Some Multiple Player Gambler’s Ruin Problems

Start: 02/11/2010 - 4:15pm
End  : 02/11/2010 - 5:15pm

Statistics/OR/Math Finance Seminar

Sheldon Ross, USC


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

Harvey Mudd College 3rd floor Sprague Refreshments at 4pm.