Bluff-catching & river indifference

A bluff-catcher is a hand that beats every bluff and loses to every value bet — second pair facing a triple barrel, a middling pair on a scary river. Its defining property: the hand's strength is FIXED while its fate depends entirely on the ratio of bluffs to value in front of it. That makes the decision pure range arithmetic — the pot- odds price sets the required bluff share, and you estimate whether the villain's line reaches it. Hand strength enters only through deciding WHICH hands qualify as bluff-catchers at all.

  1. Price the call.Bet divided by final pot — the exact share of the betting range that must be bluffs.
  2. Count the value region.Rebuild the villain's line street by street; how many combinations reach the river this strong?
  3. Estimate the bluff region.Which missed draws and air actually arrive here — and does this player pool fire them?
  4. Pick the best catcher.Among equivalent-strength hands, prefer the one whose cards block value and unblock bluffs.

Worked example: indifference by the numbers

River pot 40bb, villain shoves 40bb. Calling wins 120bb total, so the price demands about 33% equity — meaning 33% of the betting range must be bluffs for the call to break even. Suppose the line arrives with 12 value combinations and 6 bluffs: a 33% bluff share, almost exactly indifference. Drop two bluffs from their range and the call bleeds; add two missed draws and it prints. The hand did nothing between those worlds — the COUNT did.