AQR Section 13 Exercise 57: Fair Game?

Is the game fair? Roll a single die. If a 6 appears, you win $2. If a 5 appears, you win $1. If any other number appears, you win 50¢. You pay $1 to play the game. The applet below simulates this game and displays a histogram of the net winnings (winnings - $1 it costs to play). Click on the RESET button to clear the data, the press the small PLAY arrow in the lower left corner to start a new simulation.
Is the game fair? If yes, why? If no, how can you change the game to make it fair?