A domino piece can be placed on a 2 × 3 checkerboard in seven different ways: The first player places the domino and the second player selects one of the six squares. If the selected square is covered by the domino, then the second player wins; otherwise the first player wins. Is this game fair? What are the optimal strategies? Can you exploit the symmetries? How do your findings generalize to larger boards?
I have difficulty in writing the payoff matrix. I know that a good strategy to choose for player 2 is to place the domino somewhere in the center however, I cannot come up with the matrix.