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Market makingMedium

A contract pays $10$ dollars times the number on one roll of a fair $6$ -sided die. A market maker wants at least $1.7$ of edge on each side, and prices must be whole numbers. The bid is the highest whole number that meets the edge requirement, and the ask is the lowest. What is the width of the market, ask minus bid?

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Hint

Find fair value, then round each side away from it.

Solution

The fair value is $10 \times 3.5 = 35$ .
The bid must be at most $35 - 1.7 = 33.3$ , so it is $33$ ; the ask must be at least $35 + 1.7 = 36.7$ , so it is $37$ .
The width is $37 - 33 = 4$ .

Answer: $4$

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