Expected value

In probability (and especially gambling), the expected value of an experiment is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value"). Thus, it represents the average amount one "expects" to win on a bet in the long run if that same bet is taken many times.

For example, an American Roulette? wheel has 38 equally possible outcomes. A bet placed on a single number pays 35-to-1. So the expected value of a $1 bet on a single number is the sum of all 38 possible outcomes: -1 × 37/38 + 36 × 1/38, or a total of -0.0263. Therefore one expects, on average, to lose about 2 1/2 cents for every dollar bet.