In a game of chuck-a-Luck, a player can bet $1 on any one of the numbers 1, 2, 3, 4, 5, and 6. Three dice are rolled. if the player's number appears k times, where k > 1, the player gets $k back, plus the original stake of $1. Otherwise, the player loses the $1 stake, some people find this game very appealing. They argue that they have a 1/6 chance of getting their number on each die, so at least a 1/6 + 1 /6 = 50% chance of doubling their money that's enough to break even, they figure, so the possible extra payoff in case their number comes up more than once puts the game in their favor.
a) What do you think of this reasoning?
b) Over the long run, how many cents per game should a player expect to win or lose playing chuck-a-Luck?