Abstract: The index policy for offense-defense shooting process, namely, how a single red shoots at a collection of blue targets to maximize the return obtained from killed blue targets, is discussed. In consideration of the limitations of previous research and the balance of the red’s excepted return and survival probability, Gittins index is introduced and expanded to solve the shooting problems. The optimality of index shooting policy is discussed. Theorem 1 and 2 are extended, and Lemma 1 is presented. Three different shooting policies, such as myopic policy, exhaustive policy and round-robin policy, are introduced for comparison, and the optimality theorem 3 of myopic policy is proposed. 2 shooting scenes are set in numerical study. The red’s mean return, mean numbers of killed blue targets and red’s death rate are calculated for 4 policies. Simulation study outcome verified the optimality of index policy.

Key words: ordnance science and technology, shooting policy, Gittins index, index policy, myopic policy