An approximative method of simulating a duel

We develop a dynamic Markovian method of simulating a battle between two infantry units. Its key feature is that the probabilities of the outcomes of the battle can be computed efficiently, without the joint distribution of the strengths of the units or their transition matrix, making the method feasible even with larger unit strengths. We find the probabilities of the outcomes to be close to the ones obtained from a more elaborate, but computationally more costly, joint Markov-chain model of strengths. Additionally, using our method we are able to compute the conditional distributions of the strength of a unit, given that it has, respectively, won the battle or been defeated by the enemy.