Two numerical methods for computing the probability of outcome of a battle of Lanchester type

Methods are developed for the computation of victory probabilities in the classical Lanchester ‘modern warfare’ model. The first method employs a bivariate normal approximation for state probabilities and a kind of steepest descents technique for the evaluation of the integral: the second proposes a truncated binomial approximation along certain diagonal lines. Both methods depend on moments. Computational performance is discussed.