Expected Value Calculator
Calculate the expected monetary value of a bet over any number of repetitions to reveal its long-run profitability. Use it to decide whether a wager offers a genuine edge over the bookmaker.
About this calculator
Expected value (EV) is the average amount you expect to win or lose per bet if the same wager were placed an infinite number of times. The single-bet EV formula is: EV = (p × profit) − (q × stake), where p is your true win probability, q = 1 − p, and profit = stake × bookmakerOdds − stake. Over a given calculation period (n bets), total EV = n × [(trueProbability / 100) × (betAmount × bookmakerOdds − betAmount) − ((1 − trueProbability / 100) × betAmount)]. 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. Finding positive-EV spots consistently is the foundation of profitable sports betting.
How to use
Example: You bet $50 per game, bookmaker odds are 2.10 (decimal), you believe the true win probability is 55%, calculated over 100 bets. 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: Total EV over 100 bets = 100 × $7.75 = $775. This means you expect to profit approximately $775 over 100 bets, assuming your 55% estimate is accurate.
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 most 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 as a reference. Without a reliable probability estimate, the EV calculation is only as good as the input it's given.
What does a positive expected value mean for long-term betting profitability?
A positive EV bet means that, on average and over a large sample, the bet returns more money than it costs. For example, a +$5 EV bet placed 500 times should yield roughly $2,500 in profit before variance. However, a single positive-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 positive-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 expected value over hundreds or thousands of bets.
Why does true win probability matter more than bookmaker odds in EV calculations?
Bookmaker odds already embed a margin (the vig), which artificially inflates 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 identifies a team's real win probability as 55% but the bookmaker implies 48%, that gap is your edge and drives a positive EV. Conversely, if your true probability estimate matches or falls below the implied probability, the bet is a losing proposition 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.