The margin in a lopsided 1.50 / 2.50 market

Question

A two-outcome market is quoted at decimal odds $1.50$ on the favorite and $2.50$ on the underdog. Solve in your head.

What do the implied probabilities sum to, and what margin is the bookmaker running? Aim: under 20 seconds.

Accepted Answer

Unequal prices change nothing about the method: convert each to an implied probability and add. \frac{1}{1.50} = \frac{2}{3} \approx 0.667, \qquad \frac{1}{2.50} = \frac{2}{5} = 0.400. Both are clean fractions (	frac{1}{1.5} = 	frac{2}{3} and 	frac{1}{2.5} = 	frac{2}{5}), so the sum is quick: \frac{2}{3} + \frac{2}{5} = \frac{10}{15} + \frac{6}{15} = \frac{16}{15} \approx 1.0667. Implied probabilities total about 106.67\%, an overround of 6.67 points, fatter than a typical coin-flip market because the book is charging up on both a strong favorite and its longshot. The fair probabilities a…

The margin in a lopsided 1.50 / 2.50 market

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