Seminars & Colloquia Calendar

Date: Thu., Oct. 12, 2023, 5:00pm (Eastern Time) 

Zoom Link [password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]

Speaker: Persi Diaconis, Stanford University

Title: GAMBLER'S RUIN WITH K GAMBLERS

Abstract: Consider (say) three gamblers with initial capital A, B , C. Each time a pair of gamblers are picked (uniformly at random), a fair coin is flipped and $1 is transfered. Eventually, one of the gamblers goes broke and the other two continue with the usual coin tossing until one is left with all A+B+C. Of interest: how long does this all take, what is the distribution of the 'elimination order' (where order 3,1,2 means that gambler C is eliminated first then A leaving B with all the money)? If the game goes on a long time and no one is eliminated where is it likely to be? AND how does all this depend on A,B,C. These questions are of interest in things like poker tournaments(world series of poker). In joint work with Stew Ethier, Laurent Saloff-Coste and Kelsey Huston-Edwards we have simulations, heuristics, bad asymptotics and some theorems. This has led to some nice 'useful' theorems of others. I'll try to explain to a non-specialist audience in 'English'.