Spotting the vig in a two-sided market

Question

A two-outcome market quotes decimal odds of $1.80$ on one side and $2.10$ on the other. Solve in your head.

What are the implied probabilities, and what is the built-in margin (the vig)? Aim: under 30 seconds.

Accepted Answer

Each side's implied probability is 1/d: - 1/1.80 \approx 0.556. - 1/2.10 \approx 0.476. For a fair, margin-free market these would sum to exactly 1. Here: 0.556 + 0.476 = 1.032. The excess over 1 is the overround, the bookmaker's margin: 1.032 - 1 = 0.032 \approx 3.2\%. To recover the market's "fair" probabilities, divide each by the total: 0.556 / 1.032 \approx 0.539 and 0.476 / 1.032 \approx 0.461, which now sum to 1. You only have positive expected value if your own probability beats these vig-adjusted numbers, not the raw 1/d implied ones. Takeaway. Summing 1/d across all outcomes reveals…

Spotting the vig in a two-sided market

Your answer

More Mental Math questions