Minimum defense frequency
Minimum defense frequency tells you how often you must keep fighting versus a bet so no bluff is ever free money — the flip side of the pot odds a bettor is laying. One formula sets the floor: MDF = pot / (pot + bet).
What MDF actually protects
Minimum defense frequency (MDF) is the share of your range you must continue with versus a bet so your opponent can't profit by betting any two cards as a bluff. Fold too often and every bluff becomes free money for them.
The formula, once
MDF = pot / (pot + bet). The bettor is risking their bet to win the current pot. If you fold more than the leftover fraction, their risk-free bluffs turn a guaranteed profit. Defending at least the MDF makes a pure bluff break even at best.
Bigger bets let you fold more
A large bet risks more to steal the same pot, so the bluff has to work more often to profit. That means you're allowed to fold more. Against a pot-sized bet you keep half your range; against a 2x-pot overbet you only need to defend about a third.
Small bets force you to defend wide
A small bet risks little to win the pot, so its bluffs only need to succeed occasionally. To deny that, you must call very wide: versus a quarter-pot bet you defend around 80% of your range, folding only your true trash.
Baseline, not a law
MDF is a theoretical default that assumes a balanced, aggressive bettor. Against opponents who almost never bluff, fold more than MDF; against habitual bluffers, defend even wider. Use MDF as the anchor you deviate from, not a rule you obey blindly.
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- MDF = pot / (pot + bet): the minimum share of your range you must continue with to stop auto-profitable bluffs.
- Bigger bets carry a lower MDF, so you're allowed to fold more; small bets force you to defend very wide.
- Quick anchors: quarter-pot ~80%, half-pot ~67%, two-thirds ~60%, pot ~50%, 2x-pot overbet ~33%.
- MDF is a balanced baseline, not a law; fold more versus non-bluffers and defend wider versus over-bluffers.
Test yourself
Answer them all — 16/20 to pass. Every answer gets an explanation.
What is the formula for minimum defense frequency?
MDF = pot / (pot + bet), the fraction of your range you must continue with.
Against a pot-sized bet, roughly what percent of your range must you defend?
MDF = pot/(pot+pot) = 1/2 = 50% for a pot-sized bet.
Against a half-pot bet, MDF is closest to:
MDF = 1/(1+0.5) = 0.667, so about 67%.
As the bet size increases, the MDF you must defend:
Bigger bets risk more, so bluffs need to work more often; you're allowed to fold more.
What is MDF designed to prevent?
Defending at least the MDF makes a pure bluff break even, denying auto-profit.
Against a two-thirds-pot bet, MDF is closest to:
MDF = 1/(1+0.667) = 0.60, so about 60%.
Against a quarter-pot bet, MDF is closest to:
MDF = 1/(1+0.25) = 0.80, so about 80%.
Against a 2x-pot overbet, MDF is closest to:
MDF = pot/(pot+2·pot) = 1/3 = about 33%.
If you fold MORE often than the MDF against a bet, the opponent's pure bluffs are:
Over-folding means bluffs win the pot often enough to show a guaranteed profit.
MDF assumes the bettor is:
MDF is a theoretical baseline against balanced betting; deviate versus known tendencies.
Against a third-pot bet, MDF is closest to:
MDF = 1/(1+0.333) = 0.75, so about 75%.
For a pot-sized bet, a pure bluff needs to succeed how often to break even?
Bluff break-even = bet/(bet+pot) = pot/(2·pot) = 50% for a pot-sized bet.
Against an opponent who almost never bluffs, you should:
MDF is a baseline; against a non-bluffer, over-folding is correct and exploitative.
Pot is 100 and the opponent bets 50. What is the MDF?
MDF = 100/(100+50) = 100/150 = about 67%.
Pot is 100 and the opponent bets 100. What is the MDF?
MDF = 100/(100+100) = 100/200 = 50%.
The maximum fraction of your range you can fold without over-folding equals:
If you must defend the MDF, the most you can fold is the remaining 1 - MDF.
Which bet size lets you fold the greatest share of your range?
The largest bet has the lowest MDF, so you may fold the most.
Defending your MDF can be done by:
Continuing means not folding; both calls and raises count toward meeting the MDF.
Why do small bets force you to defend a wider range?
A small bet's bluff needs only occasional success, so you must fold rarely to deny it.
Pot is 60 and the opponent bets 30. What is the MDF?
MDF = 60/(60+30) = 60/90 = about 67%, the same as any half-pot bet.
Review — all 20 questions & answers tap to expand
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What is the formula for minimum defense frequency?
Answer pot / (pot + bet)
MDF = pot / (pot + bet), the fraction of your range you must continue with.
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Against a pot-sized bet, roughly what percent of your range must you defend?
Answer 50%
MDF = pot/(pot+pot) = 1/2 = 50% for a pot-sized bet.
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Against a half-pot bet, MDF is closest to:
Answer 67%
MDF = 1/(1+0.5) = 0.667, so about 67%.
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As the bet size increases, the MDF you must defend:
Answer Decreases
Bigger bets risk more, so bluffs need to work more often; you're allowed to fold more.
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What is MDF designed to prevent?
Answer An opponent profiting from bluffing any two cards
Defending at least the MDF makes a pure bluff break even, denying auto-profit.
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Against a two-thirds-pot bet, MDF is closest to:
Answer 60%
MDF = 1/(1+0.667) = 0.60, so about 60%.
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Against a quarter-pot bet, MDF is closest to:
Answer 80%
MDF = 1/(1+0.25) = 0.80, so about 80%.
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Against a 2x-pot overbet, MDF is closest to:
Answer 33%
MDF = pot/(pot+2·pot) = 1/3 = about 33%.
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If you fold MORE often than the MDF against a bet, the opponent's pure bluffs are:
Answer Profitable
Over-folding means bluffs win the pot often enough to show a guaranteed profit.
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MDF assumes the bettor is:
Answer A balanced, aggressive opponent
MDF is a theoretical baseline against balanced betting; deviate versus known tendencies.
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Against a third-pot bet, MDF is closest to:
Answer 75%
MDF = 1/(1+0.333) = 0.75, so about 75%.
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For a pot-sized bet, a pure bluff needs to succeed how often to break even?
Answer 50%
Bluff break-even = bet/(bet+pot) = pot/(2·pot) = 50% for a pot-sized bet.
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Against an opponent who almost never bluffs, you should:
Answer Fold more than MDF suggests
MDF is a baseline; against a non-bluffer, over-folding is correct and exploitative.
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Pot is 100 and the opponent bets 50. What is the MDF?
Answer 67%
MDF = 100/(100+50) = 100/150 = about 67%.
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Pot is 100 and the opponent bets 100. What is the MDF?
Answer 50%
MDF = 100/(100+100) = 100/200 = 50%.
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The maximum fraction of your range you can fold without over-folding equals:
Answer 1 minus the MDF
If you must defend the MDF, the most you can fold is the remaining 1 - MDF.
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Which bet size lets you fold the greatest share of your range?
Answer A 2x-pot overbet
The largest bet has the lowest MDF, so you may fold the most.
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Defending your MDF can be done by:
Answer Calling or raising
Continuing means not folding; both calls and raises count toward meeting the MDF.
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Why do small bets force you to defend a wider range?
Answer They risk little to win the pot, so bluffs succeed with fewer folds
A small bet's bluff needs only occasional success, so you must fold rarely to deny it.
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Pot is 60 and the opponent bets 30. What is the MDF?
Answer 67%
MDF = 60/(60+30) = 60/90 = about 67%, the same as any half-pot bet.