BQM 222

    Keywords: Question

I ran into this beast in a pro game. How would I play it? In the game white's move at a carried a very large threat, so black would block at b. It seems like white a dominates d, but how do black c and d compare?

[Diagram]
 



Bill: Could you show more of the board? And which game was it? Thanks. :-)

[Diagram]
Lin (W) - Sakata  

It comes from this Honinbo title game: [ext] http://gobase.org/games/japan/titles/honinbo/22/game-4.sgf

Here white chose W1 over a move on circle.

Bill: This is a fearsome infinitesimal in chilled go. How to play it?

For the answer, let's set up a difference game.

[Diagram]
Difference game  

First we mirror the bottom of the board, changing the colors of the corresponding stones. This produces an even position. Then we let Black play the black+circle stone and White play the white+circle stone, to compare these two plays for Black. If one play is better than the other, this position will favor the player who made that play.

[Diagram]
Difference game, Black first  

First, Black takes profit with B1 - B3. Then White pushes in with W4 and Black connects with B5. After B7 Black has one more point in the bottom than White has in the top. Black to play wins the difference game.

[Diagram]
Difference game, White first  

W1 is sente. Then W3 and B4 are miai. The result is jigo. Jigo is good for the second player, Black.

Black to play can win the difference game, while White to play cannot. Thus the difference game favors Black and the hane, black+circle, is better, unless the ko situation tells against it.


Now, how should White play it?

[Diagram]
Difference game II (White's plays)  

Here we set up the difference game to compare White's options. Does White play the hane-tsugi in the bottom, or block off the corridor in the top?

[Diagram]
Difference game II, Black plays first  

B1 pushes and W2 plays hane-tsugi. Then B5 pushes, but with W6 the result is jigo.

[Diagram]
Difference game II, White plays first  

White plays the hane-tsugi at W1, and B4 pushes, but finally White wins by 1 point.

White to play can win the difference game, while Black to play cannot. So the difference game favors White, and the hane-tsugi is correct unless the ko situation dictates otherwise.


Thanks Bill! So it's a { * | 0^2 Miny-6 } then? It looks less like a beast written like that :).

Bill: Looks that way. :-) It looked more fearsome before I realized that B4 in the Difference game, White first diagram was the right local play. ;-)


Bill: The natural followup question is how Lin's play compares with the hane-tsugi on the bottom. We can answer that question with a difference game, too.

[Diagram]
Difference game, original board  
[Diagram]
Difference game, mirror board  

Bill: First we set up the difference game with White making Lin's play on the original board and Black playing the hane-tsugi on the mirror board.

[Diagram]
Difference game, White plays first  
[Diagram]
 

White starts with sente, threatening the middle Black group, and then plays the hane-tsugi on the original board. Now the bottoms of the two boards are miai, and are equal. Black has nothing better than B6, but W7 wins the difference game by 1 point.

[Diagram]
Difference game, Black plays first  
[Diagram]
 

B11 at a.

Black starts with the hane, B1, which leaves the bottom on the first board as a STAR in chilled go. Now we are on familiar territory. The rest of the game plays itself. Each player advances in the corridors until B9. Black wins the difference game by 1 point.

Since each player, playing first, wins the difference game, which play is better depends upon the rest of the board.


BQM 222 last edited by Dieter on July 5, 2008 - 12:48
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