Expected Value
The average mathematical outcome of a bet over many repetitions, expressed as profit or loss per unit wagered.
Detailed Explanation
Expected value (EV) is the probability-weighted average outcome of a bet, representing what a player will theoretically win or lose per unit wagered over infinite repetitions. A bet with +EV returns more than it costs in the long run; -EV bets cost the player money on average. Nearly all casino bets have negative expected value — the house edge ensures the casino profits over time.
Calculation: EV = (Probability of Win × Amount Won) − (Probability of Loss × Amount Lost). For a roulette straight-up bet on an American double-zero wheel: EV = (1/38 × 35) − (37/38 × 1) = 0.921 − 0.974 = −$0.053 per $1 wagered (a house edge of 5.26%).
Positive expected value bets exist in exploitable situations: a skilled card counter in blackjack, an edge-sorted baccarat player, or a poker player with a significantly superior range against a specific opponent can achieve +EV play. In poker specifically, EV analysis is the foundation of all bet-sizing and calling decisions — whether a call has positive or negative EV determines the correct action regardless of short-run results.
Related Entries
Advantage Play
Card Counting
A blackjack technique that tracks the ratio of high to low cards remaining in the shoe to gain a mathematical edge.
Casino Fundamentals
House Edge
The mathematical advantage the casino holds over the player on any given bet, expressed as a percentage.
Casino Fundamentals
Theoretical Loss
The mathematically expected average loss for a player based on their action and the house edge.
Casino Fundamentals
Variance
The statistical measure of how much actual results deviate from the expected value over a series of bets.