# Math

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A carnival game consists of rolling a single fair die, with the following results: you win \$8 for a 6, \$7 for a 5, and lose \$3 for any other number. Set a probability distribution, and calculate (already did) the

Expected value = .50
Variance= 24.58
standard deviation= 4.96

What fee should be charged to make it a fair game?

• Math -

The equally probable monetary results of a toss are +8,+7,-3, -3, -3 and -3. The expected result is (15-12)/6 = 0.50, a 50 cent gain. I assume you calculated the variance correctly also.

The breakeven charge for a toss should be 50 cents. This is true regardless of the standard deviation. If the House charges more than 50 cents, the player will lose in the long run. Sixty cents would be a fair charge that allows a House profit. As a sucker bet, they might try to charge \$1.

• Math -

If all the possible outcomes are independent, one merely has to add the expected return of each outcome, so...

"fair game" charge = 8(1/6) + 7(1/6) + (-3)(4/6)
= .50

So in the "long run" at a 50 cents charge both the player and the house would break even.

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