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2006-02-27
Source: Solution follows
Linear Go is Go played on a 1 by N "grid". For 1 by N Go, the Japanese rules' concept of life is ill-defined, so Linear Go uses the Situational SuperKo rule (no repeating a position with the same player to play), along with Chinese area scoring. Assume no komi. Two consecutive passes ends the game. Linear Go may actually be more complex than Go played on a square board with the same number of points. For example, proving optimal play on a 6x6 board is almost surely vastly easier than doing so for a 1x36 board. Hopefully the solution below will give you an appreciation for how, even for a "trivial" 1x6 position, optimal play is far from trivial! (But haven't we all come to expect such surprises from Go?)
So Black wins by 1 point.
But can Black do better than pass?
So White must counter-sacrifice with 6!
So the conclusion is that Black 1 was too greedy.
Black can do no better in the original position
than to pass for the 1 point win.
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Problem diagram.
What if Black sacrifices with 1 to try to take
the whole board?
White must capture with 2, and 3 is Black's best
chance. No matter what, black can make a capture
on the next move. Things don't look so simple
any more.
Black 5 threatens to capture White 4 next,
and then to capture again by playing in the
right "corner". At that point, White cannot
recapture because of the Superko rule, and
Black would take the entire board.
With 7 Black has wiped White off the board, but
the play at 8 shows that White still has resources.
White 10 is forced. and to justify Black's
original sacrifice at 1, Black must try 11.
And White 12 is forced.
Black 13 is forced.
White 14 finally puts an end to Black's mischief.
White takes the entire board.