Mutual Damage

Question starts here  

is a typical endgame hane, which threatens heavy damage to White's territory if unanswered.

BillSpight: It is also what is normally called a double sente. It is worth around 9 points (miai), I believe, a huge play.

No mutual damage  

Locally, the sequence comes to a pause after and Black has sente. He then uses his sente to execute another endgame hane.

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  

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.

Bill's idea  

Willemien just giving Bills idea (as written above) a diagram how will this end?

If B defends - loss

B defends - loss by 1 point  

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.

Mutual damage  

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.

BillSpight: And White c threatens a snapback at d.

aLegendWai: A difficult question. But who will win finally?

celebrir: I guess White is winning

Andy: Because of this extra snapback aji in the black position on the bottom, I wonder if would be more correctly played at ? ^[100]

Road to White's win I  

A interesting thing is, that defending with at a results in a bigger lose for Black. At least in my variations.

Road to White's win II  

Now White leads with two points on the board + komi. So there is at least enough chaos to take the advantage.

Mutual damage -- better for b?  

Is this a better line for black? The stones aren't threatened by .

forky: worse or equivalent. black's space for damage up to a is smaller than white's down to b