Life In 19x19

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[go]$$c Mistake 6
$$ ---------------------------------------
$$ | . . . O . . . . a . . . . . . . . . . |
$$ | . X O X X O O X X O . . . . X X X X . |
$$ | . X O X . O X . X O . . X X O X . . X |
$$ | X X O X . O X . X O . O X O O O X X . |
$$ | . O X X X O X . . X X O O X O X O O . |
$$ | O . O O O O X . b X O O . . O X O . . |
$$ | . O . O . O . X X O X O . . O X O . . |
$$ | X . O . X O O X O O . . X . . X . . . |
$$ | X O . . X . X O . . . . . O X X X O . |
$$ | . X X , . . X O . O . . . O O X O . . |
$$ | 1 O X . . . X O . O X . . . . O O . . |
$$ | O . O X . . X X . X O . . . . . . . . |
$$ | . O O . . . . . . X O . . . . . . . . |
$$ | . . . . . . . . . X O . O . . . . . . |
$$ | . . . O . . X . O O X O . . . . . . . |
$$ | . . O , . . . . . , X X O O O O O O . |
$$ | . . O X . . X . . . . X X O X X X X . |
$$ | . X X . . . . . . . . . c X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

A [ko] has developed along the left side. Which ko threat should White play, ''a'', ''b'' or ''c''?

If White wins the ko then White kills 3 black stones and connects two groups which become completely safe.

If Black wins the ko and White can't connect his group, then Black kills 18 white stones, gets a few extra points of territory, and puts pressure on the lower left white group.

I don't know how to calculate the value K of the ko but it must be at least 50 points. That's gigantic.

White has two local ko threats at "b", one at E19 and one at "a". The moves at "b" threaten to save 18 white stones, kill 14 black stones and make a few intersection switch hands. There may be a capturing race but anyway it is clear that the value of the ko threats at "b" is larger than K. The ko threat at E19 is a bit smaller but still maybe larger than K. On the other hand, a move at "a" only threatens to save 18 white stones, so is worth about 36 points. The ko threat at "c" is of similar size.

On the other hand, Black has 2 big ko threats around O14 which are worth about 40 points, and otherwise nothing very big. So in principle White should win the ko.

In general the players start with the largest ko threat but this is not always true. If several ko threats that work (i.e. to which the opponent will necessarily respond) are available then it is better to use the smallest ko threat that work, and save larger ones for the future.

The ko threats at "b" certainly work, maybe the one at E19 too, but I am not sure that the ko threats at "a" and "c" are enough.

Solution