Otherwise he will have to play another stone on the right to prevent White's atari at c.

W+3  

Black has two poins on the left and 10 points on the right.
White has four points at the bottom and 11 points at the top.
White wins by 3 points.

(NB: don't forget to count the captured stones.)

Variation 2  

White can try blocking at , knowing that she can win a ko fight. However, Black does not need the ko to improve on the solution diagram...

Imperfect reversion  

Now note that if White captures at a and connects, we have reverted to the solution diagram except that has been added inside White's territory. In addition each side has captured one stone near a but they offset each other. Final result? W+3.

Variation 3  

White plays after reading out that she can't let Black capture here. However, is a big play with the follow-up at as absolute sente. Play continues to but White's winning margin has been reduced to a single point.