Price a Die Roll

Question

I'll pay you, in dollars, whatever a fair six-sided die shows. What is the fair price of this game?

Accepted Answer

mathbbE[X] = frac1+2+3+4+5+66 = frac216 = 3.5. The fair price is 3.50: pay less and you have positive edge, pay more and the seller does. Two facts to internalize, because every market-making interview builds on them: - For a uniform die 1..n, mathbbE = fracn+12. - "Fair value" or theo is just the expectation; a market maker quotes a bid below it and an offer above it. When an interviewer says "make me a market on a die roll," they're asking for something like 3.3 bid / 3.7 offer around this number.

Price a Die Roll

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