The asymmetric nn-player gambler’s ruin problem with ties allowed and simulation

The gambler’s ruin problems with more than two players for the symmetric and asymmetric cases have already been studied in the literature. Therefore, some specific generalizations of the ruin problems have been investigated. In this work, the asymmetric nn-player gambler’s ruin problem with equal initial fortunes of dd dollars, 1≤d≤n+11≤d≤n+1, and ties allowed is considered and 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 and the results are tested. The simulation results verify the validity of the proposed formulas.