Suppose Player 1 believes that Player 2 will play Heads 30% of the time and Tails 70%. What is Player 1's expected payoff if she plays Heads?
E(H) = .3 x 1 + .7 x -1 = -.4
What is her expected payoff for playing Tails?
E(T) = .3 x -1 + .7 x 1 = .4

   If Player 2 is showing Heads with a probability of .3 and Tails with a probability of .7 then Player 1 will maximzine her expected payoff by always playing the pure strategy Tails. On average Player 1 should expect to win .4 for playing Tails and lose .4 for playing Heads. Be sure you understand why she would never play Heads.

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