DUEL_SIMULATION
Simulation of a Duel

DUEL_SIMULATION is a FORTRAN77 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) )

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 FORTRAN77 version and a FORTRAN90 version and a Mathematica version and a MATLAB version.

Related Data and Programs:

BROWNIAN_MOTION_SIMULATION, a FORTRAN77 library which simulates Brownian motion in an M-dimensional region.

FAIR_DICE_SIMULATION, a FORTRAN77 program which simulates N tosses of 2 dice, making a histogram of the results.

HIGH_CARD_SIMULATION, a FORTRAN77 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 FORTRAN77 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.

POISSON_SIMULATION, a FORTRAN77 library which simulates a Poisson process in which events randomly occur with an average waiting time of Lambda.

REACTOR_SIMULATION, a FORTRAN77 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, FORTRAN77 programs which simulate the game of Snakes and Ladders.

THREE_BODY_SIMULATION, a FORTRAN77 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.

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.f, the source code.
• duel_simulation.sh, BASH commands to compile the source code.

List of Routines:

• DUEL_SIMULATION simulates a duel.
• DUEL_RESULT returns the outcome of a single duel.

You can go up one level to the FORTRAN77 source codes.