Consider a game in which a player rolls one die. If an odd number comes up, the player wins the number of dollars showing on the die. If an even number comes up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game fair? (Assume that there is no cost to play the game.)

The die has six sides.

Three are of an even (loosing) number: 2, 4, 6

Three of an an odd (winning) number: 1, 3, 5

The even numbers are greater.

The average even (loosing) number is 4.

The average odd (winning) number is 3.

On average, you can expect to loose half-a-dollar.

(If you want a math equation)

E = (1/6) (1) + (1/6) (-2) + (1/6) (3) + (1/6) (-4) + (1/6) (5) + 1/6 (-6)

E = (1/6) (1-2+3-4+5-6) = -3/6=-1/2