De-vig a four-runner race

Question

A four-horse race is quoted at decimal odds: Runner 1 2.40, Runner 2 3.80, Runner 3 4.50, Runner 4 7.00. Find the bookmaker's overround and the fair win probability of each runner.

Accepted Answer

Step 1: raw implied probabilities (1/	ext{odds}): \frac{1}{2.40} = 0.4167, \quad \frac{1}{3.80} = 0.2632, \quad \frac{1}{4.50} = 0.2222, \quad \frac{1}{7.00} = 0.1429. Step 2: the overround. S = 0.4167 + 0.2632 + 0.2222 + 0.1429 = 1.0449, so the bookmaker's margin is about 4.49\% across the four-way book. Multi-runner books usually carry a larger overround than a two-way market because the margin is spread over more outcomes. Step 3: de-vig by normalizing. Divide each raw probability by S: P1 = \frac{0.4167}{1.0449} = 0.399, \quad P2 = \frac{0.2632}{1.0449} = 0.252, P3 = \frac{0.2222}{1.0449…

De-vig a four-runner race

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