The overround in a three-way match market

Question

A football match is quoted three-way: home win at $2.10$ , draw at $3.40$ , away win at $3.80$ . Solve in your head.

What do the three implied probabilities sum to, and what is the bookmaker's margin? Aim: under 30 seconds.

Accepted Answer

The margin trick does not care how many outcomes there are: sum the reciprocals of every quoted price and compare to 100\%. \frac{1}{2.10} \approx 0.476, \qquad \frac{1}{3.40} \approx 0.294, \qquad \frac{1}{3.80} \approx 0.263. Fast reads: 	frac{1}{2.1} is a bit under 	frac{1}{2} = 0.5, about 0.476; 	frac{1}{3.4} is between 	frac{1}{3}=0.333 and 	frac{1}{4}=0.25, near 0.294; 	frac{1}{3.8} a touch above 	frac14, about 0.263. Add them: 0.476 + 0.294 + 0.263 \approx 1.033. The implied probabilities total about 103.3\%, an overround of roughly 3.3 points. Divide each reciprocal by 1.033 to…

The overround in a three-way match market

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