Stochastic Duels with Limited Ammunition Supply

In a previous paper the ground work was laid for a new theoretical model of combat called the “stochastic duel.” The principal elements of the model were fixed kill probabilities on each round fired, a random time between rounds fired, and unlimited ammunition supply. This paper extends the solution to those more realistic cases of limited ammunition supply. The general solution (as a quadrature) is obtained and it is applied to several specific examples. The special case of finite, fixed ammunition supply is treated separately.