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last roll situation
Posted By: scotty
Date: Monday, 7 July 2014, at 9:26 a.m.
In Response To: last roll situation (Bob Koca)
blue has 6 rolls which win the game for him immediately. Blue will miss 5/6 of the time. White has 23 rolls which win IF blue misses, for a (5/6)*(23/36) chance to win. This is 115/216. 50% would be 108/216, so eyeballing it, white wins about 53% of the games on his single roll. White is better than 50% so blue must necessarily be worse than 50%. Blue has no cube here, since his doubling window begins at 58.5% ATS. Cube action : no double.
IF blue does miss, white will have a cube. We already know, using contemporary MET that white needs 15 winning rolls ATS, and white has 23. White has only 6 pips remaining, and will certainly bear off in 2 rolls
Should blue accept white's cube?
At this score, if blue drops the cube, the score will be 1a, 3a, in favour of white, and blues MWC will be about 25%.
If blue takes and wins, the score will be 1a, 2a, Crawford, in favour of blue. Blues MWC = 67.7
If blue takes and loses, his MWC = 0
Blue is risking 25% to gain 42.7% eyeballing the numbers OTB 25/67.7 (quick and dirty estimate) = approx 37%
(3/2)*67.7 is nearly 100, (3/2) *25 = 37.5 round down to compensate for error in the denominator Second estimate, multiply by 1.1/2 to get number of dice rolls needed to accept cube... 1.1 * 67.7 is close to 72...divide by two to make it approx 36, do the same for 25, and we can clearly see we need more than 13 winning rolls to take the cube, even though the estimate underestimates the number of rolls needed to take the cube.
blue needs about 37% MWC to accept a cube, which is slightly more than the 13 winning rolls which blue has.
Further, blue has no more than 13 rolls which give him some chance to roll again, and even so, still might not bear off his last checker, so a white cube would be a definite drop for blue.
Blues winning chances are 1 in 6. If he misses, he doesn't get a second chance.

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