De-vig an American-odds moneyline

Question

A game is posted in American moneyline odds: Favorite -140, Underdog +120. Convert to implied probabilities, remove the vig, and give the fair probabilities and fair moneyline.

Accepted Answer

Step 1: American odds to raw implied probability. - Negative odds -140: \dfrac{140}{140 + 100} = \dfrac{140}{240} = 0.5833. - Positive odds +120: \dfrac{100}{120 + 100} = \dfrac{100}{220} = 0.4545. (The rules: for a negative price -m, probability = m/(m+100); for a positive price +m, probability = 100/(m+100).) Step 2: the overround. S = 0.5833 + 0.4545 = 1.0379, so the vig is about 3.79\%. Step 3: de-vig by normalizing. P	ext{fav} = \frac{0.5833}{1.0379} = 0.562, \qquad P	ext{dog} = \frac{0.4545}{1.0379} = 0.438. Check: 0.562 + 0.438 = 1.000. Fair probabilities: about 56.2\% favorite, 43.8…

De-vig an American-odds moneyline

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