What is Expected Value?
Expected value is the statistical average winnings or losses per wager calculated through probability and payout analysis. A bet with positive expected value produces mathematical profit across extended play. A bet with negative expected value produces inevitable mathematical losses. Casino games feature negative expected value through house edge ensuring mathematical player disadvantage. Positive expected value opportunities exist in games like poker and sports betting where skill or information advantage creates favorable odds. Expected value guides decision-making by quantifying whether specific wagers are profitable long-term.
Calculating Expected Value
Expected value calculation multiplies outcome probability by payoff amount for all possible outcomes. A coin flip bet paying 2:1 on heads has expected value: (0.5 × 2) + (0.5 × -1) = 0.5 or 50 cents profit per dollar wagered. A roulette red bet with 48.6% probability and 1:1 payout has expected value: (0.486 × 1) + (0.514 × -1) = -0.028 or approximately -2.8 cents per dollar wagered. Expected value calculations quantify mathematical advantage or disadvantage precisely. Professional bettors calculate expected value for every potential wager before committing funds.
Positive vs Negative Expected Value
Positive expected value opportunities produce long-term profits as probability exceeds implied odds. A poker hand offering positive expected value against opponents should be played aggressively. A sports bet with 55% estimated probability on -110 odds offers positive expected value worth consistent wagering. Negative expected value opportunities guarantee long-term losses regardless of short-term results. Casino games with 3% house edge represent negative expected value despite entertainment value. Players should accept only positive expected value wagers in pursuit of profit, avoiding negative expectation despite psychological appeal.
Expected Value and Variance
Expected value represents mathematical average across extended play while individual results vary substantially through variance. A positive expected value bet might lose frequently through short-term variance before profit manifests. Extended play across thousands of wagers allows expected value to dominate variance effects. Short-term results frequently deviate from expected value through luck. Understanding expected value as long-term mathematical concept rather than short-term prediction prevents misinterpreting variance as evidence against sound expected value analysis.
Expected Value in Different Games
Casino games feature negative expected value through house edge ensuring mathematical losses. Blackjack with basic strategy offers approximately -0.5% expected value. Slots typically offer -2% to -5% expected value. Roulette offers approximately -2.7% expected value. Poker offers positive expected value for skilled players against weaker opponents. Sports betting offers positive expected value for bettors with superior probability estimation. Expected value varies substantially across games, making game selection crucial for profit pursuit.
Expected Value and Bankroll Management
Expected value guides bankroll sizing determining sustainable wager amounts. Positive expected value bets justify larger wagers through Kelly criterion calculations. Negative expected value bets should receive minimal wagering preserving bankroll for superior opportunities. Extended play revealing true expected value requires adequate bankroll surviving inevitable downswings. Insufficient bankroll depletes before positive expected value manifests through thousands of bets. Expected value analysis informs appropriate risk sizing ensuring bankroll sustainability during extended play.
Expected Value and Decision Quality
Making decisions based on expected value separates professional gamblers from casual players. Expected value analysis prevents emotional wagering on mathematically unfavorable opportunities. Expected value focus enables accepting losses on individual wagers that possess positive expectation overall. Professional bettors obsess over expected value optimization rather than individual win-loss records. Expected value discipline requires wagering only on favorable opportunities despite psychological appeal of other options. Superior long-term results depend on consistently making expected value-positive decisions.
Frequently Asked Questions
Q: What is expected value?
A: Expected value is the average amount of money a player expects to win or lose per wager based on probability and payout calculations.
Q: How is expected value calculated?
A: Expected value multiplies probability by payoff for all outcomes then sums them. Formula: EV = (Probability Win × Payout) - (Probability Loss × Loss Amount).
Q: What is positive vs negative expected value?
A: Positive expected value produces long-term profits. Negative expected value guarantees mathematical losses. Casino games feature negative expectation through house edge.
Q: Why does variance affect expected value perception?
A: Variance causes short-term results to deviate from expected value through luck. Extended play across thousands of wagers allows expected value to dominate variance.
Q: How does expected value differ between games?
A: Casino games feature negative expected value through house edge. Poker and sports betting offer positive expected value for skilled players with information advantages.
Q: How should expected value guide betting decisions?
A: Players should accept only positive expected value wagers in profit pursuit. Negative expected value bets should receive minimal wagering preserving bankroll.