Expected Value Calculator
Odds plus your true probability, as expected value per bet.
This prices a bet against a probability you supply. It does not tell you the probability is right, and that is the input the answer turns on.
Expected value
+2.50%EV
That is the edge if the chance really is 50.00%. It came from stripping the margin out of the two sharp-book prices, which is the most defensible baseline available without a model of your own.
Your price
2.05
decimal odds
Min odds to bet
≥ 2.00
decimal odds
Average return
$102.50
$100 staked, +$2.50
1. The bet
The chance it actually wins
your side 51.22%other side 51.22%over 100%
Use the sharpest, highest-limit book you can find for both sides. The fair price is only as good as the market it came out of.
Every price field reads an American price (+150). Switch the format above to enter prices the way your book quotes them, or open the odds converter to see one price in all of them.
Result over 50 bets
44%
of 50-bet runs finish at a net loss
44 of every 100 50-bet runs finish at a net loss. The other 56 of 100 finished at break even or better.
Typical run
+$125
over 50 bets
Average run
+$125
44% of runs ended below the average
- 10th
- −$900
- 25th
- −$285
- median
- +$125
- 75th
- +$535
- 90th
- +$1150
net lossbreak even or bettermiddle half of runsfar ends not drawn (under 0.05% of runs each)
That per-bet average is the mean of the distribution above, scaled to 50 bets it is +$125 total. Individual +EV bets still lose often: 44% of 50-bet runs at this edge still finish behind, which is the mean hiding exactly what it always hides.
The spread is exact, not simulated: a bet with a fixed chance repeated 50 times is a binomial process, so every one of the 51 possible win counts is weighted by its exact probability at the 50.00% chance used above, none of them sampled.
Bets needed to tell this edge apart from noise
| Edge | N₀ (starts to show) | Bets to confirm at 95% |
|---|---|---|
| 1% | 10,504 | 40,351 |
| 2% | 2,626 | 10,090 |
| 3% | 1,167 | 4,484 |
starts to showconfirmed at 95%bars on one scale
At your current price of 2.05, this is how many repetitions of the same bet it takes before the edge starts to outweigh the swings around it (N₀), and how many it takes to confirm the edge against zero at 95% confidence, the same standard the closing line value calculator holds a bettor’s own sample to.
A much smaller average edge over a handful of bets is well inside what no edge at all produces. The confirm column is always about four times the N₀ column (95% confidence's z of 1.96, squared), which is how much longer a real edge takes to prove than it takes to start showing.
The chance is the input that decides this
The price is a fact you read off a screen. The chance is not, and this calculator will hand back a confident percentage whether you researched it or guessed it. Guessing is the common failure, and it does not feel like guessing: you back your own read, your read is a little generous, and the tool faithfully reports an edge that was never in the market.
The standard discipline is to stop supplying the number yourself. Take the sharpest two-way price you can find, strip its margin out, and use what is left as the baseline. Then bet only where a softer book is offering clearly more than that. It is what the de-vig entry above does, and it is the difference between measuring an edge and hoping for one.
De-vig a market with three prices or more (or with the power and Shin methods, which split the margin unevenly and fit a heavy favorite better), or read how to get an honest probability.
Value drill, bet or pass?
You get the model's true probability and the book's price. Hit Bet if it's +EV, Pass if not, you have a few seconds each. The drill hands you the true chance. Real betting does not.
Written and reviewed by Alexander Korsager · last reviewed September 27, 2026 · corrections
The idea
What this tool shows
Expected value is the average result of a bet if you could place it many times. It is positive when the price you get is longer than the true odds, the book is paying you more than the risk is worth. That gap is your edge.
The calculator takes two inputs, and only one of them is a fact.The odds you can bet are on the screen in front of you. The chance the bet actually wins is not, and it is the input that decides the answer: enter a chance a couple of points too generous and a losing price comes back looking like a winning one, with no sign on the page that anything went wrong.
So the tool asks where the chance came from before it asks what it is.The default path is the one our guide to expected value recommends: take a sharp bookmaker's two-way price, strip the margin out of it, and use what is left as the baseline. You can also enter a fair price or a probability directly, and the result names which of the three it used, because a positive number means something different depending on the answer.
