Add a second stone and sacrifice both
- increase liberties and require the opponent more moves to capture.
- make opponent's eyespace less efficient.
- induce opponent's capturing moves touching to the edge, thereby reducing liberties.
- make later atari not a ko.
- make a meaningful recapture.
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Add a second stone
Direct atari: not so good
Direct block: also not good
one point in gote
Black has just played the crosscut at . (Sakata calls vulgar style in the context of the discussed game, but that is another matter. There are plenty of occasions where this sequence is perfectly OK.)
It is clear that is going to be captured. Nevertheless Black adds another stone, in accordance with the proverb.
The thinking behind Black's line of play becomes clear in this diagram. Black has forcing moves at , and . Thanks to his larger sacrifice, he has a move on the outside () and two which seal off the corner. (Note that makes a a gote follow-up for White. See /continuation for further explanation.)
In summary: adding the extra stone increases the (marked) liberties of the black group. As White needs more moves to capture it, Black gets more forcing moves.
The simplest example is this corner shape. If Black is allowed to play at 1, he secures two eyes very efficiently. White simply adds a stone to be captured. Two stone capture consumes more eyespace for making an eye.
See Gokyo Shumyo, Section 1, Problem 74 / Solution. White avoids a ko by adding a sacrifice stone (see the first Variation diagram).
For example, Long L group with an outside liberty can only live by adding a sacrifice stone. See Diagram titled Variation 2.
Another example is from late endgame: