Fold Equity Calculator

Three outcomes, and nothing else

Heads-up, one bet, one decision. Call the pot before your bet P, your bet S, and the part of it your opponent can actually match C. Measuring everything as a change from where you sit now, there are exactly three branches:

• They fold, and you win +100, the pot as it stands.
• They call and you win, so you take +200: the pot plus the 100 they matched.
• They call and you lose, which costs 100. Only the matched part is ever at risk, which is what matters against a short stack.

EV = fold% × P + call% × [ equity × (P + C) − (1 − equity) × C ]

Take the spot the calculator opens on: a pot of 100, a shove of 100, and 20% equity on the occasions you are called. The called branch on its own is worth -40, so against an opponent who never folds this is a losing bet. Every percentage point of fold equity adds +1.4 to that, and at the 50% the calculator assumes the shove is worth +30. That is the whole model. The rest of this page is reading it from different directions.

The break-even fold percentage

Because EV is a straight line in the fold percentage, there is one crossing point and it has a closed form. Write L for the money the called branch expects to lose, and the shove breaks even when

Break-even fold% = L ÷ (L + P) = 40 ÷ (40 + 100) = 28.57%

It is the classic risk-over-risk-plus-reward, except that the risk is not the whole bet. It is what being called actually costs you once your equity is counted, which is why a draw needs fewer folds than a hand with nothing. The same line printed out shows how much room for error you have:

The line crosses zero at 28.57% folds. Above it you are printing money at a rate of +1.4 per point; below it you are donating at the same rate.

The pure bluff is the same formula with the equity set to zero

Put your equity when called at zero and the break-even fold percentage collapses to the figure most players already know: the bet divided by the pot plus the bet. Risking 100 to win 100 needs a fold 50% of the time, which is the same thing as the 50% minimum defence frequency seen from the other side. No separate rule is needed, and this tool does not use one: it is the general formula evaluated at zero equity. It is also the mirror of minimum defence frequency, so the number you see here and the number in the MDF calculator always add up to a hundred.

The bets are rounded to cents for display while the percentages come from the exact sizing, so a third of 100 shows as 33.33 and still needs the honest 25%.

Equity when called moves the number a long way

A semi-bluff is cheaper than a bluff because the called branch is no longer a write-off. The same sizings, this time with 30% equity when called, show how far the requirement drops. 4 of the 7 sizes need no fold equity at all: they make money against an opponent who never folds, so folds are a bonus rather than the point.

So the equity input is worth measuring rather than guessing, and it has to be your equity against the hands that call, not against the range your opponent started the street with. A calling range is tighter and stronger, so using the wrong one flatters every shove you put through any calculator. Build the calling range in the range equity calculator, or use the odds calculator for a specific hand. A semi-bluff with a real draw behind it is a different bet from the same sizing with air.

The question can also be asked backwards. Fix the fold percentage and the same equation gives the equity the hand needs when called: at 40% folds this shove needs 11.11%, and at 50% folds it needs nothing at all. A fold 50% of the time already pays for the bet, so the hand needs no equity when called.

Worked spots

The short caller is the row people get wrong. The shove breaks even when your opponent folds 33.33% of the time. At the 50% you have assumed it makes 25. Your opponent can only cover 200 of it, so 300 of the bet comes back and only 200 is ever at risk. Shoving 500 at a player who holds 200 is not a 500 bluff, and pricing it as one overstates the risk by 300. It also lays them a better price than the headline size suggests: they need 40% to call and are laid 1.5 to 1.

The value shove runs the other way. This shove needs no fold equity: against an opponent who never folds it is still worth 208, so every fold is a bonus. You are far enough ahead that a call is better news than a fold, so treat this as a value bet rather than a bluff. Once your equity when called passes 58.33% at this size, a call is better news than a fold and the EV line slopes downwards, which is the formal version of the advice not to blast your opponent off a hand you beat. "More fold equity is always better" is simply false, and the crossover has a closed form: (P + C) ÷ (P + 2C).

Check it from the other seat

Your fold percentage is a guess about a person, and the best sanity check on it is the price you are laying them. They are risking 100 to win 200, so they need 33.33% equity to call. That is 2 to 1 on their money, and it means a player defending correctly against this size folds 50% of the time and no more. If your shove needs 28.57% folds and correct defence gives you 50%, you have a margin. If it needs more than that, you are relying on a mistake, which is fine as a read on a particular opponent but not as a default. The pot odds calculator and how to calculate pot odds work that side in detail.

Where this model stops being true

Every calculator that publishes a single fold-equity number is standing on assumptions. These are ours, stated rather than buried:

• The model is heads-up: one pot, one opponent, one decision. Every figure here assumes a single player behind you.
• Multiway is a different and harder calculation, and is deliberately not attempted. Two opponents do not fold independently: their ranges overlap through the cards they hold, the first player's action changes the price the second one is getting, and being called by one while the other folds is a branch with its own equity and its own pot. Multiplying two fold percentages together is not a conservative shortcut either, because the error runs in both directions: folds are positively correlated on the same board, which pushes the chance of getting through above the product, while each opponent defends tighter with another player still to act, which pushes it back down. We do not know which way it lands in a given spot, so we publish no number for it.
• Equity when called means your equity against the hands that actually call, not against your opponent's whole range. Take it from the equity calculator with their calling range rather than their opening range, or the answer flatters the shove.
• The bet is assumed to end the action, which is what makes an all-in the clean case. With money left behind there are further streets to play, and neither your fold equity nor your equity when called is settled on this street alone.
• Chips are treated as money. In a tournament, losing chips costs more prize equity than winning them gains, so scale the losing branch with the bubble factor before trusting the answer.
• Rake is ignored. In a raked cash game the pot you pick up is slightly smaller than the pot shown, which raises the fold percentage a bluff needs.

Three of those have tools of their own. Whether a shove was available at all is a question about the stacks, which the SPR calculator measures. Tournament chips need the losing branch scaled by your bubble factor first, and short stacks are usually better served by the push/fold chart. Rake takes a slice of the pot you pick up, which quietly raises every percentage in the bluff column: the rake comparison shows how large that slice is where you play.