A player pays 1 to play a game where three fair dice are rol

A player pays $1 to play a game where three fair dice are rolled. If three 6s are obtained the player wins $500, and otherwise the player wins nothing. What are the expected net winnings of this game? Would you want to play this game? Does your answer depend upon how many times you can play the game?

Solution

Expected net winnings = $1.32

You would want to play this game, because you are on average, going to more than double your money.

Chance of 3 6\'s are (1/6)^3 = 0.4629% of winning $500.

And 99.537% of losing $1

Multiply the odds by the winnings and add them for the expected net winnings of $1.32.