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Hyper dice backgammon of finite size. (English) Zbl 1414.91083

Summary: In this note, we extend the notion of standard backgammon to a more general setting and call it hyper dice backgammon (or HD-gammon for short) of size \(n \geq 6\) (a positive even integer) by extending the regular die to a hyper die (i.e., hyper cube) with \(n\) faces and the board from 24 pips to \(4n\) pips, where \(n = 2k \geq 6\) and there are \(4k+3\) checkers for each player. The rules of the game are similar to the rules of standard backgammon when \(n = 2k = 6\) and the number of the \(n\)-sided dice depends on \(n\). Finally, we include a list of references related to some theoretical studies on standard backgammon.

MSC:

91A60 Probabilistic games; gambling
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Full Text: Euclid