The vig behind American odds of -110 / -110

Question

A two-outcome market is quoted in American odds at $-110$ on each side (the standard US sportsbook line: risk $\$ 110 $to win$ $100$). Solve in your head.

What do the implied probabilities sum to, and what margin is the book running? Aim: under 20 seconds.

Accepted Answer

American odds of -110 mean you stake \110 to win \100, so the implied probability is your stake over the total return: \frac{110}{110 + 100} = \frac{110}{210} = \frac{11}{21} \approx 0.5238. Both sides are priced the same, so sum them: 2 	imes \frac{11}{21} = \frac{22}{21} \approx 1.0476. Implied probabilities total about 104.76\%, an overround of roughly 4.76 points, the familiar "-110 juice" a sportsbook charges on a coin flip. Equivalently, -110 is decimal odds 1 + 	frac{100}{110} \approx 1.909, and 	frac{2}{1.909} \approx 1.0476, the same answer through the reciprocal-of-decimal-odds r…

The vig behind American odds of -110 / -110

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