The formula
EV = (probability of winning × amount won) − (probability of losing × amount lost).
Positive EV means the bet is profitable on average. Negative EV means you'll lose money in the long run — no matter how it feels in a single session.
The 'long run' is what beginners undervalue. A +EV offer can lose ten times in a row and still be correct to play the eleventh time.
Where EV shows up in matched betting
- Casino bonus offers — is the retained value greater than the wagering cost?
- Extra place horse racing — is the probability of the extra place hitting worth the qualifying loss?
- 2Up football — is the probability of a 2-goal lead high enough to compensate the qualifier?
- Refund reloads — does the trigger event occur often enough to make the qualifying loss profitable?
Applied to casino offers
A '£20 bonus, 20× wagering, £5 max stake' offer requires £400 of total wagering (bonus × 20). If the qualifying game has a house edge of 1%, expected wagering cost is £4. Retained value of the bonus is around £16. This is +EV.
Matched-betting services publish EV calculators that do this maths for you. Trust the maths, respect the variance.
Applied to sports reloads
A '£10 free bet if a red card occurs' offer requires the probability of a red card in your chosen match multiplied by the expected retained value of the free bet, minus the qualifying loss.
In practice: qualifying loss ~50p, probability of a red card in a Premier League match ~20%, retained value of a £10 free bet ~£8. EV per fixture: (0.20 × £8) − £0.50 = £1.10.
Kelly's tips
- ✦Only play +EV offers. Emotional 'this feels lucky' bets are −EV in disguise.
- ✦Track EV alongside actual result — over 50+ offers, they converge.
- ✦If an offer's EV is below £1, weigh it against the time cost of running it.
Common mistakes
- ✕Chasing losses on a variance run of +EV casino offers, forgetting that variance evens out over dozens of offers, not one session.
- ✕Confusing high variance with negative EV — they're not the same.
- ✕Overestimating trigger probabilities without a source. If you're guessing, use conservative estimates.
FAQs
Can EV lie?
The maths doesn't, but bad inputs do. Use conservative estimates of house edge and never round rollover requirements down.
How many offers before EV converges?
Roughly 30–50 similar offers is where variance stops dominating results. This is why sample size matters.
Is arbitrage the same as +EV?
No — arbitrage is guaranteed profit from price mismatches (zero variance). +EV is expected profit with real variance.
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