Expected value, in one page.
Expected value (EV) is the single number that decides whether a casino bonus is worth your money. Headline bonus size lies. EV does not. This page explains what EV is, how to calculate it, and how to use it to read any offer in under a minute.
the one rule
If EV is positive, the bonus is mathematically worth taking. If EV is negative, the expected cost is the negative number.
where it shows up
Every casino on this site has an EV score. It is the number we put first because it is the only one that matters.
common range
Most welcome bonuses land between −€80 and +€20 in EV. Truly positive offers are rare and short-lived.
What expected value actually is
Expected value is the average amount of money you would gain or lose per attempt if you took the same bonus offer thousands of times. It is a theoretical average, not a prediction of any single session. Treat it as the long-run price tag on the bonus.
A bonus with an EV of −€40 does not mean you will lose exactly €40. It means that across a large enough number of identical sessions, the average outcome is a €40 loss. Some nights you walk away ahead. Most nights you walk away behind. The casino is comfortable either way because the average is on their side.
The casino is the long-run player. They run the same wager millions of times across millions of accounts. Their average outcome is exactly what the math says. Yours is one sample.
The formula
Every EV calculation we publish boils down to a single subtraction.
core formula
EV = effective bonus − expected loss
effective bonus
The face value of the bonus, minus anything that erodes it: cashout caps, expired free spins, restricted withdrawal balances. Often lower than the headline.
expected loss
The total amount you must wager to unlock the bonus, multiplied by the house edge of the eligible games. This is the long-run cost of clearing the bonus.
Both terms are in euros. If the first is bigger than the second, EV is positive. If not, the bonus has a negative expected value and the size of that negative number is what the bonus actually costs you on average.
A worked example
Take a typical welcome offer: a 100% match bonus up to €100, with a 35x wagering requirement on the bonus only, on slots with a 96% Return To Player (RTP).
step by step
100% up to €100, 35x WR, 96% RTP
Step 1. Deposit €100 to claim the €100 bonus. Bonus balance is now €100.
Step 2. The wagering requirement is 35x the bonus. Total wagering needed is 35 × €100 = €3,500.
Step 3. House edge on a 96% RTP slot is 100% − 96% = 4%. Expected loss across €3,500 of wagering is 4% × €3,500 = €140.
Step 4. EV = €100 − €140 = −€40.
The headline said "free €100". The math says you pay €40 on average to receive it. That is the difference between marketing copy and EV.
Positive, negative, and zero EV
positive EV (rare)
The bonus is mathematically a gift. Take it. These usually appear briefly during promotional pushes, or on offers with low WR, high RTP, and no cashout cap.
zero EV
You break even on average. The bonus is fair compensation for the house edge you absorb. Worth taking if you wanted to play anyway.
negative EV (most)
The bonus costs you money on average. The negative number is the price tag. Most welcome offers in this market land here.
Negative EV is not always a reason to skip a bonus. If you enjoy the play, a small negative number is the entertainment cost. A −€10 EV is cheaper than dinner. A −€100 EV is a different conversation.
Why headline bonus size lies
Operators compete on the size of the number at the top of the page. €200, €500, €1,000. None of those tell you what the bonus is worth. Two offers with identical headline values can have wildly different EV.
offer A
€200 bonus, 40x WR on bonus + deposit, 95% RTP eligible slots, €100 cashout cap. EV ≈ −€120.
offer B
€200 bonus, 20x WR on bonus only, 97% RTP eligible slots, no cap. EV ≈ +€80.
Same headline. €200 difference in expected value. The headline is a marketing number. EV is the real one.
What changes EV
Five things move EV. Most operators tune all five against you. We pull the values from the published terms and run them through the same formula.
- Wagering multiplier. A 35x requirement doubles to 70x of total wagering if it applies to bonus + deposit instead of bonus only. See the wagering requirements guide.
- Game RTP. A 97% slot has half the house edge of a 94% slot. Same wagering, half the expected loss. See the RTP and house edge guide.
- Cashout caps. A €100 cap on a €200 bonus clips your upside but not your downside. See the cashout caps guide.
- Game eligibility. Restricting to a single low-RTP slot can lift the house edge from 4% to 8%, doubling expected loss.
- Time limits. A 7-day window to clear €3,500 of wagering is a different cost than a 30-day window. Short windows push you toward higher-bet, higher-variance play that compounds the expected loss.
What EV does not tell you
EV is a long-run average. It is silent on variance. Two bonuses with identical EV can have very different ranges of outcomes.
A −€40 EV on low-variance blackjack means most nights end somewhere near −€40. A −€40 EV on a high-volatility slot means most nights end near −€100 and a few nights end near +€500. The average is the same. The experience is not.
If you want to see variance, run the offer through our simulator. It plays the bonus 10,000 times and shows the full distribution, not just the mean.
How to use EV in practice
Three rules cover most situations.
- Treat EV as your budget. If the EV is −€40, that is the expected price of the entertainment. Set a deposit limit that assumes you pay it.
- Compare EV, not headlines. When two operators look similar, sort by EV. The cleaner number wins more often than not.
- Take positive EV when it appears. Genuinely positive offers exist, usually briefly. Our bonus comparison table flags them at the top of the list.