University of Miami
Department of Mathematics
College of Arts and Sciences

Larry Shepp
Rutgers University Statistics Department
Member of the National Academy of Sciences
Member of the American Academy of Arts & Sciences
Member of the Institute of Medicine

will present

A Tale of Two Casinos; How to Gamble If You Must, revisited

Friday, February 9, 2007, 3:30pm
Ungar Room 402

Refreshments at 3:00pm in Ungar Room 521
All interested persons are welcome to attend.


Abstract: In the well-known casino of Dubins and Savage there is only one {\em subfair} gamble available. Imagine you are in this casino and must multiply your current fortune by say 10 because you have a gambling debt to repay and you will be killed if you do not repay it. This is the theme of the 1965 book, "How to Gamble If You Must", by L. Dubins and Jimmie Savage which showed that you maximize your chance of survival if you play "boldly": bet your entire fortune or just enough of it to reach the goal.

Some people think that this is so obvious it does not even require proof, but there are variants which are even more "obvious" that are false. For example, suppose your entire fortune is reduced by dividing by $1+a$, where $a$ is a small positive number, after every bet. Now it is even more obvious that you want to minimize the number of bets by playing boldly, and bold play is indeed optimal for certain initial fortunes, but in general, Robert Chen showed that bold play is not optimal; you can get a strictly greater survival probability by making a smaller bet when your initial fortune belongs to a certain infinite set.

These are old results, but my colleagues and I have revisted these questions and we have many new insights which I will present. It's surprising when one can get new results on a 40 year old problem.

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