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| XGID=---BBDE---------A----dcdA-:1:1:1:61:3:5:0:11:10 | |||||
| Blue to play 61 | |||||
eXtreme Gammon Version: 2.10
The Dillies have a few rolls that we won’t like when we stay back, especially 31 and 21. Even if they roll one of them, however, we might enter immediately. When that happens, the only cost for staying back is 1 pip. Surprisingly, when the Dillies roll a doublet, we are not hurt as badly as when they can make their 1pt. With high doublets, it won’t make a difference if we run now, and with a low doublet, they may choose not to bear off any checkers. 11 is the doublet that makes the biggest difference. It let’s the Dillies put us on the bar and bear off at the same time. Even then, we would only be facing a three-point board.
What could really hurt us is dancing, but the odds of that happening are something like (Dillies roll 31 or 21)*(dance) + (Dillies roll 33 or 11)*(dance).
(4/36)*(16/36) + (2/36)*(9/36) = 82/1296 = 6.3%
Note, however, that if we run, the Dillies would use most of these rolls (31, 21, and 33) to bear off. That would also increase the odds that we lose a gammon. With those rolls, we are hurt no matter whether we run or stay.
With many other rolls, we are better off if we stay. That way, the Dillies cannot use aces, for instance, to split to their 1pt. They will also probably want to stay even on their rear point. This will slow down their bear-off, and make it easier for us to save the gammon.
With the rest of the rolls, it’s a wash. If the Dillies can bear-off two or four checkers safely, it does not hurt us to have stayed.
I have written this quickly, so it is likely that I overlooked some things. I hope, nevertheless, this will be of some help.
Mike