Richard McGovern - Marist College
Ruined Gamblers: Cautious and Bold
Suppose that you play the game of chance repeatedly against another player until one of you bankrupts the other. What is the probability that you will ultimately win? The solution to this problem is well known when both players place the same minimal bet on each game, but it becomes trickier when other betting strategies are allowed. This talk uses a technique borrowed from dynamical systems to solve the problem in the case where you adopt the boldest reasonable betting strategy. How should your relative skills affect your betting strategy? Is boldness or caution a better strategy?
Audience:
This talk should be easily accessible to undergraduates. It assumes no previous mathematical knowledge beyond elementary probability and arithmetic, but it poses a problem whose solution is unknown, at least to me.
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