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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
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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