The Two-Dimensional Asymmetric Gambler's Ruin Problem with n Players and Simulations

摘要

In this article, the asymmetric n-player gambler's ruin problem is considered, when the players use equal initial fortunes of d dollars and d euros, 1 < d < n + 1. In each round an unfair coin is tossed to decide the currency. The expected ruin time and the individual ruin probabilities are computed. It is proved that the ruin time and which player is ruined are independent events. Finally, some special games are simulated. The simulation results verify the validity of the proposed formulas. As an innovation, the present study makes a combination of the n-player and multi dimensional games which can be viewed as a starting point for future studies.