Bluffs vs value by street

The MDF and pot-odds topics both answer a question from the defender's side: given a bet size, how much of my range has to keep playing? This topic asks the same math from the opposite seat. If you're the one betting a polarized range — the best hands plus some bluffs, the same shape the 3-bet/4-bet topic describes preflop — how many of those bets can honestly be bluffs before your opponent's calling decision stops being close?

The cleanest place to answer that is the river: no more cards are coming, so a river bluff has zero remaining equity — it either wins right now because the defender folds, or it loses at showdown. Bet the size of the pot (10bb into 10bb) and the defender is laying themselves 2:1 on the call (10bb to win 30bb), which by the pot-odds topic's c / (p + c) formula requires 33.3% equity to call profitably. A pure bluff-catcher — a hand that beats every bluff and loses to every value bet — has exactly that much "equity": the chance the bet in front of it is a bluff. So that same number is also the bettor's breakeven bluff frequency — roughly 1 bluff for every 2 value bets (about a third of the betting range) makes the bluff-catcher's call and fold exactly equal in EV. Bluff more than that and the defender profits by calling; bluff less and the bettor is leaving free value on the table — bets that would have kept printing profit against a defender who's still folding correctly.

That's the aggressor's mirror of MDF. MDF (pot / (pot + bet)) tells the defender the minimum share of their whole range that must keep playing so a bettor can't profit by firing every hand as a bluff. The bluff:value ratio here tells the bettor the maximum share of their own betting range that can be a genuine zero-equity bluff before that same defender's call turns automatically profitable. Same bet, same pot, two different — related — thresholds computed from the same pot-odds arithmetic, one per seat: a pot-size bet is 33% bluffs for the bettor but 50% MDF for the defender — different questions, not a typo.

Smaller bets need fewer bluffs to stay balanced. A half-pot bet (5bb into 10bb) only supports about 25% bluffs, because the defender is being asked to risk less to see the same showdown, so it takes proportionally fewer bluffs to make that cheaper call indifferent. Bigger bets need more — which is exactly why the biggest bets a range fires are also its most bluff-heavy ones, in proportion, even though the same big sizing is also the one described on the Bet sizing topic as needing the strongest hands to justify it at all.

Bettor's max bluff share vs. bet size

Drag the pot and bet-size sliders and watch the bettor's-side bluff ratio move alongside the defender's-side MDF, for the same bet.

Bettor's max bluff share of this bet33.3%
Ratio (value : bluff)2.0 : 1

bluff share = bet / (pot + 2 × bet) = 10.0 / (10 + 20.0) = 33.3%

A bluff-catcher facing this bet needs 33.3% equity to call profitably (the pot-odds topic's c / (p + c), applied here). Since a bluff-catcher's whole equity here IS "how often is this a bluff," that same number is also the bettor's ceiling: bluff more than this share of the betting range and a bluff-catcher's call turns automatically profitable (over-bluffing); stay under it and every added bluff still shows a profit against a defender who's still folding correctly. For comparison, this bet's MDF — the defender's-side number from the MDF topic — is 50.0%: a related question with a different answer, computed from the same pot and bet.

None of this is a fixed frequency to hit on every street — it's the ceiling a polarized river bet's bluffs are measured against, because the river is the one street where a "bluff" cleanly means zero remaining equity. Earlier streets don't fit the same clean box. On the flop and turn, ranges typically run more bluff-heavy than the river math above would suggest — not because the pressure math changes, but because most flop and turn "bluffs" aren't really zero-equity at all. A continuation bet with a backdoor flush draw, an overcard-and-a-gutshot, or a pair of live undercards still has real outs to become the best hand later — a semi-bluff, not a pure bluff — so a range can profitably carry more of them than the pure-bluff indifference math above allows, and there are more streets left to keep applying pressure or change plans. As the hand moves toward the river, that backup equity keeps disappearing: fewer cards are left to come, so what started as a semi-bluff either connects (and becomes value) or has genuinely nothing left. By the river, a bet's bluffing portion is down to the hands with real backup — usually a blocker to the value the defender needs to keep calling with — which is why river ranges are the most value-weighted of the three postflop streets, and why the clean 2:1-price-to-33%-bluffs arithmetic above is river-native rather than a rule for every street.