(from 2010 exam) Consider a 'battleship' type game played on a 4 4 board.

(from 2010 exam) Consider a ‘battleship’ type game played on a 4 × 4 board. Player 1 secretly chooses a location for a domino (there are 24 possibilities but that is not so crucial to answering this question). Player 2 secretly chooses a position (among the 16 different possibilities). Player 1 wins $1 (and player 2 loses $1) if the domino does not occupy a position chosen by player 2 else player 2 wins $1 (and player 1 loses $1). One would quess that the value of the game is 12/16. Give a proof of this fact. Explicitly considering the 24 × 16 payoff matrix would probably be unproductive but you can use properties of the payoff matrix. Note: Only one student got this question on the final exam.