A player pays $3 to play a game. A die is rolled. If the number on the die is 1, 2, or 3, the game is lost. If the number on the die is 4, 5, or 6, the die is rolled again. In this case the player wins if the second number is odd and loses otherwise. How much should the player win if the game is fair? (In a fair game the probability of winning times the amount won is what the player should pay.)