THE MATHEMATICAL ANALYSIS OF A SIMPLE DUEL

The principles and techniques of simple Markov processes are used to analyze a simple duel to determine the limiting state probabilities i.e., the probabilities of occurrence of the various possible outcomes of the duel. The duel is one in which A fires at B at a rate of r sub A shots per minute starting at time t o and with a single shot kill probability of P sub A and B fires at A at a rate of r sub B shots per minute starting at time delta and with a single shot kill probability of P sub B, and this exchange of fire continues until either A or B, or both are killed.