FAQ
Questions players ask
How is expected value calculated?
EV per unit = p × (odds − 1) − (1 − p), where p is the true win probability (1 divided by the fair odds). Multiply by your stake for the money figure.
Is a positive EV number a value bet?
Only if the probability you entered is right. The arithmetic is exact, but it prices your bet against your estimate, not against reality, so a positive figure is a statement about your estimate as much as about the price. That is why it is worth getting the probability from a sharp market rather than from your own read of the game.
Where do I get the true probability?
The standard method is to de-vig a sharp market. Take the two-way price at a high-limit bookmaker, remove the margin so the two sides sum to 100%, and use that as your baseline. This calculator does that inline for a two-way market; for three or more outcomes, or for the power and Shin methods, use the no-vig calculator. Your own model is the alternative, and it has to be good enough to beat a sharp book before it improves on this.
What counts as a good EV?
Professional bettors commonly cite 1 to 3% as strong, but that figure is a round number passed around rather than a derived one, and on its own it tells you less than it sounds like it does: an average edge in that range over a handful of bets is well inside what no edge at all produces, the same problem the closing line value calculator prints a confidence interval to address rather than a single percentage. What actually separates a real edge from noise is whether it holds up once you have enough bets for variance to stop explaining it, not which side of 1% the average sits on, and the sample-size table puts a number on exactly that: at even money, a 1% edge needs tens of thousands of bets to confirm, a 3% edge needs a few thousand. A much larger number on a single bet usually means your probability estimate is off, or the price is about to move, not that you found free money.
Do I need +EV on every bet to profit?
No, only on average. Individual +EV bets still lose often; profit comes from placing many of them over time. The distribution panel shows exactly how often, at your own inputs and chosen number of bets, rather than leaving that as an unmeasured claim.
Methodology
How this is calculated
EV per unit staked is p × (odds − 1) − (1 − p), for a win probability p and a decimal price. It is the average profit per unit over many repetitions of the same bet, and it is zero at the price 1 / p.
The figure printed as the minimum odds to bet is that price rounded up to the next hundredth, not to the nearest one: 1 / p is rarely a price any book quotes (a fair chance of 51.15% breaks even at 1.9550), and rounding it to nearest would print 1.95, a price the same panel scores at −0.26%.
Rounding up means the printed figure is always a price the bet is not already losing at, which is what the label claims. The break-even rate shown beside it is 1 / odds, the rate at which the price you are taking finishes level.
Where the probability is de-vigged from a market, it is the proportional method: each side's implied probability divided by the two-side total, so the pair sums to 100%.
Common misreadings4
- A positive number is not a verdict on the bet. It is the edge your own probability implies, and the probability is the part nothing here can verify.
- A large edge is usually evidence of a bad estimate rather than of a mispriced market. In a liquid market, a price several points off the fair value is more often a stale line, a different rule set, or a market you have misread than free money.
- The break-even rate implied by the price you are betting is not the chance of the outcome. The bookmaker's margin is inside every price it publishes, so the chance the book expects is lower than that figure.
- Positive EV does not mean you can size the bet freely. How much to stake is a separate question about your bankroll and the size of your edge, and getting it wrong ruins accounts that were betting +EV the whole time.
Assumptions5
- The bet is a single win or lose outcome at a fixed price, staked level, with the stake returned on a win. A push, a partial payout or a bet that can be settled in more than two ways is not this calculation.
- The probability entered is the true chance of the outcome. Everything the tool prints is conditional on that, and nothing on the page can check it.
- The de-vig entry assumes the two prices belong to one two-way market and that the margin is spread proportionally across the sides.
- The average return figure ignores commission. On an exchange, a commission on winnings reduces it.
- The distribution panel models n repetitions of the exact same bet: same price, same stake, same probability, independent of each other. A reader who compounds stakes between bets, who bets a changed price after the market moves, or whose bets are correlated with each other (the same game from two angles, a system with dependent legs) is not the process the panel prices, and the spread it shows would be narrower or wider than the real one in ways this page cannot know.
Limits5
- The proportional de-vig shares the margin evenly in relative terms, which is closest to right on a balanced market. On a heavy favorite the power and Shin methods generally land nearer the market's real probabilities, and those live in the no-vig calculator.
