Gambling terms, explained straight

Odds, Probability & Bankroll

Expected value gambling

Expected value is the average result you can expect from a bet over many plays, found by weighing each possible outcome by its chance of happening.

Formula
EV = Σ (Probability × Payout) for all outcomes1
Roulette example
EV = 18/38 − 20/38 = −2/38 ≈ −5.26% per $1 bet3
House edge
A negative EV is the house edge, the casino's built-in advantage4

Key points

  • EV tells you the average gain or loss per wager over many repetitions, not the result of a single bet.1
  • In casino games, EV is typically negative; the house edge is the player's negative expected value.5

Common questions

What is expected value in probability?

In probability, expected value is the long-run average of a random variable. For a bet, it is the sum of each possible outcome multiplied by its probability.2

How to calculate expected value in sports betting?

For a simple win/lose bet, use: EV = (Pwin × profit) − (Plose × stake). Assign probabilities based on your own analysis, not the bookmaker's odds.1

Where this term is used

Odds & probability Odds Explains how odds represent probability and payout, the inputs to expected value. Odds & probability Roulette payouts Shows the payouts and probabilities used to calculate roulette's negative expected value. Odds & probability Betting odds Covers the different formats of odds and how they convert to implied probability. Odds & probability Kelly criterion A bankroll management formula that uses expected value to determine optimal bet size. Odds & probability Kelly betting Practical application of the Kelly criterion for sizing bets based on expected value. Odds & probability Martingale strategy A betting system that doubles after losses, which does not change the expected value of each bet.

Sources

  1. Expected Value in Player Prop Betting wizardofodds.com Provides the definition, formula, and calculation method for expected value in betting.
  2. Expected value - Wikipedia en.wikipedia.org Gives the general mathematical definition of expected value.
  3. Gambling mathematics - Wikipedia en.wikipedia.org Supplies the roulette EV calculation example.
  4. Gambling disorder is associated with reduced sensitivity to expected ... pmc.ncbi.nlm.nih.gov Establishes that negative EV is the house edge.
  5. Casino - Wikipedia en.wikipedia.org Confirms the house edge as the casino's advantage.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.