A player rolls a die and can win the number of dollars equal to the number on the die except when the die shows a 6. If a 6 is rolled, the player loses $6. If the game is to be fair, what should be the cost to play?
So, what is a fair game? A fair game is something where the expected value is zero. Let’s plug in all the numbers and the unknown (the cost) in the expected value calculations.
E = (1 + 2 + 3 + 4 + 5)/6 – 6/6 = 9/6 = 1.5
The expected value is $1.5. So the game can charge $1.5 to make it fair.
