Positive EV (+EV) betting means only taking bets whose odds pay more than the outcome’s true chance deserves. Expected value is the average result per bet over many repeats, so a +EV bet is expected to come out ahead over the long run, even though any single bet can still lose.
This is the plain-English version of that idea: the formula once, one worked example, and where a fair price actually comes from.
What does EV mean in betting?
EV is expected value. It is the average result per bet if you could place the same wager many times at the same price.
+EV vs −EV in one sentence each
+EV means the odds pay more than the fair chance of the outcome, so the average result is positive.
−EV means the odds pay less than that chance, so the average result is negative.
A slot machine is the familiar −EV case. Put in $1 over and over and the machine returns something like $0.93 on average. The gap is the house edge. A +EV bet is the other way around: the price, not the casino, is the one that is short.
Why the sportsbook starts with the edge (the vig)
A sportsbook does not post a fair coin at +100 / +100. Both sides of a toss are usually −110. Each −110 price implies a 52.38% chance, and the two sides together imply 104.76%. The extra 4.76 percentage points are the vig (also called juice): the book’s cut, built into the price before anyone has an opinion. You can convert odds to implied probability for any single number. Removing the vig from both sides is the next step.
How to calculate expected value (with one worked example)
The formula is:
EV = (Win probability × Profit if you win) − (Loss probability × Stake)
The +150 example
Say the posted price is +150 and your fair chance for that side is 45%. On a $100 stake:
Profit if it wins: $150
Stake if it loses: $100
Win probability: 0.45
Loss probability: 0.55
EV = (0.45 × $150) − (0.55 × $100) = $67.50 − $55.00 = +$12.50
So the average result is +$12.50 per $100 stake, which is +12.5% of the stake. The +150 price itself implies only a 40% chance (100 / 250). Your 45% fair chance is higher than that 40%, which is why the average is positive. Redo this example in our EV calculator.
Where does the “true” probability come from?
The formula needs a fair chance. The odds do not contain one. You have to bring it.
Removing the vig (devigging) from a sharp line
Devigging takes the vig out of a two-way line so the two chances add up to 100%. Here is a sharp book at −110 / −110:
Implied probability of −110 is 110 / 210 = 52.38%.
Both sides add up to 104.76%. The extra 4.76 points are the vig.
Fair probability of each side is 52.38 / 104.76 = 50%.
A 50% fair chance is even money, +100.
If another book offers +105 on one of those sides, +105 implies 100 / 205 = 48.78%, which is less than the 50% fair chance. The odds are longer than fair. On a $100 stake the EV is (0.50 × $105) − (0.50 × $100) = +$2.50. That is a small edge on a liquid market. It can still lose. Run the same two prices through the no-vig calculator, and read the longer version in no-vig fair odds.
Sharp books vs. soft books
A sharp book’s line is the usual source of that fair chance, because sharp books take informed action and move. A soft book’s line is where the better price often shows up, because it was built with less of that pressure. The background is in how sharp books help you find +EV bets.
Model projections as a second opinion
A model is a second estimate of the fair chance, built from stats rather than from one book’s line. OPTIMAL grades lines with its own models: how the Optimal EV model builds a fair price is the write-up. The grade is a way to scan. It is not a substitute for checking the price yourself.
How to find +EV bets
Get a fair price. Devig a sharp two-way line, by hand or with the no-vig calculator.
Compare it with the best available odds. That is line shopping: the same side is a different bet at +105 than at −110.
Check the EV%. A price that pays more than the fair chance is +EV. The EV calculator does the arithmetic.
Size the stake. A small share of the bankroll is what keeps a cold week from ending the season. See bankroll management for EV bettors.
Track results and the closing line. Write down the price you took and the price the market closed at. Over a large sample, beating the close tells you more than a short run of wins and losses.
EV Cheat Sheets list lines OPTIMAL has already graded, which is the same comparison with the lookup done for you.
What is a good EV percentage?
There is no single good number. The useful question is whether the edge is the kind you can trust.
About 1% to 3% on a spread, total or moneyline is a small disagreement on a market many books price. Those are usually the edges worth a second look.
A few percent more on that same kind of market is a wider disagreement. It is still an average, not a result.
A double-digit EV% on a thin player prop is often a stale number, a book that has not moved, or an input that is off. A bigger percentage is a reason to check the price, not a reason to bet more.
The percentage is only as good as the fair chance you typed in.
Is +EV betting profitable? What the math does and doesn’t promise
The math says this: if the fair chance is right, and you get the price, the average result over many repeats is positive. “Expected” is that average. It is not a forecast of the next bet, the next night, or the next month.
Short samples lie. A run of 20 or 50 bets is mostly variance. Losing weeks happen to a real edge. A winning week can just as easily be noise.
Three things the average does not include:
You may not get the bet. Books limit accounts, cut limits, or reject the wager. A price you cannot place has an EV of zero in practice.
The line moves. The +105 you calculated may be −105 by the time the bet is in.
A book can void a leg. A price that is gone, or a bet that is graded dead, is not the bet in the calculator.
None of that makes the formula wrong. It means the formula describes the price, and your results describe the bets you actually got down.
Why player props are where most +EV shows up
Main markets are priced by a lot of money and a lot of books, so the gap between a sharp line and a soft line is usually small. Player props are priced more thinly, and books disagree more often. That is where a devigged fair price and the best available odds tend to separate. The longer version is why player props are the market where most +EV shows up.
+EV vs. arbitrage vs. “sharp” betting
These get lumped together. They are three different jobs. How the Arbitrage model handles both sides covers the middle row on its own.
| Approach | What you do | What can still go wrong |
|---|---|---|
| +EV betting | Take one side priced above its fair chance | That bet loses |
| Arbitrage | Bet both sides, sized so the payouts cover each other | A book voids a leg, or the line moves before both bets are in |
| Sharp betting | Use a sharp book’s price as the fair-value reference | The sharp price is wrong, or it moves before you bet |
Key takeaways
+EV means the price pays more than the fair chance. The average is positive. Any one bet can lose.
The formula is win probability times profit, minus loss probability times stake. At +150 with a 45% fair chance, that is +$12.50 per $100.
The fair chance is not in the odds. It comes from devigging a sharp line, or from a model you can check.
A small edge on a liquid market is usually more meaningful than a huge edge on a thin prop.
Track the closing line and the stake you actually got. The calculator’s average only shows up in the bets that get placed.
