Quoting a two-way market on two dice

Question

I roll two fair six-sided dice and pay you their sum. You have to make me a two-way market: a price at which you'll sell me the payout (your ask) and a price at which you'll buy it from me (your bid).

What is fair value here? Quote a sensible market, and state your edge on each side.

Accepted Answer

Fair value = expected payout. For one die the expected value is 3.5, so for the sum of two independent dice: E[	ext{sum}] = 3.5 + 3.5 = 7. Fair value is 7. That is the number you'd be indifferent trading at if you had to trade at a single price. Quote around it with edge. You don't quote at 7, you'd make nothing. You quote a spread around it, say 6.5 bid / 7.5 ask (a one-point half-spread): - If I sell you the payout at your bid of 6.5: you pay 6.5 now for something worth 7 on average, so your expected profit is 7 - 6.5 = 0.5. - If I buy the payout from you at your ask of 7.5: you collect 7.…

Quoting a two-way market on two dice

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