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BGonline.org Forums
I am now also convinced
Posted By: Rick Janowski In Response To: I am now also convinced (AP)
Date: Thursday, 22 August 2013, at 11:05 p.m.
With regard to optimal play, Appendix 3 of my paper "Take-Points in Money Games" < http://www.bkgm.com/articles/Janowski/cubeformulae.pdf > attempts to quantify how Jacoby modifies initial cube action. The key criteria is whether the player doubling has a greater or lesser gammon rate than the opponent(ignoring backgammon's for the sake of simplicity). With equal gammon rates there should be significant change, but where the doubler's gammon rate is higher than the opponent's doubling points are generally earlier. Kauder paradoxes are extreme cases of this effect where a position may be a correct double with negative equity. Conversely, where the doubler's gammon rate is less than that of the opponent, Jacoby has the effect of delaying the initial doubling point. Latto's paradox positions are extreme examples where an initial double may be later than a redouble, which would never happen in money backgammon where Jacoby is not used.
Tables A4 to A6 in the article illustrate how gammon rates effect cube action. As generally the player making an initial double has often developed a strong or threatening position by threatening to blitz or prime the opponent, it is more likely that the gammon rate will be higher than the opponent's. Consequently, Jacoby should tend to make initial doubles slightly earlier than without Jacoby for optimal play. For sub-optimal, I tend to think Jacoby has an increased effect in causing early initial cubes.
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