Dieu Nguyen Dinh. A mathematical analysis of tactics in a riverine ambush

Monterey, California: Naval Postgraduate School, 1972. — 75 p.This thesis examines different strategies for a patrol boat in a riverine ambush before and after the ambush. Mathematical models employing concepts from games of strategy and statistical decision theory are used to study optimal tactics for the patrol boat before the ambush. A matrix game with the payoff a function of combat outcomes and combatant utility functions is used to study the optimal tactics for the boat and the ambushers. Using concepts of the statistical decision theory, various principles of choice are used to choose the appropriate decisions among all courses of action for the patrol boat. Several combat models are used to investigate the patrol boat's tactics after the ambush has commenced. A deterministic Lanchester-type model with lethalities of fires that very linearly with range is used to determine the casualty ratio between the two opponents. A stochastic model with constant attrition rates is used to calculate part of the probability distribution of the number of combattants alive at time t after the initiation of the ambush. Finally, a stochastic duel with displacement is used to determine the probability that one side would win in the ambush.