Simulation of a Duel

DUEL_SIMULATION is a C program 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 made available on this web page are distributed under the GNU LGPL license.


DUEL_SIMULATION is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a Mathematica version and a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a C library which simulates Brownian motion in an M-dimensional region.

FAIR_DICE_SIMULATION, a C program which simulates N tosses of 2 dice, making a histogram of the results.

FOREST_FIRE_SIMULATION, a C program which simulates the occurrence of fires and regrowth in a forest, displaying the results using X Windows, by Michael Creutz.

HIGH_CARD_SIMULATION, a C program which simulates a situation in which you see the cards in a deck one by one, and must select the one you think is the highest and stop; the program uses GNUPLOT for graphics.

ISING_2D_SIMULATION, a C program which carries out a Monte Carlo simulation of an Ising model. a 2D array of positive and negative charges, each of which is likely to "flip" to be in agreement with neighbors.

LIFE_OPENGL, a C program which uses OpenGL to display the evolution of John Conway's "Game of Life", by Simon Green.

POISSON_SIMULATION, a C library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

REACTOR_SIMULATION, a C program which a simple Monte Carlo simulation of the shielding effect of a slab of a certain thickness in front of a neutron source. This program was provided as an example with the book "Numerical Methods and Software."

SNAKES_AND_LADDERS, C programs which simulate the game of Snakes and Ladders.

STRING_SIMULATION, a C program which simulates the behavior of a vibrating string.

THREE_BODY_SIMULATION, a C program which simulates the behavior of three planets, constrained to lie in a plane, and moving under the influence of gravity, by Walter Gander and Jiri Hrebicek.

XISING, a C program which models the variations in ferromagnetism in a material, displaying the results using X Windows.

XWAVES, a C program which simulates the behavior of solutions of certain forms of the wave equation, displaying the results using X Windows.


  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:

You can go up one level to the C source codes.

Last revised on 04 September 2012.