HAND LIBRARY · RIVER
Hand study: a River pot-sized bet needs 33.3% call equity
The River removes future betting from the simple call equation, but the opponent range and blockers still determine whether your hand actually reaches the one-third threshold.
INSTANT MATH
Break-even call equity
Enter the pot after the opponent’s wager but before your call, then enter the call amount.
The arithmetic
The pot starts at 100. The opponent bets 100, so the pot is 200 before your decision. Calling costs 100 and creates a 300-chip showdown pot.
Break-even equity = 100 ÷ (200 + 100) = 33.3%.
Convert the threshold into a range question
A pure bluff catcher beats bluffs and loses to value. Ignoring ties, it needs the opponent to bluff at least one third of the betting range for the call to break even.
Blockers matter because your exact cards can remove value combinations, bluff combinations, or both.
Do not confuse MDF with a hand-level call
Minimum defense frequency is a range-level concept under a simplified model. It does not say every bluff catcher must call, nor does it identify which combinations defend best.
A hand-level decision still requires the actual range, card removal, and available actions.
CONTINUE IN FLOPFORGE
Analyze the actual River cards
Enter the River board, exact hand, pot, wager, and opponent range instead of relying on the generic one-third threshold.FAQ
Questions this page should not hide
Why is the threshold one third?
You risk 100 to contest 300 after calling: 100/300 = 1/3.
Does a tie change the calculation?
Yes. Equity counts half the pot for a tie, so use win probability plus half the tie probability.
Is minimum defense frequency the same as pot odds?
They are related in simplified zero-sum models, but MDF applies to a range while pot odds evaluate the price of a specific call.