DUEL_SIMULATION
Simulation of a Duel

DUEL_SIMULATION is a Python program which simulates N instances of a duel between two players.

Player 1 fires at player 2, and hits with a probability of P(1). If Player 1 misses, then Player 2 fires at Player 1, hitting with a probability of P(2).

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

The simulation is intended to estimate the probabilities that a player will survive, and the number of turns required.

The exact probability that player 1 will survive is

P(1) / ( P(1) + P(2) - P(1) * P(2) )

P(2) * ( 1 - P(1) ) / ( P(1) + P(2) - P(1) * P(2) ).

Licensing:

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

Languages:

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

Related Data and Programs:

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

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

Reference:

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:

• duel_simulation.py, the source code.
• duel_simulation.sh, runs all the tests.
• duel_simulation.txt, the output file.

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