Guide 2 of 8 / 7 min read
Expected Value in Betting: How to Know if a Bet Is Worth Making
One bet, priced two ways
- Fair
- 1.90
- Offered
- 2.10
- EV
- +10.5%
You make this bet a 52.6% chance, a fair price of 1.90. At 2.10 it needs 47.6% to break even, so a $100 stake averages $110.53 back over many bets like it: an average gain of $10.53 a bet.
Expected value, or EV, is the average result of a bet if you could make it thousands of times. A positive-EV bet makes money on average; a negative-EV bet loses on average. Every bet you place has an EV whether you calculate it or not, the only question is whether you know the sign.
Written and reviewed by Alexander Korsager · last reviewed September 29, 2026 · corrections
The short version
EV is an average
Expected value is the average result of a bet made thousands of times, not a promise about any single one.
Two numbers set the sign
Your honest probability that the bet wins and the price on offer decide whether the EV is positive or negative.
The close is the scoreboard
Consistently beating the closing price is the best available proxy for long-run EV, long before results confirm it.
You cannot measure EV directly from wins and losses in the short run, because variance drowns it out. But you can estimate it before you bet, from two numbers: your honest probability that the bet wins, and the price on offer.
01 / 04
The formula
For a bet at decimal odds o that you believe wins with probability p, the expected value per unit staked is: EV = p x (o - 1) - (1 - p). The first term is what you win when you are right; the second is the stake you lose when you are wrong.
When you are right52.6% × 1.10
+0.579When you are wrong47.4% × 1.00
-0.474
- EV per unit staked
- +0.105 (+10.5%)
The guide’s example at 2.10: what the wins add, less what the losses take.
If your fair estimate is 1.90 (about 52.6% to win) and a bookmaker offers 2.10, EV works out to +10.5% per unit staked. Over many bets like that you would expect to grow your stake by about 10.5% of turnover.
Fair 1.90 vs. offered 2.10
52.6% fair win probability
47.6% implied by the offered price
5.0 points gap, +10.5% EV
Your fair price says this wins 52.6% of the time; the offered price implies only 47.6%, and that 5.0 points gap between the two bars above is where the +10.5% expected value comes from. Methodology and sourcing below.
02 / 04
Getting an honest probability
The hard part is p. If you just use your gut, you will overrate your own picks and see edges that are not there. Two disciplines help.
- 50.6%2 points lower+6.3%
- 52.6%Your estimate+10.5%
- 54.6%2 points higher+14.7%
At 2.10 the bet breaks even at 47.6%. Everything above that depends on an estimate.
- De-vig the market. Take a sharp bookmaker's two-way price, strip out the margin so the two sides sum to 100%, and use that as your baseline probability, then only bet when a softer book offers meaningfully more than the sharp fair price.
- Be honest about uncertainty. If you are not confident your estimate is within a couple of percent of the truth, treat a small edge as noise and pass.
03 / 04
Closing line value
The best available proxy for long-run EV is closing line value, or CLV: did you consistently beat the price the market settled on just before kick-off? The closing line is the sharpest estimate the market produces, so beating it repeatedly is strong evidence your bets are +EV, long before your results confirm it.
- When you bet
- 2.10needs 47.6%
- At kick-off
- 1.90needs 52.6%
The close is the market's last and sharpest estimate. It asks more of this bet than your price did.
If you are regularly taking 2.10 on selections that close at 1.90, you are almost certainly a winning bettor even during a losing month. If you are taking prices that then drift out, the reverse is true.
You beat the closeclosing line value +10.5%
Taken2.10Close1.90The price drifted outclosing line value -9.5%
Taken1.90Close2.10
Price taken divided by the closing price, minus one.
04 / 04
EV is not a single-bet promise
A +EV bet can and often will lose. EV is an average over a large sample, and the sample has to be genuinely large (hundreds or thousands of bets) before results track expectation. That gap between edge and outcome is variance, and it is why bankroll management and stake sizing matter as much as bet selection.
- Wins, +1.10
- 52.6%
- Loses, -1.00
- 47.4%
The average of the two is +10.5% per unit staked. No single bet ever pays that.
Put a number on it. At this guide's own example (fair 1.90, offered 2.10, about a 10.5% edge), the edge starts to outweigh the noise after roughly 99 bets, and confirming it against zero at 95% confidence takes roughly 381. At a more realistic 2 to 3% edge after de-vigging, the same price, those figures grow to roughly 1,763 and 6,772: a smaller edge does not need a slightly bigger sample, it needs one that is roughly 18 times larger.
Bets needed before results track expectation
This guide's own example: fair 1.90, offered 2.10 (about +10.5%)
~99 bets, edge visible
~381 bets, confirmed at 95%
A realistic 2-3% edge after de-vigging (shown at 2.5%, the FAQ's own midpoint, same 2.10 price)
~1,763 bets, edge visible
~6,772 bets, confirmed at 95%
“Edge visible” is N0, the point where cumulative standard deviation first equals cumulative mean. “Confirmed at 95%” is always about 3.84 times longer (Z952), the same standard the CLV calculator applies to a bettor’s own observed sample. This is not a target to hit: it describes how long a real edge takes to become statistically visible, not a number of bets to go place. The bars above are log-scaled to fit both rows on one chart, so the visual gap between them understates how much larger the real gap is. Methodology and sourcing below.
