Expected value (EV)
Expected value (EV) is the average result of a bet if you could repeat it a huge number of times, found by weighting each possible outcome by its chance.
Also called EV, expectation, expected return
To find the expected value of a bet, multiply each possible result by its probability and add them up. For casino games it is negative for the player. That loss, as a share of the stake, is the house edge.
Example. You bet 10 on red at European roulette. There are 37 pockets and 18 are red. You win 10 with probability 18/37 and lose 10 with probability 19/37. EV = 10 × 18/37 − 10 × 19/37 = −10/37 ≈ −0.27. On average each such bet costs about 0.27, which is 2.7% of the stake.
The same sum works for a bonus: EV = bonus − (total wagering × house edge). This is a simple estimate that assumes you finish the wagering. The wagering calculator works it out.
What people get wrong. EV is not what will happen on any one bet. No single spin loses 0.27: you win 10 or lose 10. EV is the long-run average, and short sessions can land far from it, depending on variance.
The other mistake is thinking a staking plan can fix a negative EV. Add up bets that each have a negative EV and the total is negative, whatever their order or size. That is why the martingale does not work.
Related terms
- House edge
The house edge is the share of each bet a casino expects to keep on average over the long run, equal to 100% minus the game's RTP.
- Return to player (RTP)
RTP (return to player) is the share of all money bet on a game that it is built to pay back to players over a very large number of bets, shown as a percentage.
- Variance
Variance is a measure of how far results are spread around their average, worked out as the average squared distance from the expected value.
- Martingale
The martingale is a betting system where you double your stake after every loss, hoping the next win recovers all your losses plus one base bet.
- Gambler's fallacy
The gambler's fallacy is the mistaken belief that a random result is more or less likely to happen because of what happened in earlier rounds.