Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: nyu notesfiles V1.1 4/1/84; site csd2.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!genrad!mit-eddie!godot!harvard!seismo!cmcl2!csd2!bleich From: bleich@csd2.UUCP Newsgroups: net.religion.jewish Subject: dreydel is an unfair game Message-ID: <42700011@csd2.UUCP> Date: Thu, 20-Dec-84 13:02:00 EST Article-I.D.: csd2.42700011 Posted: Thu Dec 20 13:02:00 1984 Date-Received: Sun, 23-Dec-84 00:24:00 EST Organization: New York University Lines: 24 Nf-ID: #N:csd2:42700011:000:738 Nf-From: csd2!bleich Dec 20 13:02:00 1984 Hint to all dreydel players: make sure that you go first! An article in the American Mathematical Monthly (Robert Feinerman, "An Ancient Unfair Game", Vol. 83, pp. 623-625 (1976) ), contains a proof that dreydel is biased in favor of the first player. The main theorem is that given p players, let Xn be the payoff on the nth spin. Then the expected value of Xn, E(Xn) is p/4 + (5/8)**(n-1) * ( (p-2)/8 ) so that if p>2, E(Xn) is a strictly monotonic decreasing function of n. The first player spins are 1, p+1, p+2, while the second player spins on 2, p+2, p+3, so the first player has a larger expected payoff at each round. Anyone know the odds on kvittlach? Happy Chanuka! Chaya Bleich allegra!cmcl2!csd2!bleich