# Math

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During a game, a balanced die is rolled. A player receives \$22 when an even number is rolled, and loses \$12 when an odd number is rolled. How much money can he expect on average in the long run?

• Math -

For a balanced die, the probability of getting an even number is n({2,4,6})/n({1,2,3,4,5,6})=1/2.
Similarly, the probability of getting an odd number is 1/2.
Thus, the expected gain/roll is
expected gain - expected loss
= 0.5*\$22 - 0.5*\$12
= \$11-\$6
=\$5 per roll on average in the long run

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