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Question starts here
No mutual damage
B defends - loss by 1 point
Road to White's win I
Road to White's win II
Mutual damage -- better for b?
The general principle of mutual damage is to accept loss of territory, rather than defend territory, provided one can inflict equivalent damage on the opponent. Hence, mutual damage is a kind of exchange.
Defending is a way to accept gote. If you pursue a mutual damage plan, not answering the opponent's destructive plays directly, the possession of sente is actually in the balance for a while. You only find out who has it when the dust settles.
A mutual damage contest can be set off by miai: one player doesn't accept the idea that the other will get both of a pair of closely equivalent plays that are ordinarily sente. It can end in a game of 'chicken' (less colloquially, who blinks first).
Mutual damage in the opening is unusual.
Experienced players will agree the game is finished after White , and it is easy to see that Black wins by 3 points. It feels not entirely fair that Black has been able to play both hanes. Indeed, White has failed to apply the principle of mutual damage.
Mutual damage is in fact an application of the miai concept to the endgame. The moment Black plays to damage White's territory, White must play the equivalent play at , if only out of self respect.
BillSpight: and answering are worth about the same. However, as Dieter says, White cannot afford to let Black get both hanes. It looks like White should play White a - Black b before . If Black has to play both points later, White a is aji keshi, but both sides will be invading, and this may be White's chance to inject some aji into Black's position. A difficult question.
See also Costly atari.
Willemien just giving Bills idea (as written above) a diagram how will this end?
If Black answers White's hane, White keeps sente to defend against Black's hane at . The game ends after ; and White wins by 1 point.
One reason many players fail to apply mutual damage, is that the situation can become very confused if either player refuses to give in as in this diagram.
Another reason is that the situation rarely is as symmetric as in this simple example. Even here it isn't quite symmetric: White a is atari whereas Black b is not.
aLegendWai: A difficult question. But who will win finally?
celebrir: I guess White is winning
A interesting thing is, that defending with at a results in a bigger lose for Black. At least in my variations.
Now White leads with two points on the board + komi. So there is at least enough chaos to take the advantage.
Still, if one player passively answers all "sente" endgame moves by the other, he or she follows a sure path to defeat.
- Mutual damage in the opening
- Costly atari
- Tedomari (the last play is important in the endgame!)
- The diagrams "Don't enclose" in Go Strategy and "Entering a large moyo" in How to Breakout of Beginning Kyu Levels, Immediate Results for middle game examples.