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[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.

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.

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.

_________________
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[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]

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[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.

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

_________________
I think I am so I think I am.