Capture three to make an eye
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An example at the edge of the board.
This works away from the edge, too.
Capturing three White stones at makes an eye too, so Black lives.
However, this proverb has exceptions too.
... kills. Since a and b are miai, White dies.
Here is another counter-example. Such an counter-example can also be found away from the side.
... recaptures. Because of and the eye around a is a false eye.
A possible heuristic to see whether the "capture three to make an eye" proverb applies is to look at the position immediately after capturing. In each of the four cases below, we see whether we can form an Black eye at either the a points. If White can occupy all the b points after Black's capture, then Black has no eye here.
A related page is capture two recapture one.
See also the pages in the Eyes Collection.