Russian Roulette

Russian roulette is a game of chance in which one or more of the six chambers of a revolver are filled with cartridges, the chamber is rotated at random, and the gun is fired. The shooter bets on whether the chamber which rotates into place will be loaded. If it is, he loses not only his bet but his life. In the case of a revolver with six chambers (revolvers with 5, 7, or 8 chambers are also common), the shooter has a 1/6 chance of dying (ignoring the fact that the probability of firing the round is always somewhat less than 1/n for a n-shot revolver because the mass of the round in the cylinder causes an imbalance, and the cylinder will tend to stop rotating with its heavy side at or close to the bottom, while the firing pin is opposite the top chamber).

A modified version is considered by Blom et al. (1996) and Blom (1989). In this variant, the revolver is loaded with a single cartridge, and two duelists alternately spin the chamber and fire at themselves until one is killed. In the case of a revolver with six chambers (and again ignoring any imbalance in a real revolver), the probability that the first duelist is killed is then 6/11.

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Blom, G. Probabilities and Statistics: Theory and Applications. New York: Springer-Verlag, p. 32, 1989.Blom, G.; Englund, J.-E.; and Sandell, D. "General Russian Roulette." Math. Mag. 69, 293-297, 1996. Miyadera, R. "General Theory of Russian Roulette."

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Russian Roulette

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Weisstein, Eric W. "Russian Roulette." From MathWorld--A Wolfram Web Resource.

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