duel_simulation, a C++ code which simulates N instances of a duel between two players.

Player A fires at player B, and hits with a probability of A_ACCURACY. If Player A misses, then Player B fires at Player A, hitting with a probability of B_ACCURACY.

The duel continues with alternating shots until only one player survives.

The simulation is intended to estimate the probabilities that a player will survive.

The exact probability that player 1 will survive is

P(1) / ( P(1) + P(2) - P(1) * P(2) )
while player 2's chance is
P(2) * ( 1 - P(1) ) / ( P(1) + P(2) - P(1) * P(2) ).


The computer code and data files described and made available on this web page are distributed under the MIT license


duel_simulation is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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  1. Paul Nahin,
    Duelling Idiots and Other Probability Puzzlers,
    Princeton University Press, 2000,
    ISBN13: 978-0691009797,
    LC: QA273.N29.
  2. Martin Shubik,
    "Does the Fittest Necessarily Survive?",
    in Readings in Game Theory and Political Behavior,
    edited by Martin Shubik,
    Doubleday, 1954,
    LC: H61.S53.

Source Code:

Last revised on 25 February 2020.