Davies' Long L

[cyclops]

$$cdiagram 1 Basic form
$$ | . . , . , .
$$ | . O O O . .
$$ | . X X a O .
$$ | . . X b O .
$$ | . e X O O .
$$ | . c X O . .
$$ | . d . . . .
$$ +-------------

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.

$$cDiagram2 B1 at b
$$ | . . , . , .
$$ | . O O O O .
$$ | 3 X X a O .
$$ | . . X O O .
$$ | 2 O X O , .
$$ | b O X O . .
$$ | 4 X 5 . . .
$$ +-------------

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

$$cDiagram3
$$ | . . . . . .
$$ | . . , . , .
$$ | . O O O O .
$$ | b X X a O .
$$ | 3 . X O O .
$$ | 1 O X O , .
$$ | 2 O X O . .
$$ | . X c . . .
$$ +-------------

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.

$$cDiagram 4, 1 at 6, 3 and 5 at c, 4 at 8
$$ | . . , . , .
$$ | 0 O O O O .
$$ | 7 X X a O .
$$ | 2 b X O O .
$$ | 6 O X O , .
$$ | c O X O . .
$$ | 8 X 9 . . .
$$ +-------------

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.

[HermanHiddema]

$$Wc black sacrifices two stones
$$ | . . , . , .
$$ | . O O O . .
$$ | . X X . O .
$$ | 5 . X O O .
$$ | 4 3 X O . .
$$ | 6 1 X O . .
$$ | 7 2 . . . .
$$ +-------------

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]

$$Wc b8 captures w7
$$ | . . , . , .
$$ | . O O O . .
$$ | 9 X X . O .
$$ | O 0 X O O .
$$ | . O X O . .
$$ | 8 O X O . .
$$ | C X . . . .
$$ +-------------

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]

is auto-atari without the outside liberty, so effectively kills in that case. With the outside liberty, creates a connect-and-die, capturing two stones and thus living.

[cyclops]

Thanks for your diagram. It is very clarifying. The decisive diagram between some or none outside liberty.