Stochastic Duels

Trevor Williams and Clinton J. Ancker
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Trevor Williams: The Johns Hopkins University, Baltimore, Maryland
Clinton J. Ancker: System Development Corporation, Santa Monica, California

Operations Research, 1963, vol. 11, issue 5, 803-817

Abstract: The relative importance of kill probabilities, rates of fire, and other parameters in a duel is considered by examining their effect on the most natural measure of effectiveness, the probability that a given side will win. In the “fundamental” duel, two contestants, A and B , fire at each other until one is killed. The time between rounds fired is a random variable of known but different density function for each, and each has a different known but fixed kill probability. The duel starts with both duelists having unloaded weapons and unlimited ammunition supplies. The general solution is obtained in quadrature form and specific solutions are derived for a particular firing time distribution and for certain variations in initial conditions. Finally, the general solution and a specific example for the duel with random initial surprise are obtained.

Date: 1963
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