MDF & Bluff Ratio Calculator

From one bet size: the equity to call, the minimum defense frequency, and the right bluff-to-value mix.

These are equilibrium reference points for one bet size against an opponent playing the same equilibrium, so their use is measuring how far a real opponent sits from balance: defending at the frequency shown makes their bluffs worth nothing rather than making you anything.

Minimum defense frequency

60.2%defend · fold at most 39.8%

Pot100Pot + bet166You defend60.2%

Bet as % pot: 66%
Caller needs = bluff share: 28.4%
Pot odds = value : bluff: 2.52 : 1
Alpha (bluff must work): 39.8%

defend 60%fold

The spot

Pot before the betBet size

Players in the pot

The same spot in the pot odds calculator is Pot 166, Bet to call 66. That page counts the pot with the bet already in it, so the figure it wants is not the one in this field.

These are the balanced baselines. Deviate hard from MDF against players who never bluff (fold more) or never fold (never bluff), the point is to measure how far off equilibrium your opponent is.

Your defense frequency at every table size, this pot and bet

Players	You defend	Drop from previous
2 (yours)	60.2%	–
3	36.9%	−23.3 pts
4	26.5%	−10.5 pts
5	20.6%	−5.9 pts
6	16.8%	−3.7 pts
7	14.2%	−2.6 pts
8	12.3%	−1.9 pts
9	10.9%	−1.5 pts

Adding a third player23.3 pts

Adding the eighth and ninth together3.4 pts

The collapse is front-loaded: adding a third player here costs 23.3 points, more than adding the eighth and ninth together (3.4 points). Most of the effect of playing multiway is spent by the time a third player is in the pot.

Every row assumes the defenders fold independently and defend alike, the same assumption the panel above uses. This is a reference shape, not a per-seat instruction.

A bet that can still improve

Written and reviewed by Alexander Korsager · last reviewed September 26, 2026 · corrections

The idea

One bet size fixes a whole set of numbers. Bet half pot and the caller needs 25% equity to continue, must defend two-thirds of their range to stop you auto-profiting with any bluff, and (if you are betting a polarized range on the river) a quarter of your bets should be bluffs, a 3-to-1 value-to-bluff ratio.

Minimum defense frequency (MDF) is the folding limit: fold more often than pot / (pot + bet) against a bet and a zero-equity bluff makes money outright. Alpha is the same idea from the bettor's side, the share of the time a bluff needs to work, bet / (pot + bet). They always add to one. Both are the heads-up case, and the players field solves the same limit for a bigger table, where the folds multiply rather than add and each defender's own share is smaller.
These are equilibrium reference points, not instructions.Against opponents who never bluff you can fold far more than MDF; against opponents who never fold you should never bluff. The value of knowing the balanced numbers is spotting how far a player deviates from them and by how much you can exploit it.

FAQ

Questions players ask

What is minimum defense frequency?

The smallest fraction of your range you can continue with against a bet before a zero-equity bluff of that size becomes automatically profitable for your opponent. For a pot-sized bet it's 50%; for a half-pot bet, about 67%.

Does MDF apply on every street?

It's a clean rule on the river, where nothing is left to come and a bluff either wins by folding you out or loses. Earlier it's an approximation, because a bluff can still improve, you can still improve, and there is more betting to come. It is also not a floor for how often you have to continue, which is the usual way it gets over-read: it marks the point where a bet with no equity stops making money on its own. Where the bettor's range is much the stronger one, most of the hands MDF would have you continue with are losing calls, and equilibrium play folds well past it.

Is the pot before or after the bet?

Before, and the field says so. A 66 bet into a 100 pot is Pot 100, Bet 66 here, and the caller is then risking 66 to win the 166 that would be in front of them. The pot odds calculator on this site uses the other convention, and its field says that: Pot after their bet already includes the bet you are facing. The same spot is Pot 166, Bet to call 66 there, and both pages then agree at 28.4% and 2.52 : 1.

Does MDF work in a multiway pot?

Yes, and the players field is what switches it on. A bet that cannot win a showdown only profits when every player folds, so the folds multiply: what has to stay under alpha is the chance of a clean sweep, and each defender's own share is 1 minus the nth root of alpha for n players facing the bet, which is one fewer than the players in the pot because the bettor is not defending. At 66 into 100 that is 60.2% heads-up, 36.9% each three-handed and 26.5% each four-handed, all three leaving the same 39.8% chance the bet takes it down. Set Players in the pot and the panel computes your own share for the table you are at, with the field's combined continuation kept beside it.

