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General theory of Russian Roulette

Ryohei Miyadera
Organization: Kwansei Gakuin High School
Department: Mathematics Department
Daisuke Minematsu
Organization: Osaka University
Satoshi Hashiba
Munetoshi Sakaguchi
Kwansei Gakuin
Revision date


We present the mathematical theory of the Russian roulette. The theory of Russian roulette has many interesting properties.

Let F[p,n,m,v] be the probability of the v-th man losing in the Russian roulette game with p-players, n-chambers and m-bullets. If we make a triangle with F[p,n,m,v], then we get a triangle of fractions where its denominator and numerator form a pascal's triangle-like pattern.

The expectation of the player’s death has very interesting properties. For example the expectation is log(2) in a Russian roulette game with 2 players.

This article includes many new mathematical theorems, but many high school students can understand them. Many of the ideas in this are presented by high school students.
Updated by authors, 16 September 2005

*Mathematics > Probability and Statistics
*Mathematics > Recreational Mathematics

Russian roulette, probability, Expectation, game.
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Elementary Russian Roulette.pdf (160.9 KB) - PDF Document
Elementary Russian Roulette.nb (83.9 KB) - Mathematica Notebook
RussianRoulette.nb (302.2 KB) - Mathematica Notebook