Expected Value · Interview Question
A fair six-sided die pays you its face value in dollars. What is the risk-neutral fair price to play this game once, and why?
How to answer
Fair price = E[payout] = (1+2+3+4+5+6)/6 = 21/6 = $3.50. Each face is equally likely with probability 1/6, so the expected payout is the mean of 1 through 6. A risk-neutral player pays up to $3.50 and would sell the game above $3.50.
Key idea: Expected value of a uniform discrete payout over 1 through 6.
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