Expected value in betting: inspect the probability assumption
Expected value is a probability-weighted average of net outcomes. The formula is straightforward; the difficult part is defending the probability you put into it.
Calculate net outcomes first
For a $20 cash stake at +150, a win earns $30 profit and a loss costs $20. If the assumed win probability is 45%, EV is (0.45 × $30) − (0.55 × $20) = +$2.50. Expected ROI is $2.50 ÷ $20 = 12.5%.
That +$2.50 is not a possible settlement for this one ticket. The ticket either earns $30 or loses $20 under these assumptions. EV summarizes an average under the probability model, not a promised result.
Change the estimate before trusting the answer
| Assumed win chance | Expected net value | Expected ROI |
|---|---|---|
| 35% | −$2.50 | −12.5% |
| 40% | $0.00 | 0% |
| 45% | +$2.50 | +12.5% |
The price stays fixed, but a ten-percentage-point range changes the conclusion completely. If your estimate cannot distinguish 35% from 45% with useful evidence, the calculator cannot resolve that uncertainty for you.
Give the probability an audit trail
Record how you formed the estimate, the information available at that time, and the exact line and odds. Evaluate predictions on outcomes not used to tune the method. A model adjusted after seeing results cannot support the same claim as a frozen forecast made beforehand.
Also ask what would change the estimate: a different player role, an injury update, a lineup change or a different market threshold. Reusing one percentage for a changed contract can create a precise-looking but irrelevant calculation.
Add pushes and costs explicitly
The general rule sums every possible net outcome multiplied by its probability. A push usually contributes zero net profit, but its probability still belongs in the complete model. For example, 45% win, 45% loss and 10% push is different from 45% win and 55% loss.
At the same +150 price and $20 stake, that three-outcome example has EV of (0.45 × $30) − (0.45 × $20) + (0.10 × $0) = +$4.50. The linked CashCord tool uses the simpler no-push model; do not enter the unconditional 45% there and expect this result. Fees and promotion terms also need their own treatment.
A positive estimate does not determine stake size
Variance, correlated exposure and estimation error remain after the EV calculation. The example does not recommend placing a bet or risking a particular amount. A larger stake multiplies both expected value and possible loss; it does not improve the underlying evidence.
Try the numbers yourself.
Open the calculator with this guide’s example inputs. Change one assumption at a time and see what changes.
Open expected value calculatorCommon questions
Can a positive-EV bet lose?
Yes. In the 45% example, the assumed probability of losing is 55%. Positive expectation and a likely individual loss can coexist.
Does a historical profit prove the probability estimate?
No. Results can vary by chance, and selective reporting can distort them. Calibration and complete before-event records require separate evaluation.
Sources and example scope
The source supports the probability-weighted EV definition. All numerical cases here are original examples; no live market or verified edge is asserted.