Make me a market on the sum of two dice

Question

Two fair six-sided dice will be rolled. The contract settles at the sum. The interviewer will buy or sell against your quote before the roll.

Make a market: give a bid and an ask, and justify the width.

Accepted Answer

Fair value. Each die has mean 	frac{1+2+3+4+5+6}{6} = 3.5, so the sum has mean E[S] = 3.5 + 3.5 = 7. Dispersion. One die has variance E[X^2] - E[X]^2 = 	frac{91}{6} - 12.25 = 	frac{35}{12}. Two independent dice: \mathrm{Var}(S) = 	frac{35}{6} \approx 5.83, \qquad \sigmaS \approx 2.4. The quote. Unlike "population of Canada," there is no estimation risk: everyone agrees fair is exactly 7, and no one can be better informed before the roll (assuming fair dice and no peeking). So you are not protecting against adverse selection, only being paid to take on outcome variance. A market like "6.5 …

Make me a market on the sum of two dice

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