Asymptotic results for the asymmetric n-player gambler's ruin problem with ties allowed

چکیده مقاله

In this paper, we consider the asymptotic results for the asymmetric $n$-player gambler's ruin problem with equal initial fortunes of d dollars, 1 <= d <= n+1, and ties allowed. It is shown that when we do not have the possibility of tie in the game, the increase in the number of players will change the ruin time from a random variable to a degenerate random variable. Also, the asymptotic results for more general cases are considered.