by Douglas Zare
1 October 2009

Duplication is one of the most fundamental tactical ideas in backgammon. Understanding the basics of duplication might separate the intermediate player from the novice, but there are aspects of duplication worth studying by experts.
There are many articles on the practice of duplication, and I particularly recommend the duplication material in Magriel's classic Backgammon. Since this is a theory column, we'll look at the theoretical foundation: Why duplication works, how much imperfect duplication is worth, and duplication of numbers versus duplication of rolls. We'll see an application of the temperature idea from combinatorial game theory to backgammon in a doubly duplicated position.
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Article text Copyright © 1999-2009 Douglas Zare and GammonVillage Inc.
In the last diagram, how do you count quintuplication of aces ? I can see two hits (19/20* and 4/5*) and one cover (17/18).
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