A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.)
Player A should show one finger with probability , two fingers with probability , and three fingers with probability .
Player B should show one finger with probability , two fingers with probability , and three fingers with probability .
Find the expected value of the game.
The expected outcome is the player A will win points per round, on average.
Solve the game with the given payoff matrix.
P = [-3 0 1; -6 0 0; 0 -1 -2]
Find the optimal row player strategy.
Find the optimal column player strategy.
Find the expected value of the game.