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Puzzles
Small chance of ending in doubles

Chuck Bower asks:
> Find a noncontact position where the probability of the game ending
> in doubles is LESS THAN 1/6.
Hmm. If we give one player exactly one checker on his 5 point, then 5 rolls
don't bear off immediately, and 20% of them (11, from the set 11, 12, 21,
13, 31) are doubles. So let's give both players 1 man on the 5. Then the
chance that the game ends with doubles is:
5/36 + 5/36 * 5/36 + 1/6 * 5/36 * 5/36 = 16.14%
That the one?
[Note: the reason you have all those 5s in there is that, purely by
coincidence, 5 doublets immediately end the game, and another 5 rolls don't
bear off.]
 walter trice




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