Calculate the figures
Illustrative mathematics only. Values do not predict outcomes or guarantee a return.
Expected value is a model-dependent average
Expected value, or EV, is an average net return implied by a specific probability model and payout assumption. For a simple win-or-lose bet, EV per unit staked equals p×(d−1) − (1−p), where p is the estimated win probability and d is decimal odds. This simplifies to p×d−1. It can be positive or negative, but a positive model estimate does not guarantee that a particular wager wins.
Worked example for probability and price
If estimated win probability is 45 percent and offered decimal odds are 2.30, expected net return per unit is 0.45×2.30−1 = +0.035, or +3.5 percent of stake. On a 20-unit stake that represents an expected net value of +0.70 units across hypothetical repetitions under the model. The individual bet could still lose its entire 20-unit stake. If the estimated probability is wrong, the calculated positive edge may disappear.
Find the break-even threshold
For decimal odds d, the estimated probability needed to break even is 1/d. At decimal odds 2.30, that threshold is roughly 43.48 percent. Comparing 45 percent against 43.48 percent produces an estimated probability advantage of about 1.52 percentage points. That is not the same unit as the +3.5 percent expected return on stake. Both depend on the price remaining available and the event settling according to the simple model.
Understand sensitivity to uncertain probabilities
Small estimation errors can reverse the sign of expected value. In the 2.30-odds example, a probability estimate of 42 percent yields 0.42×2.30−1 = −0.034, or −3.4 percent per unit staked. A single probability percentage is often less trustworthy than a defensible range supported by input data, a documented method and out-of-sample tests. The calculator does not generate its own probabilities or verify the user’s forecast.
Model assumptions and excluded adjustments
The tool assumes exactly two settlement states: a full win at the supplied decimal odds or a full loss of stake. It does not automatically incorporate bookmaker fees, exchange commissions, tax, cash-out valuation, partial payouts, no-bets, voids, bonuses or correlated outcomes. Estimated probability must be a number strictly between zero and one hundred percent, and decimal odds must be above 1.00.
Interpret an estimated positive value responsibly
Expected value is a planning statistic, not an instruction to wager. Realized outcomes can be volatile over long sequences, and repeated selection can expose a player to losses despite a favorable hypothetical average. Consider practical constraints, the quality of your model, the number of opportunities and whether the activity remains within an affordable entertainment budget. Do not borrow, chase losses or interpret a model as financial advice.
Use the tool alongside probability education
Start by reading the odds guide to separate implied prices from independently estimated probabilities. Use the odds converter to check the intended price format, then enter an evidence-supported probability into this EV tool. Compare multiple plausible probability assumptions rather than optimizing only for the most favorable number. If the underlying evidence is weak, the appropriate conclusion can be to decline the bet.
Compare three assumptions instead of one
Suppose the offered decimal price is 2.10. With an estimated win probability of 45 percent, EV per unit is minus 0.055. At 48 percent, EV is plus 0.008, and at 52 percent it rises to plus 0.092. These are illustrative outputs, not evidence that any of those probabilities is correct. A small adjustment in estimated probability can reverse the conclusion, highlighting that the source and calibration of the estimate matter more than the calculator itself. Use a plausible range rather than insisting on one favorable number.
Separate return on stake from total return
The expected net return from a one-unit win-or-lose wager is the estimated probability of a win multiplied by the potential net gain, minus the probability of a loss multiplied by the unit at risk. It is different from the gross return that would arrive after a winning settlement. For example, at decimal 2.00 and an estimated 50 percent chance, EV equals zero units per unit stake in the simple model. The winning payout would still be two units gross, and a losing settlement would still lose the stake entirely.
Do not infer certainty from an edge estimate
Positive expected value does not remove dispersion in realized results. An estimate might be based on incomplete injury information, stale market prices, selection bias or an insufficiently tested model. The arithmetic can be exactly correct while the assumed probability is not. Track when an estimate was made and which events were included, then compare expected outcomes with later results using a clearly defined process. If that evidence is unavailable, a number displayed by the tool should be treated as a sensitivity illustration, not a reason to wager.
Related guides and responsible gambling
For additional explanations, read the odds and probability guide, value betting guide, sports betting strategies, and responsible gambling information. Independent support is available from the National Council on Problem Gambling. Promotional links on this site refer to Shuffle, not bet365.