Implied Probability & the Vig
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Odds Are Probabilities in Disguise
Every set of betting odds encodes a probability — the chance the sportsbook believes each outcome will occur. Understanding this connection is the foundation of every strategy on this site: arbitrage, matched betting, and eventually +EV betting.
We introduced the formula in How to Read Odds. This guide goes deeper: where the vig comes from, how to measure it, and what it means for your bets.
Calculating Implied Probability
The Formulas
Positive American odds (+X): prob = 100 ÷ (X + 100)
+130 → 100 ÷ 230 = 43.5%
Negative American odds (−X): prob = X ÷ (X + 100)
−150 → 150 ÷ 250 = 60.0%
Decimal odds: prob = 1 ÷ decimal
2.30 → 1 ÷ 2.30 = 43.5%
The Overround: Why Probabilities Exceed 100%
In a perfectly fair market, the implied probabilities of all outcomes would add up to exactly 100%. That is not what you get from a sportsbook.
Standard −110/−110 spread market
That excess — 104.8% instead of 100% — is called the overround (sometimes called the "juice" or "vig"). The sportsbook built in a 4.8% buffer across both sides. No matter which team wins, the book keeps a portion of every dollar wagered.
Calculating the Actual Vig
The overround tells you the total implied probability, but the vig (the book's actual profit margin per dollar bet) is slightly different:
Vig Formula
vig ≈ (overround − 1) ÷ overround
At 104.8%: (0.048 ÷ 1.048) ≈ 4.6%
On a $100 bet at −110, the book earns about $4.60 in the long run.
Fair Odds: Stripping Out the Vig
If you want to know the true underlying probability of an outcome — without the book's margin — you can back it out:
Fair Probability Formula
fair prob = implied prob ÷ total overround
At −110/−110: 52.4% ÷ 104.8% = 50.0%
The book is pricing a coin flip. Fair odds would be +100 on both sides.
This is useful when comparing odds across books: which book's line is closest to the true probability, and which is giving you the most value on a particular side?
Why This Matters for Matched Betting and Arbitrage
Both strategies work by finding situations where the vig is overcome by external value:
- Arbitrage:Two books price the same event with different odds. When the implied probabilities of the best odds from each book sum to less than 100%, there's a risk-free profit gap.
- Matched betting: A sportsbook promo (bonus bet, profit boost) adds value to one side of a market. That added value effectively pushes the combined implied probability below 100%, creating profit space. The vig is still there — the promo just outweighs it.
The vig is the reason you can't profit long-term from straight gambling. It's also the wall that promos and odds gaps allow you to climb over.