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BGonline.org Forums
I should have been able to figure this out
Posted By: Daniel Murphy In Response To: I should have been able to figure this out (neilkaz)
Date: Saturday, 26 May 2012, at 2:00 a.m.
Assume White knows his take point on a 4-cube and Blue's take point on an 8-cube at 7-away all.
White might note that White's main winning chance is for Blue to miss once in two rolls while White does not miss on his first roll. If that happens White's second roll doesn't matter.
White misses exactly half the time on his first roll -- any 3 or 2 except doublet 22 and 33.
White might make a rough estimate of the chance that Blue misses at least once in two rolls as 50%. That's an approximation of a closer estimate, 25/36*25/36 = 625/1296 = 48.22%.
(Still ignoring White's roll, the exact number is, I believe, 10/36 + 1/36*19/36 + 20/36*11/36 = 46.22% and, figuring in White's roll, it is, I believe, 10/36 + 1/36*33/36*19/36 + 20/36*33/36*11/36 = 44.68%.)
Back to rough estimates, 50% * 1/2 would give Blue 1/4 = 25% GWC, and 48% * 1/2 would give White 24% GWC.
(And .4622 * 1/2 = 23.11% GWC, and .4468 * 1/2 = 22.34% GWC)
OTB, White might estimate 25% or 24% GWC, knowing that both numbers have slightly overestimated Blue's actual chance of missing, but also estimating or guessing that White has enough other ways to win to give White a take. For instance, White could win by rolling a good doublet on his first roll (that's worth about 25/36*3/36*25/36 = 1.1%), or win with a miss on his first roll and a good doublet on his second roll as long if White misses at least once (I think that's worth 22.34% * 1/2*5/36 = 1.5%).
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