Work through the net outcomes
Suppose a $100 bet pays +120 and your estimated win probability is 50%. Winning produces $120 net profit; losing produces a $100 net loss. Weighting those outcomes gives (0.50 × $120) − (0.50 × $100) = $10 expected profit. Dividing by the $100 stake gives 10% expected ROI. The $10 is a long-run average under the assumptions, not a possible settlement of that single bet.
Edge and EV use different units
At +120 the price implies 45.45%. A 50% estimate is about 4.55 percentage points above that break-even probability. That probability difference is often called edge. Expected ROI is 10% because it also reflects the payout. Label an edge against a no-vig market separately from an edge against the offered price: they answer different questions.
Test how fragile the estimate is
Keep +120 and a $100 stake, but lower the estimate to 46%. EV falls to $1.20. At 44%, EV is −$3.20. A small input change can reverse the conclusion near break-even. Run a plausible range of probabilities before treating a positive result as meaningful. The calculator checks arithmetic; it cannot validate the estimate.
Know what this calculation leaves out
The calculation assumes either a win or a loss. With a possible push, use separate win, loss and push probabilities: EV = probability of win × net win − probability of loss × stake, with zero profit for a refunded push. Taxes, fees, promotions, limits and stale prices may alter the result. A positive expectation still includes a real chance of losing.
Examples are hypothetical and rounded. These calculators explain arithmetic; they do not establish a model’s accuracy or guarantee an outcome.