Expected Value (EV)
Definition
The average amount a player can expect to win or lose per bet over the long run. Calculated as (probability of winning × win amount) - (probability of losing × loss amount). A positive EV means the bet is profitable long-term; negative EV means it loses money.
Expected value, commonly abbreviated as EV, is the average outcome of a bet if it were repeated an infinite number of times. It is calculated by multiplying each possible outcome by its probability and summing the results. For example, a $10 bet on a fair coin flip paying 2 to 1 has an EV of ($20 x 0.5) - ($10 x 0.5) = +$5. A positive EV means the bet is profitable long-term; negative EV means it loses money.
In casino gambling, almost every bet has a negative expected value for the player. A $10 bet on red in European roulette has an EV of roughly -$0.27, because the probability of winning (18/37) multiplied by the $10 payout minus the probability of losing (19/37) multiplied by $10 yields a negative number. This negative EV is the house edge expressed in dollar terms.
Professional gamblers and advantage players focus exclusively on finding positive EV opportunities. Card counters in blackjack identify moments when the remaining deck composition favors the player, creating a temporary positive EV. Sports bettors seek lines where bookmaker odds are mispriced. Poker players profit because they compete against other players rather than the house, and skill creates a positive EV against weaker opponents.
Understanding EV helps you evaluate any gambling proposition objectively. A lottery ticket with a $2 cost and a 1-in-10-million chance at $5 million has an EV of -$1.50, making it a poor bet mathematically. However, EV alone does not capture the full picture: variance, risk of ruin, and personal utility all matter. A bet can be positive EV but still inappropriate if the variance is too high relative to your bankroll.
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The mathematical advantage the casino has over the player, expressed as a percentage of each bet that the casino expects to keep over the long run. For example, a 2% house edge means the casino expects to keep $2 for every $100 wagered. Different games and bets within games have different house edges.
VarianceA measure of how much results deviate from the expected value in the short term. High variance games have bigger swings, including longer losing streaks and bigger wins. Low variance games produce more consistent, predictable results.
Return to Player (RTP)The percentage of wagered money that a game returns to players over time. RTP = 100% - House Edge. A slot with 96% RTP has a 4% house edge. Higher RTP means better odds for the player.
Kelly CriterionA mathematical formula that calculates the optimal bet size to maximize long-term bankroll growth. The formula is f* = (bp - q) / b, where b = net odds, p = win probability, q = loss probability. Most professionals use fractional Kelly (half or quarter).
EquityYour share of the pot based on the probability of winning the hand. If you have a 40% chance of winning a $200 pot, your equity is $80. Equity changes with each new card dealt.
ProbabilityThe likelihood of a specific outcome occurring, expressed as a number between 0 and 1 (or 0% and 100%). In a fair coin flip, the probability of heads is 0.5. Understanding probability is fundamental to evaluating any casino bet.
Law of Large NumbersA mathematical theorem stating that as the number of trials increases, actual results converge toward the expected value. This is why casinos always profit long-term because they play enough hands for the house edge to reliably manifest.
Edge PercentageThe mathematical advantage expressed as a percentage. A player edge means positive expected value; a house edge means negative expected value. Even a small edge (1-2%) becomes significant over thousands of bets.
Expected Goals (xG)An advanced soccer statistic measuring the quality of scoring chances. Each shot is assigned a probability of becoming a goal based on historical data. xG helps identify underperforming or overperforming teams for betting value.
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Frequently Asked Questions
What is Expected Value (EV)?
The average amount a player can expect to win or lose per bet over the long run. Calculated as (probability of winning × win amount) - (probability of losing × loss amount). A positive EV means the bet is profitable long-term; negative EV means it loses money.
What terms are related to Expected Value (EV)?
Related concepts include: House Edge, Variance, Return to Player (RTP), Kelly Criterion, Equity, Probability, Law of Large Numbers, Edge Percentage, Expected Goals (xG). Understanding these terms together gives you a more complete picture of the concept.
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