Expected value (EV)

Expected value is the average result a bet or decision would produce if it were repeated many times, weighting each possible outcome by its probability. For a simple bet, EV = (probability of winning × amount won) - (probability of losing × amount staked). A bet with positive expected value, often called +EV, is expected to be profitable on average over many repetitions, even though any single instance of it can still lose.

Expected value differs from the actual result of any one bet or decision, which is only one draw from a range of possible outcomes; a +EV bet can lose, and a negative-EV bet can win, purely from variance. Analysts often use implied probability to estimate the probabilities that feed the calculation, and compare a bet's own estimated probability against the market's to decide whether a positive edge exists.

Beyond betting, expected value is a general decision-making tool used anywhere outcomes are uncertain, from evaluating a decision tree of business choices to estimating risk with Monte Carlo simulation. The main pitfall is confusing a favorable expected value with a certain or even likely favorable outcome: a bet can have strong long-run expected value and still produce losing streaks over a small number of tries, which is why tracking realized results alone, without a large sample, is a weak way to judge whether a decision was sound.