What is expected value (EV)?
Expected value (EV) is the average result of a bet if the same bet were repeated a very large number of times. Multiply each possible outcome by its probability and add them up. For casino bets the answer is negative for the player: that negative amount, as a share of the stake, is the house edge.
Definition
Expected value is a weighted average. Each outcome of a bet is weighted by how likely it is, and the weighted outcomes are added together.
EV = (chance of winning × amount won) − (chance of losing × amount lost)
A bet with an EV of zero is "fair": neither side gains on average. A casino bet is priced below fair, so its EV is negative for the player and positive for the house.
A worked case
KES 100 on red at a single-zero roulette wheel. Red wins on 18 pockets of 37 and pays 1 to 1; the other 19 pockets lose the stake.
EV = (18/37 × 100) − (19/37 × 100) = −100/37, about −KES 2.70. Each such bet costs KES 2.70 on average, although no single spin ever produces that result: it is either +100 or −100.
The full table of bets is in the guide to the roulette house edge.
How it relates to other terms
House edge is the negative EV expressed as a percentage of the stake. Return to player is the other side of the same figure: 100% minus the edge. Both are explained in the guide to how RTP and house edge work.
Regulation 20(2) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires licensees to display the "house edge and average return to the player". Those displayed figures are expected values. They describe the average, not what will happen in the next round.
What EV leaves out
EV says nothing about how bumpy the route is. Two bets with the same EV can differ sharply in how often they win and how large the swings are, which is the subject of the entry on volatility.
Questions and answers
Does negative expected value mean I will lose every time?
No. It means the average over many repetitions is a loss. Single rounds and short sessions can end ahead or behind; the more rounds are played, the closer the overall result tends to sit to the average.
Can a staking plan turn a negative EV bet into a positive one?
No. The expected value of a series of bets is the sum of the expected values of each bet. Adding up negative numbers in a different order or size still gives a negative total.