How many of my bets should be bluffs?

For a polarized river bet, the bluff share equals the pot odds you're laying the caller: bet / (pot + 2·bet). Half pot → 25% bluffs; pot → 33%; a 2x overbet → 40%.

Methodology

How this is calculated

Every figure in the panel comes from one quantity: the bet as a fraction of the pot. Call it s. The price the caller is being laid is s / (1 + 2s), because they put in the bet to win the pot plus that bet, which at the shipped 66 into 100 is 66 / 232, or 28.4%.

Minimum defense frequency is 1 / (1 + s), the share of a range that has to keep playing before a bet that cannot win at showdown makes money on its own, and alpha is the remainder, s / (1 + s), which is how often such a bet has to take the pot uncontested to break even.

The bluff share of a polarized river bet is s / (1 + 2s) again, and the repeat is a theorem rather than a duplicated cell: at equilibrium a polarized bettor bluffs at exactly the price they are laying, which is what leaves the caller indifferent.

The same identity makes the value-to-bluff ratio, (1 + s) / s, the same number as the pot odds printed two cells away, so the six cells carry four distinct figures, two of them shown twice under different names.

Only the semi-bluff line reads the sizes themselves rather than the ratio: it is fold equity times the pot, plus, for the times you are called, your equity in the pot that then exists (the pot plus both bets) less the bet you put in.

Common misreadings5

Defending at the frequency shown does not make you money, it makes their bluff worth nothing. At the shipped 66 into 100, continuing with 60.2% of your range removes the automatic profit from a bet that could never win a showdown, and says nothing at all about whether the spot is a profitable one for you.
Folding more than alpha is only a mistake against a balanced opponent. Against a player who bluffs less often than the equilibrium share, folding well past 39.8% is the correct response, and being able to see how far past is most of the reason for knowing the balanced figure in the first place.
In a multiway pot the printed frequency is the field's job and not yours. A bet with no showdown value profits only on the sweep, so what must stay under alpha is the product of the folds, and with n players facing the bet each one's share is 1 minus the nth root of alpha rather than the heads-up 1 minus alpha. At the shipped 66 into 100, alpha is 39.8%: heads-up that is 60.2%, three-handed it is 36.9% each and four-handed 26.5%. The players field is what picks between them, and leaving it at two in a three-way pot puts 23 points of range in as calls the spot never asked for, a gap that widens with every extra player.
This is a property of a range, not an instruction for the hand in front of you. It says what fraction of everything you could be holding has to keep playing, which is satisfied by continuing with the top of that range and folding the bottom of it. No bet size implies anything about one specific holding.
A large semi-bluff figure is mostly the hand you already had. At the shipped defaults the panel reads +42.2 chips; set equity when called to zero and +0.4 of it remains. The other 41.8 is your share of the pot on the times you get called, which you held before you bet and would keep some of by checking. The figure is measured against folding, and folding is not the alternative available to a hand with 30% equity.

Assumptions8

Only the ratio matters. The pot and the bet are two fields, but the panel reads a single number out of them. A 66 bet into 100 and a 660 bet into 1,000 produce an identical panel, because every figure in it is a function of the bet-to-pot ratio alone. The semi-bluff line is the one output that reads the sizes, since chips are what it returns.
The pot field is the pot before the bet goes in, which is the opposite of the convention on this site's pot odds calculator, where the field is the pot after the bet and so already contains the bet being faced. Both fields are labeled with the convention they use, and each page prints the other one's numbers for the spot you have entered. The same spot is Pot 100, Bet 66 here and Pot 166, Bet to call 66 there.
The bluff has no equity at all. Minimum defense frequency and alpha are both derived against a bet that cannot win a showdown, so the only way it profits is by folding the other range out. A bet that can still improve is not that bet, and neither figure is the right threshold against it.
The bluff share and the value-to-bluff ratio assume a polarized bettor on the river. They come from the case where one player holds either the best hand or nothing, the other holds a hand that beats only the nothing, and no card is left to come. Loosen any of those and the ratio stops being the equilibrium one.
Players in the pot counts everybody in it, one of whom is the bettor, so the exponent the defense figure uses is one less than the number on the pill. At two the panel is the heads-up case throughout and is identical to what it printed before the control existed. Above two the folds multiply rather than add, so what has to stay below alpha is the chance everybody folds, and the headline becomes each defender's own share of that rather than the field's combined one.
The multiway split assumes the defenders are interchangeable: each folds independently of the others and defends at the same frequency. Real players are neither, and position, stack depth and the order they act in all move the true shares around, so the equal split is a reference point rather than a per-seat answer. It is a materially weaker guide than the heads-up figure, which comes from a solved toy game rather than from an assumption of symmetry.
One decision, then showdown. The defender calls or folds once and the hand ends: no raise, no later street, and no rake taken out of the pot either side is playing for.
In the semi-bluff panel, fold equity is your estimate and nothing checks it, and the equity field has to be your equity against the hands that actually call rather than against the opponent's whole range. Those are rarely the same number, and the one you want is normally the lower of the two.

