Minimum Defense Frequency: How Much You Must Call

Minimum defence frequency is the share of your range you must continue with so that a bet cannot show a profit as a pure bluff. The formula is pot divided by pot plus bet: against a half-pot bet you defend about 67% of your range, and against a pot-sized bet 50%. Fold more often than that and any two cards become a printing press against you. It is one of the few pieces of GTO theory you can work out at the table in two seconds, and one of the most frequently misapplied.

The formula that runs everything

Every bet offers your opponent a price on a bluff. Bet $50 into a $100 pot and that bluff risks $50 to win $100, so it needs a fold more than a third of the time to break even. Your job as the defender is to fold less often than that.

MDF = pot ÷ (pot + bet), and the bluff's break-even fold rate is bet ÷ (pot + bet). The two always add up to one.

So against that $50 bet you continue with 100 ÷ 150 of your range, or 67%. Fold 40% instead and you have handed over a bluff that needed to work 33% of the time and got 40%. On one hand that is a few dollars. Across a year of river decisions it is a visible slice of your win rate.

Notice what is missing: your cards. MDF is a property of the bet size alone, which is what makes it usable in real time. You are pricing the attack, not the hand. Most solver software spells it minimum defense frequency and abbreviates it to MDF.

The numbers worth memorising

Bets come in about seven sizes. Learn what each one demands and the arithmetic stops happening at the table.

Bet size	You must defend	Bluff needs to work
Quarter pot	80%	20%
Third pot	75%	25%
Half pot	67%	33%
Two-thirds pot	60%	40%
Three-quarters pot	57%	43%
Pot	50%	50%
Two times pot	33%	67%

Three things fall straight out of that table.

• Small bets are punishing to fold to. A quarter-pot bet asks you to keep 80% of your range in. Against someone who fires small on every street, folding feels cautious and is the most exploitable thing you can do.
• Large bets buy folds, but they cost. A pot-sized bet only needs half your range gone, and in exchange it has to be right half the time, so the bettor must bring real value hands along with the bluffs.
• The curve is steepest at the small end. Going from a pot bet to a double-pot bet only drops your defence from 50% to 33%. Going from half pot down to quarter pot pushes it from 67% up to 80%.

Defending is not the same as calling

Continuing is defending. A raise spends the same budget as a call, and it often defends better, because it takes away whatever equity the bluff had left and charges it again to see the next card.

Facing a half-pot river bet you might call with 55% of your range and raise with 12%. That is 67%, and you have met the threshold without calling anything close to two thirds of the time.

MDF is also a range statement, never a hand statement. No individual hand defends 67%. You draw a line through your range at the point where continuing stops being worth it and fold everything below it. On K♥9♦4♠2♣7♥ facing a half-pot river bet, A♠K♠ is a trivial continue and the marginal decision lands somewhere around 8♠8♦.

Why the threshold sits where it does

The number is not arbitrary. It comes from the place every GTO threshold comes from: making an opponent indifferent between the options in front of them.

Defend exactly 67% against a half-pot bet and a pure bluff breaks even. Bluffing and giving up are worth the same, so the bettor gains nothing by choosing one over the other and cannot punish you by bluffing more often. That indifference is the entire point. MDF does not win you money — it removes one specific way of losing it.

Run the same equation from the other side and you get how much fold equity a bluff needs before it turns a profit. Bettor and defender are solving one problem from opposite ends, which is why the two numbers always sum to 100%.

Where minimum defence frequency stops applying

MDF answers one narrow question: can a bet made with nothing profit against me? That assumes the bettor could be holding any two cards, and the assumption breaks constantly.

• On the flop and turn, bluffs are not pure. A bet with a flush draw is not risking its whole stake, because it wins some pots when called. Bluffs with equity need fewer folds, so the raw formula understates what you owe on early streets rather than overstating it.
• When the bettor has no bluffs available. On a board where their range contains almost no natural bluff candidates, they cannot reach the maximum bluffing frequency even if they want to. Fold past the threshold and nothing bad happens.
• When the defence compounds. Defending 67% on the flop, 67% of that on the turn and 67% again on the river leaves under 30% of your starting range by showdown. That is the maths working correctly, not a leak — but it means a flop fold is not the same size of error as a river fold.

Treat MDF as a soft floor on the flop and turn, and as a real target on the river, where the bluff has no cards left to improve with.

MDF against real opponents

Look at your last ten river folds facing a half-pot bet. If eight of them were folds, you defended 20% against a threshold of 67%, and anyone who noticed could bet any two cards into you for free.

The reverse is the more profitable half. Most low-stakes players fold far past the threshold, which means your own small river bets are earning whether or not you have a hand. bluff catching on the river is where theory and population tendency diverge most sharply: the solver defends 67%, while against a specific opponent who only bets nutted hands the correct answer is to fold nearly everything.

Both adjustments start from the same number. Move away from it in whichever direction the opponent's real bluffing frequency points.

Putting it to work

1. Price the bet before anything else. A pot odds calculator gives you the equity your call needs and the share of your range that has to continue, in one step, before you have time to talk yourself into a story.
2. Decide where the line falls, not whether this hand feels strong. Ask which part of your range sits above the cut on this board against this betting range.
3. Spend part of the budget on raises. Continuing 60% and raising 7% beats calling 67% against a range that folds to pressure.
4. Adjust for their bluff supply last. Count the hands they can plausibly be bluffing with. If the answer is close to none, fold and stop worrying about exploitability.

Minimum defence frequency will not tell you what to do with 8♠8♦ on a particular river. It tells you whether the folding habit you have built across a thousand rivers can survive contact with a thinking opponent, and for most players the honest answer is that it cannot.