Every bet is a price on a probability. Expected value (EV) is the number that says whether that price is good: the average profit or loss per bet if you could place the same bet thousands of times. Profitable betting is nothing more — and nothing less — than repeatedly taking prices with positive EV and sizing them so variance can't kill you first.
The formula
For decimal odds and a win probability p, EV per 1 unit staked is:
EV = p × (odds − 1) − (1 − p)
Example: you estimate a team wins 55% of the time and the price is 2.00. EV = 0.55 × 1.00 − 0.45 = +0.10 — you expect to make 10 cents per shekel/dollar staked, on average, over the long run. The same bet at 1.80 gives EV = 0.55 × 0.80 − 0.45 = −0.01: identical opinion, losing bet. The opinion isn't the edge — the price is.
The bookmaker's margin (the hill you must climb)
Add up the implied probabilities (1 ÷ odds) of every outcome in a market and you'll get more than 100%. A typical two-way market at 1.91 / 1.91 implies 52.4% + 52.4% = 104.7% — that extra 4.7% overround is the bookmaker's built-in margin. It means a coin-flip bettor at 1.91 doesn't break even; they lose about 4.5% of everything they bet, automatically. Sharper books and main lines carry margins of 2–5%; obscure markets and same-game parlays can hide 10–30%+, which is exactly why they're marketed so enthusiastically.
Break-even win rates
The implied probability is also your break-even win rate at that price:
| Decimal odds | American | Break-even win rate |
|---|---|---|
| 1.50 | −200 | 66.7% |
| 1.91 | −110 | 52.4% |
| 2.00 | +100 | 50.0% |
| 2.50 | +150 | 40.0% |
| 3.00 | +200 | 33.3% |
Convert any format instantly with the free odds converter. The table explains the most common self-deception in betting: a 55% win rate feels excellent, but at odds of 1.80 (break-even 55.6%) it slowly loses money.
Where does a real win probability come from?
The formula is trivial; the input p is the entire game. Three honest sources, in ascending order of difficulty:
- The market itself. Remove the margin from the odds and you get the market's probability estimate. You won't beat the market using only the market, but it calibrates your intuitions fast.
- Your own record. After a few hundred tracked bets, your actual hit rates by league, market and odds band are evidence about where your estimates run hot or cold — see how to track your bets.
- A model or deep domain knowledge. The classic path, and the hardest: your model must beat the closing line, not just pick winners.
That last phrase is the bridge to the metric serious bettors live by: if your bets consistently beat the closing price, you are demonstrably finding +EV regardless of recent results. That's closing line value, and it's measurable from bet one.
EV in practice: the checklist
- Estimate the probability before looking at the price (anchoring is real).
- Compute the EV at the actual price offered. Negative or marginal → pass. Passing is a profit skill.
- Size by bankroll rules, not conviction — see bankroll management and the Kelly calculator.
- Record the bet, then grade the process with CLV — over months, your CLV and segment ROI reveal whether your probability estimates deserve to be trusted.
SmartBet Lab automates step 4 completely (synced bets, real closing lines, per-segment ROI) and helps with step 2: the pre-bet second opinion mirrors your own record in that league, market and odds band before you commit — your history arguing with your impulse, never a tout selling a pick.