Limits6

Minimum defense frequency is an auto-profit threshold, not the frequency a solver defends at. It marks where a bet with no equity stops printing by itself, and equilibrium play departs from it whenever the ranges are not the clean case. The gap is not small: on a QQ3 rainbow board, where the preflop raiser's range is far the stronger, a third-pot bet puts MDF at 75% while a solver folds close to half its range, because most of the hands MDF would continue with are losing calls.
The bluff ratio is a river number. Earlier there are cards to come, so a bluff carries equity, the defender can improve, and there is more betting behind: the indifference the ratio is derived from does not exist yet. Reading it as a flop bluffing target is the most likely way this page misleads.
Nothing here knows a specific card. Blockers, the combinations your own two cards remove from the range you are up against, move real equilibrium frequencies and are outside any model whose only input is a bet size.
Defending means continuing, not calling. A raise defends. The page prints one number covering the whole of that and cannot say how much of it should be raises, which on many boards is the larger part of it.
The semi-bluff figure stops at showdown. It treats the pot after a call as the pot plus both bets with nothing further going in, so it prices no river bet you will face, no fold you make later, and no extra money you collect on the times you improve.
No rake, and no pay ladder. Chips are worth their face value here, which they are not in a tournament: the ICM calculator is where that difference gets priced.

Evidence

The panel figures are computed by betTheory in math.ts, and math.test.ts pins them at three sizes: half pot (25% price, 66.7% MDF, 33.3% alpha, 25% bluffs, 3 : 1 value to bluff), pot (33.3%, 50%, 50%, 2 : 1) and a double-pot overbet (40% price, 33.3% MDF), plus the identity that MDF and alpha sum to one across five bet sizes.

The model is the standard river toy game in which one player holds the nuts or nothing and the other a bluff-catcher, whose published equilibrium has the defender calling 1 / (1 + s) against a bet of s pots and the bettor bluffing so that bluffs are s / (1 + 2s) of the betting range: those are the two formulas this page computes, and their agreement is why the caller's required equity and the bluff share print as one number.

The derivation and the QQ3 under-defending example are both from GTO Wizard's public write-ups of toy games and of MDF and alpha, retrieved 2026-09-09; Chen and Ankenman's The Mathematics of Poker is the standard text for the method, though this particular game is not credited to any one originator.

The multiway figures quoted in the FAQ and the misuse note are the same alpha read across n independent defenders, since a bet with no showdown value profits only when all of them fold: solving (1 - d) to the power n = alpha gives d = 1 - alpha to the power 1/n, which returns the heads-up minimum defense frequency at n = 1.

GTO Wizard's public write-up on multiway pots states that nth-root rule and publishes a defense table this reproduces, 91% heads-up against a tenth-pot bet falling to about 26% each nine-handed, and 99% falling to 44% against a hundredth-pot bet, retrieved 2026-09-10. multiwayMdf in math.ts computes that rule and math.test.ts pins it: the three figures quoted above at 66 into 100, both anchors from that published table, the identity that two players returns exactly the heads-up figure betTheory already gave, and the derivation itself, that each defender's fold raised to the number of defenders comes back to alpha.

A passing test means the code computes those formulas correctly, not that the clean case they come from is the spot you are sitting in.

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