# Expected Value > Expected value is the average result of a bet over many repetitions. Learn the formula, trading and prediction market examples, and why EV alone is not enough. Source: https://learn.tradelabsai.com/math/expected-value/ Track: Math and Statistics · Level: Intermediate · Updated: 2026-10-03 Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice. Cite as: TradeLabs Learn, "Expected Value", https://learn.tradelabsai.com/math/expected-value/ Expected value (EV) is the average outcome you would get if you could repeat a decision many times. It combines how likely each outcome is with how much you win or lose in each case. A trade or bet with positive expected value makes money on average over time; one with negative expected value loses money on average, no matter how often it happens to win. EV is the single most important concept for judging whether a strategy, a bet or a prediction market position is worth taking. ## The formula ``` EV = Σ (probability of outcome × value of outcome) ``` For a simple win or lose trade: ``` EV = (win probability × average win) - (loss probability × average loss) ``` In trading, EV per trade is often called expectancy. See [Expectancy](https://learn.tradelabsai.com/risk/expectancy/). ## Worked trading example **Example: A setup with a 40% win rate** A breakout strategy wins 40% of the time. Winners average $300 and losers average $120. EV = 0.40 × $300 minus 0.60 × $120 = $120 minus $72 = +$48 per trade. Despite losing 60% of the time, the strategy makes about $48 per trade on average. Over 200 trades, that is roughly $9,600 before costs, though the actual result will vary around that figure. If costs average $20 per trade, net EV falls to $28. See [Transaction Costs](https://learn.tradelabsai.com/orders/transaction-costs/). ## Prediction market example A prediction market share pays $1 if an event happens. If it costs 35 cents and you estimate a 45% chance: ``` EV = 0.45 × $1 - $0.35 = +$0.10 per share ``` If your estimate were 30%, EV would be minus 5 cents. Prediction market profits over time come from paying less than the true probability. See [Reading Odds as Probabilities](https://learn.tradelabsai.com/prediction-markets/reading-odds-as-probabilities/) and [Prediction Market Strategies and Risks](https://learn.tradelabsai.com/prediction-markets/prediction-market-strategies/). ## EV of common gambles | Bet | Approximate EV per $1 | |---|---| | American roulette (single number) | About minus $0.053 | | Fair coin flip at even money | $0 | | Typical lottery ticket | Often minus $0.40 to minus $0.50 | Casinos and lotteries operate on negative EV for players. Many trading behaviours, such as paying high costs, overtrading and buying overpriced long shots, push traders into negative EV without realising it. ## Why positive EV is not enough ### Variance and ruin A positive EV bet can still bankrupt you if you bet too much. With high variance, a run of losses can wipe out an account before the average has time to show up. Position sizing matters as much as EV. See [Risk of Ruin](https://learn.tradelabsai.com/risk/risk-of-ruin/) and [Kelly Criterion](https://learn.tradelabsai.com/risk/kelly-criterion/). **Example: Same EV, different risk** Bet A: 50% chance to win $110, 50% chance to lose $100 (EV +$5). Bet B: 1% chance to win $10,400, 99% chance to lose $100 (EV +$5). Both have the same EV, but Bet B loses 99% of the time. With limited money, you may run out long before you hit the rare win. ### Uncertain estimates EV depends on your probability and payoff estimates. If you overestimate your win rate or underestimate losses, your "positive EV" may be negative. Estimates should come from large samples and honest testing. See [Backtesting Methodology](https://learn.tradelabsai.com/research/backtesting-methodology/) and [Overconfidence](https://learn.tradelabsai.com/psychology/overconfidence/). ### Costs and slippage Small edges can disappear after commissions, spreads, slippage and funding costs. ## Using EV in practice 1. **Estimate win rate and average win and loss** from a large sample of trades. See [Trading Journal](https://learn.tradelabsai.com/start-here/trading-journal/). 2. **Include all costs.** 3. **Calculate EV per trade** and check it is clearly positive. 4. **Size positions** so that normal losing streaks are survivable. See [Position Sizing](https://learn.tradelabsai.com/risk/position-sizing/). 5. **Recheck regularly** as markets change. ## Frequently asked questions ### What is expected value in trading? The average profit or loss per trade over many trades, calculated from the probability and size of wins and losses. ### Can a positive expected value strategy lose money? Yes, in the short term, because of variance, and even in the long term if positions are sized too large and a losing streak causes ruin. ### How do I calculate expected value? Multiply each possible outcome by its probability and add the results; for a simple trade, win rate × average win minus loss rate × average loss. Next, learn why results converge over time in [Law of Large Numbers](https://learn.tradelabsai.com/math/law-of-large-numbers/). ## Continue learning - Next lesson: [Law of Large Numbers](https://learn.tradelabsai.com/math/law-of-large-numbers/) - Previous lesson: [Probability for Traders](https://learn.tradelabsai.com/math/probability-for-traders/) - Related: [Probability for Traders](https://learn.tradelabsai.com/math/probability-for-traders/): Probability is the language of uncertainty in trading. Learn the core rules, independent vs dependent events, odds, and how probability shapes sizing and edge. - Related: [Expectancy](https://learn.tradelabsai.com/risk/expectancy/): Expectancy is the average amount you win or lose per trade. Learn the formula, how win rate and payoff combine, expectancy in R and how to improve it. - Related: [Kelly Criterion](https://learn.tradelabsai.com/risk/kelly-criterion/): The Kelly criterion finds the bet size that maximises long term growth given your edge. Learn the formula, worked examples and why most traders use less. - Related: [Risk of Ruin](https://learn.tradelabsai.com/risk/risk-of-ruin/): Risk of ruin is the chance that losses drain your account beyond recovery. Learn what drives it, see simulated numbers and how to keep it low. - Related: [Reading Odds as Probabilities](https://learn.tradelabsai.com/prediction-markets/reading-odds-as-probabilities/): Learn to turn prediction market prices into probabilities, adjust for spreads and long shot bias, compare with your own estimate and find value with expected value.