Betting mathematics
Odds Value Calculator: Expected Value & Break-Even
Compare a price with your own probability estimate. Expected value is an average under that assumption, not the payout you will receive on one bet.
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Expected value and betting odds
For stake S, decimal odds D and estimated win probability p as a fraction, EV = p × S × (D − 1) − (1 − p) × S = S × (pD − 1). Expected return on stake is pD − 1. Break-even probability is 1 ÷ D.
At 2.20, a $100 winning ticket profits $120 and a losing ticket loses $100. If each outcome is assumed 50% likely, expected net value is 0.5 × $120 − 0.5 × $100 = $10. The actual one-bet result is still +$120 or −$100, not $10.
Your probability estimate drives the result
Using the quote’s own reciprocal probability always produces zero EV before costs. To assess value you need a separate estimate, and estimation errors can reverse the conclusion. The implied odds calculator converts a quote into its price-based percentage; the no-vig calculator removes margin proportionally from a complete market.
At a 40% estimate and odds 2.20, expected return is −12%, a −$12 average per $100 under that model. A positive expected value does not imply a guaranteed win, a safe stake or an achievable price.
Assumptions and related comparisons
The model has one win and one loss outcome, no pushes, commission or taxes. For changes between your quote and the final market quote, use the closing line value calculator. For allocating a budget across all quoted outcomes, use the arbitrage stake calculator.