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SMITH and JONES: The Undoubled Game

Posted By: Timothy Chow
Date: Wednesday, 31 May 2017, at 12:28 a.m.

In Response To: SMITH and JONES: The Undoubled Game (Nack Ballard)

Nack, I don't think that your modified opening position works.

First of all, when you suppose that "backgammon were instead played with the opening position shown below," am I correct to assume that you're hypothesizing this starting position only for the 2a2a score? That is, if somehow the game were to terminate in D/P, then the ensuing Crawford game would be played starting from the standard opening position (rather than using your modified position again)? It sounds like you are, since you're talking about using XGR++, which uses a MET based on rollouts from the standard position, but I wanted to confirm.

If we assume this (and therefore a standard MET), then Bob Koca's proof seems to apply to your starting position. That is, when it's your first opportunity to double, you will not have already lost your market. The strategy "double at first opportunity, always take if doubled, and play checkers as if it were DMP" will achieve at least 50% winning probability against any player that always accepts your double. Since you haven't lost your market when you offer your double, the opponent can't hold you to less than 50% by dropping the double, so this strategy must be optimal.

I don't think XGR++ can be trusted for equities as small as you're talking about.

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