Expected Value Calculator
Calculates the expected monetary value of a bet over any number of repetitions, revealing its long-run profitability. Use it to decide whether a wager offers a genuine edge over the bookmaker's price.
Last updated: May 2026
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About this calculator
Expected value (EV) is the average amount you expect to win or lose per bet if the same wager were placed infinitely many times. The single-bet formula is EV = (p × profit) − (q × stake), where p is your true win probability, q = 1 − p, and profit = stake × decimal_odds − stake. Over n bets (calculation period), total_EV = n × [(trueProbability/100) × (betAmount × bookmakerOdds − betAmount) − ((1 − trueProbability/100) × betAmount)]. Variables: betAmount (stake per bet), bookmakerOdds (decimal), trueProbability (your estimate, 0–100%), calculationPeriod (1, 10, 100, or 1000 bets). A positive EV means you have an edge; negative EV means the bookmaker has the advantage. The key variable is trueProbability — your own estimate of the real chance of winning, which must be more accurate than the implied probability embedded in the odds. Edge cases: EV is a long-run average, not a guaranteed per-bet outcome — a +$5 EV bet placed 10 times can lose money due to variance; the 'expectation' converges only over hundreds or thousands of bets. EV calculations don't account for variance or risk of ruin; a high-EV but high-variance proposition can bust your bankroll before the EV materializes (this is why Kelly Criterion is used to size +EV bets responsibly). For correlated bets (parlays, same-game multis), single-bet EV math doesn't apply — joint probability must be modeled directly. EV also ignores fixed costs like commissions, currency conversion, and bookmaker-account risk.
How to use
Example 1: $50 stake, decimal odds 2.10, true probability 55%, 100-bet period. Step 1: profit if win = $50 × 2.10 − $50 = $55. Step 2: single-bet EV = (0.55 × $55) − (0.45 × $50) = $30.25 − $22.50 = $7.75. Step 3: 100-bet EV = 100 × $7.75 = $775. Verify: implied probability of 2.10 odds is 1/2.10 ≈ 47.6%; your 55% estimate represents a 7.4 percentage-point edge, which translates to roughly 7-8% of stake per bet — consistent with the $7.75/$50 = 15.5% ROI per bet shown here (the higher ROI reflects the multiplier effect of odds > 2.00). Example 2: $100 stake, odds 1.80, true probability 50%, 1 bet. Step 1: profit if win = $100 × 1.80 − $100 = $80. Step 2: EV = (0.50 × $80) − (0.50 × $100) = $40 − $50 = −$10. Verify: implied probability at 1.80 odds is 1/1.80 ≈ 55.6%; your 50% estimate is below implied, so EV is negative — the bet is a long-run loser.
Frequently asked questions
How do I calculate the expected value of a sports bet accurately?
To calculate EV accurately you need two things: the bookmaker's decimal odds and your own true probability estimate for the outcome. Profit = stake × odds − stake, then EV = (yourProbability × profit) − ((1 − yourProbability) × stake). The challenging part is estimating true probability better than the market does — this requires building your own model, tracking line movements, or using sharp bookmaker prices (Pinnacle, Asian Handicap markets) as a reference for true probability. Without a reliable probability estimate, EV calculation is only as good as the input. Most pros backtest their probability model against historical data before staking real money.
What does a positive expected value mean for long-term betting profitability?
A positive EV bet returns more money than it costs on average over a large sample. A +$5 EV bet placed 500 times should yield roughly $2,500 in profit before variance. However, a single +EV bet can still lose money in the short run — EV describes the long-run average, not any individual outcome. Consistently identifying and betting only +EV opportunities is the core discipline that separates professional bettors from recreational ones. Variance decreases as sample size grows, meaning your actual results converge toward EV over hundreds or thousands of bets. Use Kelly Criterion or fractional Kelly to size your +EV bets responsibly so variance doesn't bust the bankroll before the edge materializes.
Why does true win probability matter more than bookmaker odds in EV calculations?
Bookmaker odds already embed margin (vig), inflating the implied probability above 100% across all outcomes. The odds tell you what the book thinks, not what the true probability is. If your model estimates a team's real win probability as 55% but the bookmaker implies 48%, that 7-point gap is your edge and drives positive EV. Conversely, if your true probability matches or falls below implied, the bet has negative or zero EV regardless of how attractive the payout looks. The quality of your probability estimation is therefore the single most important factor in long-run betting success. Without sharper-than-market probabilities, no staking system — Kelly, flat, or otherwise — can produce profit.
What are common mistakes when calculating betting expected value?
Confusing your gut-feel probability with a model-derived probability — emotional optimism inflates win rates and produces phantom EV. Forgetting to subtract the stake when computing profit ('profit = stake × odds' instead of 'stake × odds − stake') doubles the apparent EV. Treating implied probability as true probability defeats the purpose of EV math — implied probability is what you must beat, not match. Failing to deduct commission, fees, and currency-conversion costs from EV overstates real profitability. Conflating single-bet EV with parlay EV — parlays have compounded margin that simple EV doesn't capture. Ignoring closing-line value (CLV) as the best real-time test of whether your probability estimates are sharper than the market's — over a large sample, beating the closing line is more predictive of long-run profit than +EV claims based on opening lines.
When should I NOT rely on EV calculations alone?
When your win-probability estimate is no better than the implied probability, EV math produces noise — focus first on building a sharper model. For high-variance bets (long-shots, exotic markets) with small expected hit rates, EV alone doesn't capture the ruin risk; use Kelly or a Monte Carlo simulation. Bets with promotional features (boosted odds, parlay insurance, free-bet conversion, profit boosts) have asymmetric returns that simple EV understates — promotional EV calculations are different. Correlated bets (parlays, SGPs, multi-event positions) don't follow single-bet EV math — model joint probability instead. Live in-play bets where odds change between when you decide and when you place are mispriced by snapshot EV. For exchange betting with lay options, you must compute both back-EV and lay-EV separately. Finally, when the bookmaker may void your bet (palpable error, late changes), the realized EV may differ from the calculated EV regardless of the bet outcome.