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The notion that a player might change his handling of the doubling cube during a match, based upon the relative strength of his opponent, is an old one. When I wrote Fish, my first book, in 1996, the advice in the backgammon literature was conjectural. Using software developed by Walter Trice I attempted to quantify such changes. Though I kept it as light as possible; Fish is a highly technical book. It is of almost no interest to the non-player, but for a serious student, ready for the challenge of, in Jeremy Bagai’s words, the “world’s most esoteric backgammon book,” it is the first and last word on the subject. Fish is available for $30 + shipping from Carol Joy Cole: cjc@tir.com. 
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From Barclay Cooke's Paradoxes and Probabilities Problem #20

White on roll. Cube action?

Barclay (Cooke) recommends that: a beginner double if playing an expert; an expert not double a beginner unless sure he’ll drop; that regardless of skill, for money this is double/take; finally, at 11-11 in a 15-point match, this is double/drop no matter who is playing. I agree with Barclay that an expert should only double if convinced his opponent will drop. Otherwise, I think doubling by anyone, at anytime, would be the greatest blunder since the Herschel Walker trade.

 

 

 
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