Expected value

In probability theory (and especially gambling), the expected value (or mathematical expectation) of a random variable 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 per bet if bets with identical odds are repeated many times. Note that the value itself may not be expected in the general sense; it may be unlikely or even impossible.

Related Topics:
Probability theory - Gambling - Random variable - Expected

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For example, an American roulette wheel has 38 equally possible outcomes. A bet placed on a single number pays 35-to-1 (this means that you are paid 35 times your bet and your bet is returned, so you get 36 times your bet). So the expected value of the profit resulting from a $1 bet on a single number is, considering all 38 possible outcomes: ( -$1 imes rac{37}{38} ) + ( $35 imes rac{1}{38} ), which is about -$0.0526. Therefore one expects, on average, to lose over five cents for every dollar bet.

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