If the pay-offs in an mXn zero-sum matrix game are drawn randomly from a finite set of number, N, then the probability of obtaining a pure strategy equilibrium, p, will be a weighted sum of the probabilities of obtaining a pure strategy equilibrium, ps, with s distinct payoffs, the weights, qs, being being the probabilities of obtaining s distinct payoffs from N. The paper also introduced the notion of separation of arrays, which is necessary and sufficient condition to be associated with a mixed strategy solution.