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capturing race problem

https://lifein19x19.com/viewtopic.php?t=10504

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capturing race problem

Posted: Sat Jun 28, 2014 1:58 pm
by macelee
A while ago I posted this capturing race:

http://www.lifein19x19.com/forum/viewto ... 10&t=10331

Now there's another game with bulky-5 big eye from a pro game recently added to Go4Go collection: http://www.go4go.net/go/games/sgfview/42384
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X O # . X O X X O O O O . |
$$ | O . O , O X X O X X . O . O X O X X X |
$$ | . . O X X O O . O O O . . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | O . X O . . O . . . O O . O O O O . . |
$$ | O O X O O O X X X . . . . . O X X O . |
$$ | O O X . O . O O X . . . . O X X X X O |
$$ | X X X X O O X . . , . . . . O X O O . |
$$ | . O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Why white had to resign? What's the outcome if white continues?

Re: capturing race problem

Posted: Sun Jun 29, 2014 12:43 am
by TheBigH
Who wins the capturing race? It looks like white has a lot more liberties, but those big eyes give you more effective liberties than you think. I can't quite read it out but it looks like B has 14 effective liberties against a similar number for white.

Re: capturing race problem

Posted: Sun Jun 29, 2014 1:49 am
by RobertJasiek
(The upper right corner can be ignored.)

Thanks to the big eye, the 1 internal liberty is Black's fighting liberty. Black has (12-5) + 4 + 1 = 12 fighting liberties.

Black can throw in once in White's eye, which thus amounts to 1 fighting liberty. White has 4 simple external liberties. Black needs 1 approach move to create the second approach defect in its basic form.

White's only ko threats are continued local semeai plays; so - except for possibly forcing Black to remove an almost-filling string of the big eye - we can assume no ko fight taking place. In each approach defect, White can recapture creating almost a basic ko shape. As the simplest strategy, in each approach defect, Black can eliminate its fighting liberties with 3 excess plays.

So - assuming no ko fight - the upper bound for White's fighting liberties is 1 + 4 + 1 + 3 + 3 = 12.

Since it is White's turn, White appears to win the semeai, but this is an illusion. Black can save one fighting liberty by not connecting the second approach defect's basic ko if, in attempt to win, White must have filled the internal liberty BEFORE Black would need to connect the second approach defect's basic ko. Let us verify this: Already White's 5th approach plays would need to fill the internal liberty. This is clearly BEFORE Black could need to connect the second approach defect's basic ko.

The remaining exercise is the verification of the assumption that White cannot construct a ko fight inside the semeai.

Re: capturing race problem

Posted: Sun Jun 29, 2014 1:51 am
by Cassandra
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X O X . X O X X O O O O . |
$$ | O . O 1 O X X O X X 6 O . O X O X X X |
$$ | 5 3 O X X O O . O O O 4 . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | O 0 X O . . O . 8 . O O . O O O O . . |
$$ | O O X O O O X X X . . . . . O X X O . |
$$ | O O X 9 O . O O X . . . . O X X X X O |
$$ | X X X X O O X 2 . , . . . . O X O O . |
$$ | 7 O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Please note that White has to occupy a shared liberty with 9.
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X O X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O . O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | . X X O . . O 2 X . O O . O O O O . . |
$$ | 1 3 X O O O X X X . . . . . O X X O . |
$$ | . . X O O 4 O O X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X O X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O 2 O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | . X X O . . O X X . O O . O O O O . . |
$$ | O O X O O O X X X . . . . . O X X O . |
$$ | . . X O O X 1 . X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X 2 X . X O X X O O O O . |
$$ | O . O O O X X 1 X X X O . O X O X X X |
$$ | O O O X X O O . O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | 6 X X O . . O X X . O O . O O O O . . |
$$ | O O X O O O X X X . . . . . O X X O . |
$$ | 3 5 X O O . O 4 X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X X X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O . O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | X X X O . . O X X . O O . O O O O . . |
$$ | 1 . X O O O X X X . . . . . O X X O . |
$$ | . . X O O 2 O X X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X X X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O . O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | X X X O . . O X X . O O . O O O O . . |
$$ | O 1 X O O O X X X . . . . . O X X O . |
$$ | 3 4 X O O X 2 X X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
The two Ko-shapes form a Double-Ko, so it makes no sense for White to pre-empt Black from connecting at 2.
Click Here To Show Diagram Code
[go]$$W
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X X X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O . O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | X X X O 3 2 O X X . O O . O O O O . . |
$$ | 1 . X O O O X X X . . . . . O X X O . |
$$ | . X X O O X X X X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . O X X . . X X O X X . . . . |
$$ | . . O . . . X X X . X O X X O O O O . |
$$ | O . O O O X X O X X X O . O X O X X X |
$$ | O O O X X O O 1 O O O X . O X X X . . |
$$ | X X X X O O O O O X X X X X X . . O . |
$$ | X X X O O . O X X . O O . O O O O . . |
$$ | O . X O O O X X X . . . . . O X X O . |
$$ | . X X O O X X X X . . . . O X X X X O |
$$ | X X X X O O X X . , . . . . O X O O . |
$$ | O O X O X X X . . . . . . . X X . . . |
$$ | O . O O O O X X X . . . . . . . X . . |
$$ | . O . . X . X O . . . . . . X O X . . |
$$ | . O X . X . X O . . . . . . . X O O . |
$$ | . . . . O O X . . X X . . . . . X O . |
$$ | . . O , . . O O O O X X X X X X . O . |
$$ | . . . O . . X O O X O O O X . X O . . |
$$ | . . . . . . . O X X . X . O X O O . . |
$$ | . . . . . . . . . . . . O . X . . . . |
$$ +---------------------------------------+[/go]
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