DUEL_SIMULATION
Simulation of a Duel

DUEL_SIMULATION is a MATHEMATICA 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) ).

Usage:

s = duel_simulation ( p, duel_num )

• p is a vector of length 2 containing the probabilities that player 1 and player 2 will hit.
• duel_num is the number of duels to simulate.
• s is a vector of length 2 containing the probabilities that player 1 or player 2 survives.

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 Mathematica version and a MATLAB version.

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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:

• duelSimulation.nb, a program that returns the estimated survival probabilities for both players, based on a number of duels.
• duelOnce.nb, a program that returns the survivor of a single duel.

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