- A de-vigged price is a good baseline only if it came from a sharp, high-limit book. De-vigging a soft book with a wide margin and slow prices returns a confident-looking number that carries that book's mistakes.
- Expected value is an average over a large sample. It says nothing about a single bet, and at a realistic 1 to 3% edge, at even money, the sample-size table above the FAQ says how large 'large' actually is: tens of thousands of bets at the low end of that band, not hundreds. Away from even money the same edge confirms on far fewer bets (a heavy favorite around 1.05 to 1.25 can be in the low thousands or even fewer), but in every case it is many more than a losing run makes intuitive, which can still sit inside an edge that is exactly as advertised.
- The figure is a snapshot of a price that moves. A market that shortens after you bet does not retroactively change the EV of the bet you made, and a market that never moves is a reason to check the estimate.
- The minimum odds figure is rounded to two decimals because that is how prices are quoted. Where a book prices in three (some high-limit books do), the exact break-even is up to a hundredth below what this page prints, so a price between the two is a small positive rather than the pass the rounded figure implies.
Evidence
The EV identity and the break-even price 1 / p are standard results in elementary probability, and the proportional de-vig follows from normalizing two implied probabilities to sum to 1.
Both are covered in math.test.ts, which sweeps the probability range to confirm that EV crosses zero at exactly 1 / p, and separately sweeps the rounded figure the page actually prints to confirm it is never a price the bet is already losing at and never a full cent longer than it needs to be.
The worked example the page ships with is pinned there too.
The distribution panel's profit spread over n bets is an exact Binomial(n, p) enumeration, not a simulation: math.test.ts checks the probabilities sum to 1 across a range of n, that the mean of the enumerated distribution matches n times the per-bet average profit exactly, and that the share of runs finishing behind falls as n grows at a fixed edge.
A passing test means the code matches the model, not that any probability you enter is the right one.
Gambling can cause serious harm. The National Problem Gambling Helpline is free, confidential and open 24/7, call or text 1-800-MY-RESET (1-800-697-3738), or chat at ncpgambling.org/chat.
Read up
Go deeper
- Our researchWhat a prediction market actually chargesPrediction markets are sold on not charging vig. We snapshotted every quotable contract on Kalshi and priced the two-way cost the way a sportsbook's hold is priced. On 78,119 markets the median came to 9.9c per dollar of payout, against 4.8c at a standard sportsbook line. On the markets people actually trade, the answer flips.
- Our researchThe longshot gap, and the spread that swallows itThe academic literature reports that prediction-market longshots are mispriced. We checked it on 12,755 settled Kalshi contracts, priced a day before they closed, and then did the part nobody had done: measured what reaching the mispricing would have cost at the same price, at the same moment, out of the same rows. In 10 price buckets out of 10, the cost was larger than the gap.
- GuideBetting Odds Explained: Decimal, Fractional, American and Implied ProbabilityHow decimal, fractional and American odds work, how to read the implied probability behind any price, and how to spot a bookmaker's margin eating your value.
- GuideExpected Value in Betting: How to Know if a Bet Is Worth MakingWhat +EV means in practice, how to work out expected value from your probability and the price on offer, and why closing line value is the honest scoreboard.
- GuideThe Kelly Criterion Explained (and Why Most People Use Half)What the Kelly criterion is, the formula for the optimal bet fraction, why full Kelly punishes hard, and how fractional Kelly trades growth for smaller swings.
- GuideDFS Pick'em Entries: The Hit Rate You Actually Need to Break EvenThe per-leg hit rate an all-or-nothing DFS pick'em entry needs to break even, what a boosted pick really changes, and where the format is legally contested.
Related tools
Try next
- No-Vig Fair Odds CalculatorStrip the bookmaker's margin out of a market to see the fair price behind every outcome.
- Odds ConverterConvert odds to any format
- Kelly StakeFind your optimal bet size
- Hedge & Cash-Out CalculatorThe stake that locks in equal profit either way a bet lands, and whether the cash-out offer beats it.
- CLV CalculatorWork out your closing line value, and whether the sample you have is large enough to mean anything yet.
- MDF & Bluff Ratio CalculatorFrom one bet size: the equity to call, the minimum defense frequency, and the right bluff-to-value mix.