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

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