Make a market on reds in 100 roulette spins

Question

Interviewer: "An American roulette wheel ( $18$ red, $18$ black, $2$ green pockets, $38$ total) is spun $100$ times. Make me a market on the number of reds. I will trade either side."

Give a bid and ask, and explain the trap.

Accepted Answer

Fair value, and the trap. A lazy quoter says "100 spins, red is like heads, fair value 50." But red covers only 18 of 38 pockets: p(	ext{red}) = \frac{18}{38} \approx 0.4737, \qquad E[X] = 100 \cdot \frac{18}{38} \approx 47.4. The two green zeros tilt the mean down to about 47.4, not 50. If you quote around 50, an informed counterparty happily sells you reds all day, harvesting the 2.6-count gap you handed them. This is adverse selection created by your own modeling error, exactly the risk to avoid. Quote around 47.4. What sets the width. With the outcome genuinely random (no one knows futur…

Make a market on reds in 100 roulette spins

Your answer

More Market Making questions