Both sides quoted at 1.95, what is the vig?

Question

A bookmaker prices both sides of an even, coin-flip-style market at decimal odds of $1.95$ . In a fair market each side would be $2.0$ (a 50% chance). Solve in your head.

What is the bookmaker's total margin (the overround), and roughly how big is it? Aim: under 10 seconds.

Accepted Answer

Convert each side to an implied probability and add them. For a fair market the two probabilities sum to exactly 100\%; anything above that is the bookmaker's built-in edge, called the overround or vig. Each side: p = 1/1.95 \approx 0.5128, so 0.5128 + 0.5128 = 1.0256. The implied probabilities sum to about 102.6\%, so the overround is roughly 2.6\%. That surplus is the margin the book collects on balanced action, no matter which side wins. Fast mental step: 1/1.95 is a hair above 1/2 = 0.5. Two of them land just over 1.0, and the excess, about 2.5 cents, is the edge. Tighter odds (closer to …

Both sides quoted at 1.95, what is the vig?

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