What is expected value?

Expected value (EV) is the average profit or loss you'd make on a bet if you could place it thousands of times over. Positive EV means the price is in your favour. Negative EV means the book has the edge.

A single +EV bet can still lose. The whole point of EV betting is making enough +EV bets that the long-run edge plays out, even when individual bets don't.

How the maths works

For a stake S at decimal odds d with win probability p:

EV = p × S × (d − 1) − (1 − p) × S

If p × d is greater than 1, the bet is +EV. The size of the edge is what tells you how good the bet actually is. A bet at +0.5% edge is technically positive, but it's barely worth taking, since variance will dominate.

Where does the win probability come from?

This is the hard part. You can estimate win probability from a model, from sharp-book pricing (de-vig the line at Pinnacle or Circa), or from a market consensus across multiple soft books. A gut-feel probability is almost always wrong. If you can't justify the number, don't trust the EV.

What's a good edge to look for?

For real opportunities, 2 to 5% edge is the sweet spot. High enough that the maths is reliable, low enough that the bets are still available at decent limits. Anything past 8 to 10% almost always means you've estimated the win probability wrong, or the book will limit you fast.

Related calculators

• Kelly calculator for sizing the bet once you know it's +EV
• Odds converter for flipping between American, decimal and implied probability
• Arbitrage calculator for when two books disagree enough that the EV is locked

For more on edges and probability, see implied probability and hold and what is +EV?