Hong Life CalculatorsUnderstanding the poker bet expected value and fold equity calculator — concept and principle
A bet in poker can win in two ways: the opponent folds and you take the pot at once, or the opponent calls and your hand wins at showdown. This calculator combines both into one expected value (EV), the average amount the bet gains per decision over many repetitions, and shows the fold percentage at which the bet exactly breaks even.
How it is calculated
EV = F × Pot + (1 − F) × [Eq × (Pot + 2B) − B]
- Pot: chips already in the middle. B: your bet. F: probability the opponent folds. Eq: your chance of winning if called.
- When called, the final pot is Pot + 2B (your bet plus the matching call). You win it with probability Eq, and you have paid B.
- Break-even fold %: F* = (B − Eq(Pot + 2B)) ÷ (Pot + B − Eq(Pot + 2B)) × 100, the value of F that makes EV = 0. If the called branch is already profitable, the calculator shows 0% (+EV even if called).
EV is measured against the chips you hold now, so a fold by the opponent counts as winning the whole pot.
The principle
Expected value weights each outcome by its probability and adds them up. The bet splits the future into two branches, fold and call, and the called branch is itself an average of winning and losing. Fold equity is the extra value created by the chance that the opponent gives up a pot they might have won. The model assumes the opponent only folds or calls (no raise) and that no more money goes in after the call.
Worked example
- Inputs: pot 100, bet 75, fold probability 40%, equity when called 35%.
- Called branch: 0.35 × (100 + 150) − 75 = 87.5 − 75 = 12.5.
- EV = 0.40 × 100 + 0.60 × 12.5 = 40 + 7.5 = 47.5.
- Break-even fold %: the called branch already wins 12.5, so no folds are needed: 0% (+EV even if called).
| Pot | EV of bet |
|---|---|
| 25 | 1.75 |
| 50 | 17 |
| 75 | 32.25 |
| 100 | 47.5 |
| 125 | 62.75 |
| 150 | 78 |
| 200 | 108.5 |
How to read the result
A positive EV means the bet makes money on average; 47.5 here means about 47.5 chips per bet over the long run. A break-even of 0% means the called branch is already profitable (12.5 > 0), so the bet wins on average even if the opponent never folds; the formula alone would give a meaningless −14.29%. For a pure bluff (Eq = 0) the threshold becomes B ÷ (Pot + B); a 75 bet into 100 must work 75 ÷ 175 = 42.9% of the time. To compare with checking, estimate the check line's EV separately; if you would simply check down with 35% equity, that is about 0.35 × 100 = 35, less than 47.5.
Common mistakes
- Using total equity instead of equity against the calling range, which is usually weaker for you.
- Forgetting that opponents can raise, which removes your equity in the called branch.
Frequently asked questions
What is fold equity?
The part of a bet's value that comes from the opponent folding, F × Pot in the formula.
Is a bet with positive EV always the best play?
Not necessarily. Checking or a different bet size can have a higher EV; compare the options.
Sources: David Sklansky, The Theory of Poker, Two Plus Two Publishing (semi-bluffing and fold equity) · Bill Chen and Jerrod Ankenman, The Mathematics of Poker, ConJelCo, 2006