Dr. Sheldon Ross (USC)

Title: Some Gambler Ruin Type Problems

Abstract: We consider two multi player variants of the classical gambler's ruin problem. In both models we suppose there are k players, with initial fortunes n_1, ... , n_k In the rst model, at each stage two of the players with positive fortunes are chosen to play a game in which each is equally likely to win, with the loser giving one unit to the winner. In the second model, at each stage each player that has a positive fortune puts one unit into a pot which is equally likely to be won by each of them. In both models we are interested in such quantities as the mean number of games played. The first model is solved by elementary arguments, whereas the analysis in the second model utilizes martingale theory.