Check yourself
Can you tell the sign of a bet?
1 / 3
Your fair price is 1.90 and a bookmaker offers 2.10. What is the EV per unit staked?
2 / 3
That bet is +EV. How often does it still lose, on your own estimate?
3 / 3
At that same edge, roughly how many bets does it take to confirm it against zero at 95% confidence?
Pick an answer to see the working. Nothing is scored or saved.
Try it
Put your own numbers through it
- Expected Value Calculator Check if a price has value
- CLV Calculator Work out your closing line value, and whether the sample you have is large enough to mean anything yet.
- Odds Converter Convert odds to any format
- Hedge & Cash-Out Calculator The stake that locks in equal profit either way a bet lands, and whether the cash-out offer beats it.
- Middle Calculator Price a middle on both sides of a moved line: what it pays, what a miss costs, and how often it has to land.
- Arbitrage Calculator Check whether two or more prices on the same event lock in a profit, and get the stake for each side.
- Lay Bet & Matched Betting Calculator Get the exchange lay stake, liability and locked-in result for a qualifying bet or a free bet.
FAQ
- How big an edge do I need to bet?
- Enough to survive your own estimation error and the bookmaker's margin. Many bettors want at least 2–3% expected value after de-vigging before they act, because smaller apparent edges are usually noise.
- Can a bet be +EV and still a bad idea?
- Yes, if it is too large for your bankroll, if it correlates heavily with other open bets, or if the edge depends on a probability estimate you do not actually trust.
- Why do bookmakers limit winning accounts?
- Because consistently beating the closing line is a reliable signal of a +EV bettor. Soft books restrict or close accounts that show it, which is why serious bettors spread action and value exchanges highly.
Where these figures come from
The bet-count figures in 'EV is not a single-bet promise' come from this site's own risk-of-ruin engine: the number of bets at which a real edge first outweighs variance (N0) and the stricter number needed to confirm it against zero at 95% confidence are the same identity, n > (z·sd/m)², that lib/distribution's betsForSignificance implements and that the CLV calculator already applies to a bettor's own observed sample; confirming at 95% is always Z95², about 3.84 times N0, because the two only differ in which z they use. The per-bet mean for each worked example is evPerUnit(p, o) in src/tools/ev-calculator/math.ts, unchanged; the per-bet standard deviation is sdPerUnit(p, o), added to that same file this pass (the two-outcome variance around evPerUnit's own mean) and checked in math.test.ts to agree with risk-of-ruin/math.ts's even-money n0Coin/betsToConfirmCoin at every price where both models apply. The guide's own showcase price (fair 1.90, offered 2.10) is section 'The formula''s existing worked example; the 2.5% edge is the midpoint of the FAQ's own '2-3% expected value' filter, shown at the same 2.10 price so the two rows differ only in the edge being asked about. Section 'The formula''s own worked-example win probability and EV percentage are also read from impliedProbability and evPerUnit at call time (src/guides/figures/ev-worked-example-data.ts), rather than the rounded, non-evaluating chain the paragraph printed before this pass (#1050); ev-worked-example-data.test.ts re-derives both figures independently, and the sample-size scenario above now imports the same pair rather than restating it, so the two cannot drift apart again.
Verification
Checked against ev-calculator's math.test.ts (evPerUnit, sdPerUnit) and lib/distribution's betsForSignificance, cross-checked against risk-of-ruin/math.ts's n0Coin and betsToConfirmCoin at a shared even-money input: agrees on both routes to the per-bet standard deviation of a win/lose bet; the resulting N0 and 95%-confidence bet counts for this guide's two worked examples (about 99 and 381 at the showcase price, about 1,763 and 6,772 at the 2.5% price); and the fixed Z95² ratio between the two figures (verified by src/guides/figures/ev-sample-size-data.test.ts, src/guides/figures/ev-worked-example-data.test.ts and src/tools/ev-calculator/math.test.ts, 2026-09-29).
Know the risk
- Treating a single +EV bet's result as evidence the calculation was right or wrong. EV is a claim about the average of many repetitions of the same bet; one bet winning or losing says nothing about whether the probability estimate that produced it was accurate.
- Using closing line value as a promise instead of a proxy. Beating the close repeatedly is strong evidence of skill, but it is still a proxy for long-run EV, not EV itself, and it says nothing about whether risk elsewhere in a bettor's approach is being priced correctly.
- Trusting a calculated EV because the formula is exact. The arithmetic is exact; the probability p that goes into it is a judgment call, and de-vigging a sharp book's price only removes the bookmaker's margin, it does not verify that the resulting estimate of the true probability is correct.
- Reading the bet counts above as a target to reach. They describe how long a real edge takes to become statistically visible, not a number of bets to go place; sizing and bankroll survival, not sample size, decide whether a bettor is still solvent by the time an edge would actually show up.
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.