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Davies' Long L
http://www.lifein19x19.com/viewtopic.php?f=15&t=2088		 Page 1 of 1
Author:  cyclops [ Mon Oct 11, 2010 5:58 am ]
Post subject:  Davies' Long L
Click Here To Show Diagram Code
[go]$$cdiagram 1 Basic form
$$ | . . , . , .
$$ | . O O O . .
$$ | . X X a O .
$$ | . . X b O .
$$ | . e X O O .
$$ | . c X O . .
$$ | . d . . . .
$$ +-------------[/go]

The status of the Long L group depends according to James Davies ( Life and Death, Ch 27 ) on the number of outside liberties a and b. If none White can get a thousand-year ko at best. If one white can't kill but can get a seki. You can check this in the next two hidden diagrams showing both main variants.
All variants start with Wc, Bd and We in the Basic Form.
I start numbering from there.

Diagram 2: No outside liberties ( a is filled ), main variant: thousand year ko. Probably settles in seki finally but remains some burden for black.
Click Here To Show Diagram Code
[go]$$cDiagram2 B1 at b
$$ | . . , . , .
$$ | . O O O O .
$$ | 3 X X a O .
$$ | . . X O O .
$$ | 2 O X O , .
$$ | b O X O . .
$$ | 4 X 5 . . .
$$ +-------------[/go]


Diagram 3: One outside liberty : main variant seki
Click Here To Show Diagram Code
[go]$$cDiagram3
$$ | . . . . . .
$$ | . . , . , .
$$ | . O O O O .
$$ | b X X a O .
$$ | 3 . X O O .
$$ | 1 O X O , .
$$ | 2 O X O . .
$$ | . X c . . .
$$ +-------------[/go]


Black cannot be prevented from filling at b and c for seki.

In both hidden diagrams outside liberties seem unimportant. So I searched for the subvariant in which the outside liberty mattered. I think it is in the next hidden diagram. But some comfirmation would be welcome.
Click Here To Show Diagram Code
[go]$$cDiagram 4, 1 at 6, 3 and 5 at c, 4 at 8
$$ | . . , . , .
$$ | 0 O O O O .
$$ | 7 X X a O .
$$ | 2 b X O O .
$$ | 6 O X O , .
$$ | c O X O . .
$$ | 8 X 9 . . .
$$ +-------------[/go]

Diagram4: If a is empty black can play b next and live. Otherwise he has to fight the ko at c. ( indirect for white )

A question for me remains why in the no outside liberty case the thousand year ko of diagram 2 is more profitable to black than the indirect ko of diagram 4.
Author:  HermanHiddema [ Mon Oct 11, 2010 6:42 am ]
Post subject:  Re: Davies' Long L
Click Here To Show Diagram Code
[go]$$Wc black sacrifices two stones
$$ | . . , . , .
$$ | . O O O . .
$$ | . X X . O .
$$ | 5 . X O O .
$$ | 4 3 X O . .
$$ | 6 1 X O . .
$$ | 7 2 . . . .
$$ +-------------[/go]


Click Here To Show Diagram Code
[go]$$Wc b8 captures w7
$$ | . . , . , .
$$ | . O O O . .
$$ | 9 X X . O .
$$ | O 0 X O O .
$$ | . O X O . .
$$ | 8 O X O . .
$$ | C X . . . .
$$ +-------------[/go]


:b10: is auto-atari without the outside liberty, so :w9: effectively kills in that case. With the outside liberty, :b10: creates a connect-and-die, capturing two stones and thus living.
Author:  cyclops [ Mon Oct 11, 2010 4:33 pm ]
Post subject:  Re: Davies' Long L
Thanks for your diagram. It is very clarifying. The decisive diagram between some or none outside liberty.
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