Seminar Details

How many coin tosses would it take until reaching for the first time either n Heads or m Tails?. Although this setup is related to the classical Problem of points, prior work by Fermat and Pascal focused on the probability of getting n Heads vs getting m Tails, rather than on the duration of the game. Using probabilistic techniques, together with symbolic computation, we derive probability generating functions, closed-form expressions, and asymptotic formulas for moments of the stopping time to reach either n Heads or m Tails. In the symmetric case when n=m, we show that the expected duration with a fair coin is a polynomial in p whose coefficients are Catalan numbers. Time permitting, we will also discuss the related problem of obtaining n Heads and m Tails. Joint work with Svante Janson and Doron Zeilberger.