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Bluffing & MDF

How often a bluff has to work, and how often you must defend so they can’t bet any two cards: minimum defence frequency.

8 steps, as text. step through the interactive version →

  1. 01, open this step in the interactive version

    They bet $100 into a $100 pot. If it’s a bluff, it has to work half the time to break even.

  2. 02, open this step in the interactive version

    You’re the one facing it. Fold too often and they profit by betting any two cards.

  3. 03, open this step in the interactive version

    So you have to keep enough hands. Defend at least pot ÷ (pot + bet), here 50%. That’s minimum defence frequency, or .

  4. 04, open this step in the interactive version

    Against a half-pot bet the bluff is cheaper, so you defend more: 67% of your range.

  5. 05, open this step in the interactive version

    Now their side. They bet with strong hands, and with some bluffs. You can only see the bet.

  6. 06, open this step in the interactive version

    If one bet in three is a , you win one call in three. That’s exactly the 33% you need to call a pot-sized bet.

  7. 07, open this step in the interactive version

    At that mix, calling and folding earn the same. Neither of you can do better by changing alone. That balance is where equilibrium starts.

  8. 08, open this step in the interactive version

    Change the bet and how often they bluff. Bluff more than the balance and you should call. Bluff less and you should fold.