Make a market on heads in ten flips

Question

Ten fair coins will be flipped. The contract settles at the number of heads. The interviewer will buy or sell against your quote before the flips.

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

Accepted Answer

Fair value. The count of heads is Binomial(n = 10, p = 0.5), so E[	ext{heads}] = np = 10 	imes 0.5 = 5. Dispersion. For a binomial, \mathrm{Var} = np(1-p) = 10 	imes 0.5 	imes 0.5 = 2.5, so \sigma \approx 1.58. The quote. Everyone agrees fair is exactly 5 and nobody can be better informed before the flips, so, just like the dice contract, your width pays for outcome variance, not adverse selection. A market like "4.5 bid, at 5.5" earns half a point of edge per trade in either direction. If the game is a single large bet, quote wider (4 at 6), since one realization can easily land two or t…

Make a market on heads in ten flips

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