A DICELESS GAME OF THE CLASSIC AND FINITE HYPER DICE BACKGAMMON: A NEW CLASS OF PARTIZAN COMBINATORIAL GAMES

Abstract

We introduce the notion of a combinatorial game defined on a finite hyper
dice backgammon (which is a generalization of the standard backgammon) by omitting
the dice from it and call it Diceless or No Chance hyper dice backgammon. Instead of a
random element, players choose their own numbers under certain constraints in full view
of the opponent. The idea for this new game is simple and converts a non-combinatorial
game (a game of chance) into an extended Partizan Combinatorial Game.