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Puzzle: Fool's mate in backgammon

Posted By: Timothy Chow
Date: Tuesday, 22 May 2012, at 10:54 p.m.

Here's a backgammon puzzle that I think is new. I haven't solved it myself so I'm not sure how interesting it is, but I think it's neither trivial nor excessively difficult (which is a necessary, though not sufficient, condition for a puzzle to be good).

What is the shortest sequence of rolls and legal plays, starting from the opening position, that produces a gin position? Assume DMP. By a "gin position" I mean a position in which one side is guaranteed to win, no matter what rolls there are in the future.

Bonus question: Does it matter whether we assume that future rolls are played "intelligently"? For example, I would normally consider the position below to be gin, but Blue could misplay 21 31 41 51 61 and lose.

Match to 1, Tied at 0-0
White on roll
White5

Blue3
GNUBg Id: HwAAQAEAAAAAAA:MAEgAAAAAAAA
XGID=-AA---------------------e-:0:0:-1:00:0:0:0:1:1

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