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Die and its mirror

Market makingMedium

Contract P pays the number shown on one roll of a fair $6$ -sided die, and contract Q pays $7$ minus that same number. P can be bought at $3.4$ and Q can be bought at $3.5$ . A trader buys $300$ units of each, and pays a fee of $0.04$ per unit on every contract bought. What is the guaranteed profit after fees?

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Hint

The payoffs always add up to a fixed amount.

Solution

One of each always returns $N + (7 - N) = 7$ in total and costs $3.4 + 3.5 = 6.9$ .
After the fee of $2 \times 0.04 = 0.08$ per pair, the profit per pair is $7 - 6.9 - 0.08 = 0.02$ .
The guaranteed profit on $300$ pairs is $6$ .

Answer: $6$

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