Strip the vig from a three-way market

Question

A soccer match is quoted in decimal odds: Home 2.10, Draw 3.40, Away 3.80. Find each implied probability, the total overround (the bookmaker's margin), and the de-vigged fair probabilities.

Accepted Answer

For decimal odds d, the implied probability is p = 1/d: p{	ext{Home}} = 	frac{1}{2.10} = 0.4762, \quad p{	ext{Draw}} = 	frac{1}{3.40} = 0.2941, \quad p{	ext{Away}} = 	frac{1}{3.80} = 0.2632. These sum to 0.4762 + 0.2941 + 0.2632 = 1.0335, not 1. The excess is the overround (vig): 1.0335 - 1 = 0.0335, about 3.35\%. A fair market would sum to exactly 100\%; the extra 3.35\% is the book's built-in edge. To recover fair probabilities, de-vig by dividing each raw implied probability by the sum (the proportional method): \frac{0.4762}{1.0335} = 46.1\%, \quad \frac{0.2941}{1.0335} = 28.5\%, \q…

Strip the vig from a three-way market

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