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BGonline.org Forums
Smallest Possible Chance to Win? - Mochy
Posted By: Stein Kulseth In Response To: Smallest Possible Chance to Win? - Mochy (Carlo Melzi)
Date: Tuesday, 18 May 2010, at 11:57 a.m.
I don't think it comes close. Håvard said the original was on the order of 10E-34, but I think he overdid it, in assuming that all combinations of doubles >= 33 would do it. White's 15 checkers have 21 pips to go so he need on average to roll better than 55. All combinations of doubles >= 44 would together average 20 pips, so somewhat less than half of these would work, then again a few other compinations with the odd 33 or 22 would also work, but in any case, I think the actual chance would be closer to the order of 10E-36.
Over to your position, of course White needs to start off with 11, then Black needs to roll 2 or 3 11's in order for White to blot, and then Black must hit. This parlay is 1/36 * 1/36 * (1/6*1/36*5/6 + 5/6*1/36*1/6 + 5/6*1/36*5/6*1/36*5/6) * 11/36, but this is still only on the order of 10E-6. Now Black basically must be better than 10E-30 to win from here, Conseider this variation:
I'd think black hits white and ending up in his outer board about 10%, then let White roll 11 to dance, black to roll 66 and take 3 off, white to roll 11 again and black roll another double. This parlay is 10% * 1/36^3 * 1/6 ~ 10E-7, from here White has 25 pips against Black 8 checkers, which would be within normal estimates, surely nowhere in the 10E-23 order.
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