A ug 2 00 4 Dreidel Lasts O ( n 2 ) Spins

Feinerman [2] and Trachtenberg [3] investigated the fairness of a simplified model of dreidel. Zeilberger [4] conjectured that the expected number of spins in a game of dreidel between two players starting with n tokens each is O(n2). Later, Banderier [1] conjectured that even in a multi-player game, the expected number of spins before one of the players goes home is O(n2). We show that the expected duration of a game of dreidel where the players start with n tokens each is O(n2), irrespective of the number of players. Let P1, P2, . . . , Pk denote the players, in the order in which they spin the dreidel. We introduce three variants of the game of dreidel.