River Bluff-Catchers: Call Price, Betting Ranges and Blockers
Start with the price of a river call
A bluff-catcher beats bluffs but loses to the bettor's value hands. In a heads-up pot, calling closes the river action: there are no future cards or bets, and a call cannot make the bettor fold.
Let P be the pot before the opponent bets B. Ignoring rake, the final pot after your call is P + 2B. The break-even showdown equity is B / (P + 2B). For an illustrative 100bb pot and a 75bb bet, the call costs 75bb to contest 250bb, so the threshold is 30%. Equity includes your share of ties. Above that threshold a call has positive incremental EV versus folding under these assumptions; it is not necessarily better than a raise.
Do not confuse equity with MDF
MDF = P / (P + B), or about 57.1% in that example. It is a reference for the fraction of the whole range continuing by calling or raising against a zero-equity bluff in a simplified model. It is not the equity required by one hand and is not a command to defend against an opponent who underbluffs.
Select bluff-catchers against the betting range
- Reconstruct the value hands and plausible bluffs that reach this size through the previous actions.
- Account for your cards: blocking value bets and leaving bluffs unblocked can improve a call. A blocker is useful only if those combinations are actually in the betting range.
- Compare the resulting equity with the call price. If the hand beats all bluffs and loses to all value, with no ties, the bluff fraction is its equity.
- Test plausible alternative betting frequencies rather than treating a guessed range as known.
See GTO Wizard's MDF explanation for the distinction between range defense and an individual call.