Player I and player II each have two pennies. Each player holds 0, 1, or 2 pennies in his left hand and the remainder of the pennies (2, 1, or 0 respectively) in his right hand. Each player reveals both hands simultaneously. If the number of coins in one of player I's hands is greater than the number of coins in the respective hand of player II, player I wins the difference in pennies; otherwise, no money is exchanged.

(a). Find the von Neumann value and the optimal strategy for each player in the game. If any player has infinitely many optimal strategies, find all optimal strategies.

(b). If player I owed $100 to player II, approximately how many rounds of the game would have to be played, on the average, to cancel the debt?

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