truel_simulation
truel_simulation,
a MATLAB 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.
Usage:
[ s, turn_average ] = truel_simulation ( p, duel_num )
where
-
p is a vector of length 3 containing the probabilities that each player
will hit the target they aim at on any given shot.
-
duel_num is the number of duels to simulate.
-
s is a vector of length 3 containing the probabilities that each
player is the survivor.
-
turn_average is the average number of turns to complete the duel.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
truel_simulation is available in
a MATLAB version and
an Octave version and
a Python version.
Related Data and codes:
truel_simulation_test
matlab_simulation,
a MATLAB code which
uses simulation to study card games, contests, and other processes
which have a random element. Usually, the purpose is to try to
predict the average behavior of the system over many trials.
Reference:
-
Martin Gardner,
"The Triangular Duel",
The Second Scientific American Book of Mathematical
Puzzles and Diversions,
Simon and Schuster, 1961.
-
Marc Kilgour, Steven Brams,
The Truel,
Mathematics Magazine,
Volume 70, Number 5, December 1997, pages 315-326.
-
Paul Nahin,
Duelling Idiots and Other Probability Puzzlers,
Princeton University Press, 2000,
ISBN13: 978-0691009797,
LC: QA273.N29.
-
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 02 April 2019.