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BGonline.org Forums
I made the right play at DMP. This isn't DMP.
Posted By: Timothy Chow In Response To: I made the right play at DMP. This isn't DMP. (Rich Munitz)
Date: Saturday, 11 December 2010, at 9:09 p.m.
Yellow doesn't care about backgammon losses but does care about saving the gammon. Getting two crossovers with 24/18 7/4 doesn't help Yellow's cause because if Black doesn't roll a 1 and Yellow rolls boxcars next, Yellow still needs Black to roll a 1 and would prefer to have a shot at Black's blot rather than a 3/36 chance of getting off the gammon by racing.
So the choice is between running with something like 24/15 or hanging back with something like 12/6 7/4. The critical variations are those in which Black rolls an immediate 1 but not 11 (other variations either transpose or lose outright). If we run then we'll hit a shot immediately with 11/36 = 396/1296 probability, plus there's a (1/36)*(20/36)*(11/36) ~ 6/1296 chance of dancing with 22 and hitting a shot on the next turn. If we don't run then we'll lose outright if Black rolls doublets; in 10/36 cases we'll get a "coup classique" double shot (so that's 20*10/1296 = 200/1296 hitters) and in 20/36 cases we'll get a single direct shot (so that's 11*20/1296 = 220/1296 more hitters). Total of 420/1296 hitters, versus ~ 402/1296 hitters in the other case. So for saving the gammon it looks like hanging back is slightly better. Since winning is a long shot but saving the gammon is a reasonable possibility, I'll go with saving the gammon ATS.
There's still the question of what exactly to play, given that we don't touch the back checkers. If we do hit a shot then we'd like to make our ace point, so either 12/9 7/1 slotting the ace point or 12/3 getting three builders for it look better than my initial instinct of 12/6 7/4 (we're not trying to race off the gammon so bearing everything in isn't important). I don't know what's best but I'll try 12/3.
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