"A soldier can hide in one of five foxholes, and a gunner can hide in four spots: A, B C, and D. The configuration looks like this: 1 (A) 2 (B) 3 (C) 4 (D) 5. If a shot is fired at a location and the soldier is in an adjacent foxhole (ex: shot is fired at B and soldier is in hole #2 or #3), the gunner received a reward of 1. Otherwise, the gunner receives a reward of 0. Assume that this is a zero-sum game
We are given that the optimal strategy for the soldier is to hide 1/3 of the time in foxholes 1, 3 and 5. For the gunner, an optimal strategy is to shoot 1.3 of the time at A, 1/3 of the time at D, and 1/3 of the time at B or C.
I have to determine the value of the game for the gunner. Honestly, I have no idea where to start. I know why the player should hide at holes one and five, but not three. How would I go about solving this>.