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What expected value means
Expected value (EV) is what a bet returns on average, per dollar, if you could place it many times. A bet with +5% EV returns $1.05 per $1 staked over the long run: some bets win, more may lose, but the price more than pays for the losses. A bet with −5% EV slowly costs you money however lucky any single result feels.
EV = p × d − 1
p = the true (fair) probability the bet wins; d = the decimal odds you're paid (stake included)
Everything in +EV betting comes down to estimating p well and getting paid a d that's high enough.
Odds are probabilities with a margin
Every price implies a probability: 1 ÷ decimal odds. At −110 (decimal 1.9091) the implied probability is 52.38%. Books build a margin into their prices, so on a two-way market the implied probabilities add up to more than 100%. At −110 on both sides, they add up to 104.76%. That extra 4.76% is the hold, or vig.
A 50/50 coin at −110: EV = 0.50 × 1.9091 − 1 = −4.55%
That's why a bettor who picks winners exactly half the time at −110 loses money: they need 52.38% to break even.
Finding the fair probability
You can't know the true probability of a game. You can estimate it, and the best public estimate is usually the betting market itself. Our tools take every book's two-way price, remove the vig (devig), and blend the books into a consensus fair probability. Then they compare each price against a fair built without that book. When one book pays more than the market's fair odds, that price is +EV.
This is market math, not a prediction model. We aren't claiming to know more than the market; we're finding books that disagree with it.
Worked example
Four books price an underdog. After removing each book's vig and averaging, the fair probability is 46.79%, so fair odds are +114. One book offers +125.
Break-even at +125: 1 ÷ 2.25 = 44.44%
Edge in probability: 46.79% − 44.44% = 2.35 points
EV = 0.4679 × 2.25 − 1 = +5.27%, or about $5.27 per $100
Two more quick ones. A fair 55% at +100: EV = 0.55 × 2.00 − 1 = +10%. A fair 50% at +105: EV = 0.50 × 2.05 − 1 = +2.5%.
Example: a sportsbook prop against the consensus
A receiving-yards Over is priced at three books: DraftKings −115 / −105, FanDuel −118 / −102, Pinnacle −120 / +100.
Devigged Over (probit): DraftKings 51.14%, FanDuel 51.82%, Pinnacle 52.28%
Fair Over = 51.74% → fair odds −107
A fourth book at −110 (1.9091): EV = 0.5174 × 1.9091 − 1 = −1.22%
A fifth book at +100 (2.00): EV = 0.5174 × 2.00 − 1 = +3.49%
The −110 is a perfectly normal price and still −EV: the market thinks the Over is a bit better than a coin flip, but not by enough to pay a full point of vig. The +100 is where the edge is. The Under at −110 would be worse still, at −7.88%.
Example: an exchange price after fees
The market's fair probability for a side is 47.5%. Polymarket US offers it at 43¢, which looks like +133.
$100 order: 233 contracts × 43¢ = $100.19
Fee = 0.0695 × 233 × 0.43 × 0.57 = $3.97
Net decimal = 233 ÷ (100.19 + 3.97) = 2.2369 → +124
EV before fees: 0.475 × 2.3256 − 1 = +10.47%; after fees: 0.475 × 2.2369 − 1 = +6.25%
Still a good price, but the fee took four points. Always judge an exchange price at its net.
Long run versus short run, in numbers
Suppose every bet you make is at −110 with a true +3% EV, so each wins 53.95% of the time. How often are you still behind?
| Bets | Chance you're behind | Standard deviation of ROI |
|---|---|---|
| 100 | 38.5% | 9.5% |
| 250 | 28.9% | 6.0% |
| 500 | 22.9% | 4.3% |
| 1,000 | 15.5% | 3.0% |
After 100 bets, a real 3% edge leaves you behind almost two times in five. Even after 1,000 bets, about one bettor in six or seven with that edge is still down. Short-run results say very little about whether your prices are good, which is why closing-line value is the better early signal.
A handy way to read EV is dollars per $100 staked: +3.49% means about $3.49 of expected profit for every $100 you bet at that price, averaged over many bets. It doesn't mean any single $100 bet returns $103.49.
What EV is not
- It isn't a forecast of this bet. The +5.27% underdog above still loses 53% of the time.
- It isn't fast. Variance swamps edge over small samples. Hundreds of bets are needed before results reflect a few percent of edge.
- It isn't certain. The fair probability is an estimate. A fair built from stale books, or modelled at a far alternate line, can be wrong.
- It isn't free money. Books limit bettors who win. The edge you can take may be smaller than the edge you can see.
How big is a good edge?
Most real edges on liquid markets are small, a few percent. Very large EV figures usually mean something is off: a stale line, a mislabelled side, a thin exchange quote or a modelled fair at a longshot price. That's why the +EV finder caps odds at +400 by default, hides off-market prices, and shows how many books back each fair. A modest edge backed by many books is worth more than a huge edge backed by one.
Where to go next
- Devig methods compared: how the vig comes off and when the method matters.
- Bankroll and Kelly: how much to stake on an edge.
- Why closing-line value matters: how to tell whether your edges are real.
- The EV calculator for any price and probability.
In build
This tool is in build on the same tested engine. The app shows what is coming and what already runs.