De-vig a three-way soccer market

Question

A bookmaker prices a football match with three outcomes: home win at decimal odds $2.00$ , draw at $3.20$ , away win at $4.00$ .

What is the bookmaker's margin, and what are the vig-free probabilities of each outcome?

Accepted Answer

Implied probabilities are reciprocals of decimal odds: p{home} = 	frac{1}{2.00} = 0.500, \quad p{draw} = 	frac{1}{3.20} = 0.3125, \quad p{away} = 	frac{1}{4.00} = 0.250. They sum to 1.0625, an overround of 6.25%. That excess is the vig spread across three outcomes. Betting the full book in proportion locks in a loss of about 	frac{0.0625}{1.0625} \approx 5.9\% of turnover. De-vig (multiplicative method): divide each by the total 1.0625 = 	frac{17}{16}: \hat p{home} = \frac{0.5}{1.0625} = \frac{8}{17} \approx 47.1\%, \quad \hat p{draw} = \frac{5}{17} \approx 29.4\%, \quad \hat p{away} = \…

De-vig a three-way soccer market

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