THE THREE-DIMENSIONAL NON-UNIFORM AND ASYMMETRIC n-PLAYER GAME WITH EQUAL INITIAL FORTUNES

Abstract

In this paper, we find expected duration time of the three-dimensional

gambler’s ruin problem with n players when the players have equal ini

tial fortunes of d in each currency, 1 ≤ d ≤ n + 1. Our result is an

extension of Hashemiparast and Sabzevari’s work when they found the

expected duration time of two-dimensional game. A limiting result when

our three-dimensional game is reduced to the two-dimensional game is

also discussed.