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Daily Quiz 2/15: XGR+ evals
Posted By: Daniel Murphy In Response To: Daily Quiz 2/15: XGR+ evals (Timothy Chow)
Date: Saturday, 18 February 2012, at 9:14 p.m.
In Position 2,
why is there such a big difference between 19/14 8/6 and 18/13 8/6?
A big part of the explanation should be simply how often Blue immediately hits White when White runs after either play.
White's Roll Blue's hits after 19/14 8/6 Blue's hits after 18/13 8/6 66 1 * 0 = 0 1 * 0 = 0 65 (1's 3's 5's) 2 * 27 = 54 (indirect only) 2 * 13 = 26 64 (2's 4's 6's) 2 * 33 = 66 (1's 4's 7's) 2 * 23 = 46 63 (3's 5's 7's) 2 * 27 = 54 (2's 5's 8's) 2 * 24 = 48 62 (4's 6's 8's) 2 * 29 = 58 (3's 6's 9's) 2 * 30 = 60 61 (5's 7's 9's) 2 * 21 = 42 (4's 7's 10's) 2 * 19 = 38 Total 274/1296 = 21.1% 218/1296 = 16.8% 4.3% more hits after 19/14 8/6. For gammon saving, whether 6-6 hits or not probably doesn't matter much. White will bear off in no more than 4 rolls. Blue will need 10 crossovers or 11 crossovers. The big swing is on White's 6-5. After 19/14 8/6 Blue hits 75% of the time and needs 9 crossovers to save the gammon to White's 9 crossovers to bear off. After 18/13 8/6, White hits 23/13*, so Blue only hits immediately 36% of the time, and needs 12 crossovers to save the gammon.
In your rollout:
Play Single wins (CL) Gammon losses (CL) 19/13 8/6 48.84% 11.32% 18/13 8/6 46.58% 13.48% Difference 2.26% 2.16% If Blue is a slight favorite after White runs and Blue hits in the outfield, then 4.3% more hits would seem to explain, mostly, why 19/13 8/6 generates 2.3% more cubeless wins.
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