Betting Expected Value (EV) Calculator with No-Vig Odds and Kelly Stake
Work out the expected value of a bet in American, decimal or fractional odds. Use your own win probability or remove the vig from sharp odds (multiplicative, additive, power or Shin), then get your edge, fair odds, a Kelly stake and the chance of being ahead after many bets.
How it works
Decimal odds d: American +A → 1 + A/100, −A → 1 + 100/A; fractional a/b → 1 + a/b · Profit if win W = stake × (d − 1) × (1 − commission) · Loss L = stake (0 for a free bet) · EV = p × W − (1 − p) × L · Break-even p = L ÷ (W + L) (= 1 ÷ d with no commission) · No-vig: implied πᵢ = 1/dᵢ; multiplicative pᵢ = πᵢ ÷ Σπ; additive pᵢ = πᵢ − (Σπ − 1)/n; power pᵢ = πᵢᵏ with Σπᵢᵏ = 1; Shin pᵢ = (√(z² + 4(1 − z)πᵢ²/Σπ) − z) ÷ (2(1 − z)) with Σpᵢ = 1 · Kelly f* = p − (1 − p) ÷ b, b = W ÷ L
Expected value is the average profit or loss per bet if you could repeat it many times. Weight the win payoff by your win probability and subtract the loss weighted by the chance of losing. The break-even win rate is the reciprocal of the decimal odds. A bet is +EV only when your true chance of winning beats that line. Enter the odds in decimal, American or fractional form, and the calculator shows them in all three. The hard part is the probability. Type your own estimate, or paste the odds a sharp bookmaker offers for every outcome. The calculator then removes the margin (the vig) to get fair probabilities. Multiplicative scaling is the common default. Additive takes the same margin off every outcome. Power and Shin take more off longshots, which fits how bookmakers usually price them. Their results for your side are shown side by side. The Kelly criterion turns the edge into a stake size as a share of your bankroll. Half or quarter Kelly is usually wiser, because your probability estimate is never exact. Under More options you can add exchange commission, mark the bet as a free bet, and set how many similar bets to project. That gives the expected profit, its spread, and the exact binomial chance of being ahead.
Worked example
Stake $100 at decimal odds 2.50 (+150, 3/2), believing you have a 45% chance. Profit if you win = 100 × 1.50 = $150. EV = 0.45 × 150 − 0.55 × 100 = 67.50 − 55 = +$12.50 per bet, or 12.5% of the stake. The break-even rate is 1 ÷ 2.50 = 40%, and 45% clears it by 5 points, so it is +EV. Kelly: b = 1.5, so f* = 0.45 − 0.55 ÷ 1.5 = 8.33% of the bankroll. Half Kelly on $1,000 is $41.67. If a sharp book prices the same market at 2.30 / 1.70 instead, the implied probabilities are 43.48% + 58.82% = 102.30%. Removing the 2.30% margin multiplicatively leaves your side at 42.50%, so the bet at 2.50 is still worth +$6.25.
Sources: Expected value — Wikipedia · Kelly, J. L. (1956), A New Interpretation of Information Rate — Bell System Technical Journal · Shin, H. S. (1993), Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims — The Economic Journal
Frequently asked questions
What makes a bet "+EV"?
A bet is +EV when your genuine win probability is higher than the break-even rate implied by the odds (1 ÷ decimal odds). Over many such bets you profit on average, even though any single bet can lose.
Where do I get my win probability?
Either build your own estimate or take it from a sharp market. Choose “Sharp odds (no-vig)” and paste that bookmaker’s odds for every outcome, your side first. The calculator removes the margin and uses the fair probability. If your only source is the same bookmaker you are betting with, you have no edge, because its odds already include its margin.
Which vig-removal method should I use?
Multiplicative (proportional) is the standard and works well for evenly matched two-way markets. With a heavy favourite, or a market with many longshots, the power and Shin methods are usually closer to reality, because bookmakers tend to load more margin onto longshots. The table under the results shows your EV under all four methods. For two-way markets, Shin gives the same answer as additive.
How much should I stake?
The Kelly criterion stakes p − q ÷ b of your bankroll, where b is the net odds. It maximises long-run growth only if your probability is exactly right, and the swings are large, so most bettors use half or quarter Kelly. When the edge is zero or negative, Kelly says not to bet.
How do I convert American and fractional odds to decimal?
For positive American odds, divide by 100 and add 1 (+150 = 2.50). For negative odds, divide 100 by the number without its sign and add 1 (−200 = 1.50). For fractional odds a/b, add 1 to a ÷ b (3/2 = 2.50, 10/11 ≈ 1.91). The calculator does this for you and shows the odds in all three formats.
Does positive EV guarantee I win?
No. EV is a long-run average. A +EV bet can lose, and the edge only shows up reliably across many independent bets. The long-run figures show how wide the swings are. With a 5-point edge at even money (55% at 2.00), you are still behind or only level after 100 bets about one time in five.
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Educational tool only — not gambling advice, and not a promise of returns. Gamble responsibly.