AN EXAMPLE OF AN UNFAIR SEQUENTIAL GAME OF PERFECT INFORMATION: A GAME-THEORETIC COMPARISON BETWEEN THE EN-GAMMON AND THE STANDARD BACKGAMMON

We introduce the notion of an unfair sequential game of perfect information as a general form of the EN-gammon, which is a concrete model of our discussion. We will discuss the unfairness of the EN-gammon when it is played for an odd number of times. We recall the notion of the EN-gammon, which is a backgammon variant and it follows exactly all the rules of the standard backgammon with the exception that both players using the entangled numbers of the dice for their turns, respectively. That is, the player who rolls the six-sided dice, plays with the face-up numbers showing on the dice and the opponent plays with the face-down numbers of the same rolling of those dice at his/her turn, respectively. In this game, only one of the players (by convention) rolls the dice till end of the game.