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Real Backgammon

Posted By: Rich Munitz
Date: Wednesday, 28 April 2010, at 5:21 p.m.

In Response To: Real Backgammon (Daniel Murphy)

Analyzed errors are real errors only if the expected equity of the actual play is less than the expected equity of the "correct" play.

When one plays to win rather than playing to minimize error rate, one attempts to create situations that will maximize the difference in error rates between the opponent and the player. For the stronger player that usually means creating complexity to generate positions that the weaker opponent will play poorly and the stronger player will play less poorly. For the weaker player that usually means creating simple, dice governed positions that will minimize the number of difficult decisions and thus reduce the skill edge held by the opponent. But sometimes it can be right for the strong player to simplify - that being when the opponent's play will be largely forced regardless, but the stronger player can pick a slightly inferior play in order to eliminate his own difficult choices (and errors) going forward.

So what matters is what is the long term effect on net error between players of the play actually made vs the "correct" play. The play choice is made once and for it to be profitable, the equity gain from future errors must exceed the equity lost from making the technically inferior play.

It seems to me that any single checker play has only so much potential ability to alter future error rates (whether increasing ones opponent's or reducing one's own). It seems reasonable that such net future error profit between two plays could easily exceed 0.010. Such technical errors would thereby be profitable. It seems unlikely that it would exceed 0.100. Such technical errors would thereby be unprofitable.

While the equity given up by 10 0.010 technical errors will always equal the equity given up by single 0.100 error, the potential for the 10 small errors to increase overall practical equity is much higher than the chance of the single large error doing so.

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