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BGonline.org Forums
Updated Crawford rule and a mini-draft of a MET
Posted By: Fabrice Liardet In Response To: A game proposal : Tandem Backgammon (Fabrice Liardet)
Date: Wednesday, 23 December 2009, at 11:00 a.m.
It seems that the following Crawford rule would be simpler, would involve more decisions (there would be interesting cube decisions at all scores except -1,-1), and doesn't seem to screw up the match equities too much :
New Crawford rule : it is allowed to double in only one of the two games when the opponent is 1- or 2-away (maybe 3-away but I am not sure that it is really necessary). This applies to all games played from those scores : there is no post-Crawford.
The following table is computed applying that Crawford condition to all scores, with a 28% gammon rate and 0% backgammon rate, under the very simplifying assumption that one of the two games chosen at random is doubled - which probably consistently underestimates the trailer's equity. The values seem rather regular, except for the -1,-2 equity being a bit on the low side.
-1 -2 -3 -4 -5 -6 -1 0.5 0.59 0.715 0.7798 0.851664 0.8976 -2 0.41 0.5 0.625 0.6898 0.773328 0.82766208 -3 0.285 0.375 0.5 0.573872 0.66756208 0.733205574 -4 0.2202 0.3102 0.426128 0.5 0.591673734 0.661516269 -5 0.148336 0.226672 0.33243792 0.408326266 0.5 0.574842772 -6 0.1024 0.17233792 0.266794426 0.338483731 0.425157228 0.5
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