In a dice game, you win if the two dice come up 11.

Question

Otherwise, you lose $2.
What should be the profit for winning to make this game fair?

(Give an exact answer. Use symbolic notation and fractions where needed.)

Answer 1

To make the game fair, we need to compute the expected value of the game and set it to zero. Let x be the profit for winning. The probability of winning (rolling a sum of 11) is 2/36 = 1/18, since there are two combinations out of the 36 total possible dice combinations (5 and 6 or 6 and 5). The probability of losing (not rolling a sum of 11) is 17/18. So we have:

Expected value = (1/18)x - (17/18)(2) = 0.

Solving for x:

(1/18)x = (17/18)(2)
x = (17/1)(2)
x = 34

So, the profit for winning should be $34 to make the game fair.