In a gambling game, Player A and Player B both have $1 and a $5 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player Bs bill. If the bills match, Player B wins Player As bill.

1. Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A.
2. Is there a pure strategy? Why or why not?
3. Determine optimal strategies and the value of this game. Does the game favor one player over the other?
4. Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player As winnings? Comment on why it is important to follow an optimal game theory strategy.

Hint: Player A wants to consider playing one of the bills all of the time