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BGonline.org Forums
Help! Why race when behind? -- Opening 21
Posted By: Rick Janowski In Response To: Help! Why race when behind? (David Rockwell)
Date: Tuesday, 23 July 2013, at 6:27 p.m.
Opening 21 for money (in response to David's question)
From XGR++ evaluations for the cubeful and cubeless variations (not rollouts), I estimated cube-efficiency coefficients for the two main plays, 21$ and 21S as follows:
21$: x1 = 0.742 (owning cube) and x2 = 0.738 (opponent owns cube)
21S: x1 = 0.727 (owning cube) and x2 = 0.721 (opponent owns cube)
When the cube is owned, the higher cube efficiency for slotting (0.015 difference) appears to have the effect of increasing the margin of superiority for 21$ by about 0.004 (0.0037 calculated). When the cube is owned by the opponent, the higher cube efficiency for slotting (0.017 difference) appears to have the effect of decreasing the margin of superiority for 21$ by about 0.004 (0.0044 calculated). Note that the marginal benefit caused by increased cube-efficiency from slotting benefits the cube-owner regardless of which player slots.
In the cube-centred position, where the equity is close to zero, the contrary effects almost cancel each other out. The net effect is to decrease the margin of superiority for 21$ by less than 0.001 (0.0007 calculated), i.e., very negligible. I also believe Jacoby considerations will have fairly negligible effect. Of course, it would be preferable to use rollout data, provided that each rollout has mutually consistent settings, but I think the XGR++ evaluations should give a reasonable picture of the cube mechanics. It is interesting to consider the average win and loss values (W and L respectively) of the two plays:
21$: W = 1.28, L = 1.30
21S: W = 1.28, L = 1.27
Assuming these values are representative, then it may be concluded that slotting doesn’t lead to a significant greater proportion of gammon wins, as appears to be the common and belief. The greater number of gammon wins is caused by the greater number of wins for slotting over splitting at the roughly the same gammon proportion. It would appear that the significant effect of slotting is to increase the proportion of gammon losses (and backgammon losses) in comparison to splitting. This may indicate that for slot vs. split plays, the gammon save play is more likely to deviate from the normal money play (or DMP play) than the gammon go play.
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