Calculators
Expected value calculator for betting
Compare your estimated chance with the break-even chance of the odds. The calculator shows expected value in dollars and percent, the break-even chance and how often even a positive EV bet loses.
+5.0% of the stake
At 2.10 (+110) you need 47.6% to break even. If the real chance is 50.0%, a $20.00 bet makes +$1.00 on average. That is a long-run average, not what one bet will do, and it is only as good as your estimate.
100 bets like this, $20.00 each
90% of outcomesAverage (EV)
After 100 bets the average result is +$100.00, but 90% of outcomes land between −$236.00 and +$436.00. The chance of being behind after 100 bets is 30.9%.
How it is calculated
EV = stake × (chance × decimal odds − 1)$20.00 × (50.00% × 2.10 − 1) = +$1.00
Break-even chance = 1 ÷ decimal odds1 ÷ 2.10 = 47.62%
After 100 bets: wins follow a binomial distributionaverage +$100.00, spread (1 SD) $210.00, chance behind 30.86%
Thin lines20 random runs, seed 1 (the link keeps the seed, so the same lines come back)
Expected value formula
EV = stake × (p × decimal odds − 1), where p is your probability
Example: $20.00 × (0.42 × 2.50 − 1) = $1.00. In brackets: your p, then the decimal odds. Average: 5.0% of stake per bet.
Break-even probability
Break-even probability = 1 ÷ decimal odds
Example: With the same decimal odds: 1 ÷ odds = 40.0%. If your p is above it, EV is positive. Below it, EV is negative.
Small change in p, opposite sign
Your estimate 42%
- Above break-even of 40.0%
- EV on a $20.00 bet: $1.00
- Average return: 5.0% of stake
- Still loses more often than it wins
Your estimate 38%
- Below break-even of 40.0%
- EV on a $20.00 bet: −$1.00
- Same decimal odds as the formula above, same stake
- The sign of EV flips
EV at different probabilities
| Your probability | Compared with break-even | EV per bet | What it means |
|---|---|---|---|
| 38% | Below 40.0% | −$1.00 | Expected loss on average |
| 40.0% | Equal | Zero | No edge either way |
| 42% | Above 40.0% | $1.00 | Average return of 5.0% of stake, only if your probability is right |
Same $20.00 stake and decimal odds as in the EV formula above. Break-even = 1 ÷ those odds.
Where your probability comes from
No-vig price
60.0% ÷ 103.5% = 58.0%Remove the margin from a two-way market, for example −150 / +130. Fair chances are a starting point, not an edge.
Decimal odds first
The formula uses decimal odds. Convert American or fractional prices before you enter your probability.
Check your estimates
Record your probability and the result for each bet. Over time this shows if your estimates hold up.
Questions
What is positive EV betting?
A bet where your estimated probability is higher than the break-even probability of the odds. Positive EV is an estimate, not a result: if your probability is wrong, the edge does not exist.
How do I calculate break-even probability?
Divide 1 by the decimal odds. With the decimal odds from the EV formula example this gives 40.0%. Convert American odds first with the odds converter.
Does a positive EV bet win most of the time?
No. At 42%, the bet loses more often than it wins. EV of $1.00 is an average. Over a hundred such bets the expected total is $100.00, and the real result can still be a loss.
What is the Kelly criterion in EV betting?
A formula that sizes a stake from your edge: (0.42 × 2.50 − 1) ÷ (2.50 − 1) = 3.3% of the bankroll. Some use a fraction, for example a quarter: 0.83%. It assumes your probability is correct. An overestimate makes it stake too much.