Consider a 3 by 3 board and suppose that Player I hides a destroyer(length 2 squares) vertically or horizontally on this board. Then Player II shoots by calling out squares of the board, one at a time. After each shot, Player I says whether the shot was a hit or a miss. Player II continues until both squares of the destroyer have been hit.The payoff to Player I is the number of shots that Player II has made. Let us label the squares from 1 to 9 as follows.
Solve the game.
Note: this problem is invariant under rotations and reflections, hence can be forged into a 2 by n game where n is the number of invariant strategies of player II. However, I don't understand the relationship between payoff of I and strategy of II here. What is the payoff for I? The cost II pays each time when he shoots a number from 1 to 9 or something else? And how to deduce this? Via probability of each calling and its consequence?