truel_simulation

truel_simulation, a Python code which simulates N instances of a duel between three players.

Player 1 fires at player 2 or 3, and hits with a probability of P(1). Then, if Player 2 is alive, he fires at Player 1 or 3, hitting with a probability of P(2). Then, if Player 3 is alive, he fires at Player 1 or 2, hitting with a probability of P(3). Play continues until only one duellist remains.

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

Licensing:

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

Languages:

truel_simulation is available in a MATLAB version and a Python version.

Related Data and codes:

brownian_motion_simulation, a MATLAB code which simulates Brownian motion in an M-dimensional region.

chuckaluck_simulation, a MATLAB code which simulates the Chuck-a-Luck gambling game.

duel_simulation, a MATLAB code which simulates N repetitions of a duel between two players, each of whom has a known firing accuracy.

fire_simulation, a MATLAB code which simulates a forest fire over a rectangular array of trees, starting at a single random location.

snakes_and_ladders_simulation, a Python code which simulates the game of Snakes and Ladders.

Reference:

  1. Martin Gardner,
    "The Triangular Duel",
    The Second Scientific American Book of Mathematical Puzzles and Diversions,
    Simon and Schuster, 1961.
  2. Marc Kilgour, Steven Brams,
    The Truel,
    Mathematics Magazine,
    Volume 70, Number 5, December 1997, pages 315-326.
  3. Paul Nahin,
    Duelling Idiots and Other Probability Puzzlers,
    Princeton University Press, 2000,
    ISBN13: 978-0691009797,
    LC: QA273.N29.
  4. 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 06 July 2022.