White to play and win  

Komi = 5.5

Black has 5 points of territory in the top right, 2 points in the middle, 2 points in the bottom right, 3 points on the bottom side, and 7 points on the left side, for a total of 19 points.

White has 6 points in the bottom left and 8 points elsewhere for 14 points of territory. Adding komi of 5.5 brings the total to 19.5 points.

White wins by 0.5.



All White has to do is make the largest play.

The hane-tsugi, W1 - W3, is a gote that gains 1 point. Then B4 - W5 is a 1 point sente. Next B6 gains 0.75 point. Finally, W7 gains 0.5 point.

White could also win with the reverse sente, W4.

Below I derive these miai values.

0.5 point gote  

B1 makes 1 point in the top left corner.

W1 would prevent Black from making that point.

The local count there is +0.5 (scores are given from Black's point of view). B1 gains 0.5 to make 1 point; W1 would gain 0.5 to make 0. The miai value of a play is thus 0.5.

0.75 point gote  

If Black plays B1, he scores 5 points in the corner. After W1, what is the count there?

Black has 3.5 points there. If he plays at a he scores 4 points, while if White plays at a Black scores 3 points. This is like the top left corner.

Before W1 the count in the top right corner was 4.25 points. W1 gains 0.75 points to make the count 3.5; B1, as in the solution, gains 0.75 points, as well, to make the local score 5.

1 point gote  

The hane-connect is a common endgame play. To evaluate it let's look at the two adjacent eyes. After Black plays White has 1 point there while Black has 7. The net local score is +6.

1 point gote  

By comparison if White plays hane-connect White gets 2 points while Black gets 6, for a net local score of +4.

The original count is +5, and whoever plays hane-connect there gains 1 point.

1 point reverse sente  

If White plays W1 she scores 7 points on the right side.

1 point sente  

But if Black plays B1 in sente, White scores only 6 points there.

To play sente with sente gains nothing on average, so -6 is the original count on the right (from Black's point of view). White's reverse sente in the previous diagram gains 1 point.


W2 = pass

To verify that B1 is sente, if White ignores it and Black plays B3 with sente, White scores only 4 points on the right side. That shows that W2 (at B3) gains at least 2 points, which makes it bigger than the reverse sente (W1 at B1). So B1 is sente.

-- Bill

BeginnersEndgameExercise4/Solution last edited by Bill on August 15, 2006 - 18:47
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