### DIMACS Graduate Student Combinatorics Seminar Series

Title: Expected Number of Spins in Dreidel

Speaker: **Sujith Vijay**, Rutgers University

Date: Monday, November 3, 2003, 1:10 pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Dreidel is a popular game played during the festival of Chanukah. Players start with an equal number of tokens, donate one token each to a common pot, and take turns spinning a four-sided top, called the dreidel. Depending on the side showing up, the spinner takes all the tokens in the pot, takes half the tokens in the pot, gives a token to the pot, or does nothing. Whenever the pot goes empty, everyone donates a token to the pot. The game continues till all players, except one, go broke.

In this talk, I will outline (what seems to be) a proof of Prof. Doron Zeilberger's conjecture that the expected number of spins in a game of dreidel between two players starting with n tokens each is O(n^2). This is joint work with Thomas Robinson. Since the result is only a few days old, scepticism is encouraged. If something goes wrong, I'll state the Riemann hypothesis and stop, and we'll spend the rest of the hour trying to rectify the error.