**TITLE:** Some Multiple Player Gambler’s Ruin Problems

**SPEAKER:** Sheldon M. Ross

**ABSTRACT:**

Suppose there are r gamblers, with gambler i initially having a fortune of n_{i}. In our first model we suppose that at each stage two of the gamblers are chosen to play a game, equally likely to be won by either player, with the winner of the game receiving 1 from the loser. Any gambler whose fortune becomes 0 leaves, and this continues until there is only a single gambler left. We are interested in the probability that player i is the one left, and in the the mean number of games played between specified players i and j. In our second model we suppose that all remaining players contribute 1 to a pot, which is equally likely to be won by each of them. The problem here is to determine the expected number of games played until one player has all the

funds.