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Expected value

The average amount a bet is expected to win or lose per bet over a very large number of repeats. Casino games have a negative expected value for players.

Expected value, or EV, is each possible result’s payout multiplied by its probability, added together. A positive EV means the bet gains on average over time, and a negative EV means it loses. Casino games are built to have a negative EV for the player, and that loss per bet is the house edge. EV describes the long run only. In any short session, results swing widely around it, so a negative EV bet can still win on a given night.

Example

A 1 unit bet on red in European roulette: win 1 with probability 18/37, lose 1 with probability 19/37. EV = 18/37 - 19/37 = -1/37, or about -0.027 units per bet.

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