Fold equity calculator for poker

How this is worked out

A pure bluff breaks even when the share of folds equals the ratio of your bet to the whole pot after it. All the arithmetic of sizing follows from that: one fraction describes the bluff, the call and the river balance alike.

Where a pure bluff wins on folds alone, a semi-bluff also wins by getting there: even when your opponent calls, the hand keeps a share of the pot. So the demand on folds drops.

A raise looks large at its face value, but your opponent does not see that — he sees the amount he has to add on top of what he already put in. That is why the sizing has to be chosen so that calling does not become automatically profitable for him.

Three formulas for one bet

In every formula the bet and the pot are shares of the pot, not chips and not blinds. The pot is taken as 100% (or as one) and the bet goes in on the same scale: 33%, say, or 0.33. In chips these formulas do not work — convert the bet into a percentage of the pot first.

• Folds needed (breakeven FE): bet ÷ (pot + bet). Below that share of folds the bluff loses money.
• Pot odds for a call: (pot + bet) : bet. That is what you win for every part you put in.
• MDF: pot ÷ (pot + bet) — the minimum share of your range you have to continue with so your opponent cannot bluff with any two cards.
• The bluff share of a bet: bet ÷ (pot + 2 × bet). On the river this same number equals the equity a call needs before any folds are counted.
• Equity to call a raise: the amount added ÷ the final pot. Your opponent counts what is left to put in, not your raise in full.

Do not confuse the three figures

The fold frequency needed, the bluff share and MDF are three different figures.

• FE: shows how often your opponent has to fold for your pure bluff to pay off.
• The bluff share: shows how much of your betting range may be made up of bluffs.
• MDF: shows how much of your own range you have to continue with against a bet so that your opponent cannot profitably bluff with any two cards.

The bigger the bet, the more often your opponent has to fold for the bluff to be profitable, and the more bluffs the betting range may hold. MDF moves the other way: against a big bet you have to defend less often.

For any one sizing FE and MDF always add up to 100%. Against a pot-sized bet, for instance, the fold frequency needed is 50% and MDF is the remaining 50%.

Careful with the equity of a semi-bluff

The field wants the equity you have when called, not the bare chance of getting there. Some outs are «dirty»: a low flush draw arrives but loses to a higher flush, and a straight on a paired board often runs into a full house. Erring low is more realistic than counting every out as clean.

Why a small raise is worse than it looks

A small raise loses twice over: it rarely forces a fold and it hands your opponent excellent odds to call. A big one demands more folds but cuts off the hands that would otherwise draw against you for free. The raise calculator shows both sides at once, so the choice of size is a deliberate one.

The «risk for reward» mnemonic

Take the pot as one and read the bet as «I risk this much to take that much». Everything else can be done in your head:

• Half pot: risk 1, reward 2 — so the bluff needs 1 fold in 3.
• Pot: risk 1, reward 1 — it needs 1 fold in 2.
• Two pots: risk 2, reward 1 — it needs 2 folds in 3.
• The general rule for a bet of n/d of the pot: FE = n ÷ (n + d), MDF = d ÷ (n + d), the bluff share of the bet = n ÷ (d + 2n).

The same fractions 3:1, 2:1 and 3:2 work both for calling on pot odds and for the value-to-bluff ratio on the river — it is one quantity read from two sides.

A separate question is how much equity your own call needs to pay for itself. That is pot odds and the outs calculator: there you work out whether the odds of getting there are enough to pay for the card.