A fair coin is tossed, and the result is shown to player 1. Player 1 must then decide whether to…

A fair coin is tossed, and the result is shown to player 1. Player 1 must then decide whether to pass or bet. If player 1 passes, then he must pay player 2 $1. If player 1 bets, then player 2 (who does not know the result of the coin toss) may either fold or call the bet. If player 2 folds, then she pays player 1 $1. If player 2 calls and the coin comes up heads, then she pays player 1 $2; if player 2 calls and the coin comes up tails, then player 1 must pay her $2. Show that if player 2 deviates from her optimal strategy, then player 1 can ensure that she earns an expected reward that is more than the value (1/3) of the game.