Hyper Dice Backgammon of Finite Size

Abstract

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.