Richard McGovern - Marist College
Ruined Gamblers: Cautious and Bold
Suppose that you play a game of chance such as poker or backgammon repeatedly against another player until one of you bankrupts the other. What is the probability that you will ultimately win? How should your relative skills affect your betting strategy? Is boldness or caution a better strategy?
The solution to this problem is well known when both players place minimal bets on each game, but it becomes trickier when other betting strategies are allowed.
This talk should be easily accessible to undergraduates. It assumes no previous mathematical knowledge beyond high-school algebra, but it poses some problems whose solutions are unknown, at least to me. It also takes brief side-trips into finite difference equations, finite state machines and elementary number theory.
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