Poker math: the right number for the right question.

Three percentages can describe the same bet and answer three different questions. This reference keeps the price of a call, the success rate of a bluff and a range-defense benchmark separate.

Use this page as a lookup during study, then follow the worked guides when a step is unclear. The table is also available as a downloadable math reference; the visible numbers and download are generated from the same exact fractions.

Start with the extra amount to call.

Call threshold = extra call / final pot after that call. Include wagers already in front of the players. Do not add a bet twice, and do not count a side pot you cannot win. For a first bet B into a pot P, a full call makes the final pot P + 2B.

At exactly 30% equity the call and fold have equal chip EV in that model. A real decision still needs a justified opponent range. On an earlier street, raw showdown equity does not automatically describe the value of calling through future action. Continue with the pot-odds workshop and the equity-realization explanation.

One table, two separate questions.

Scope: heads-up first bets, no rake, no further betting and no side pots. The call column uses equity, including ties. The bluff column assumes a bluff always loses when called. These are break-even thresholds, not recommended actions or observed opponent frequencies.

Call equity and pure-bluff fold thresholds, rounded to two decimals

First bet size	Call equity	Folds for bluff
Quarter pot	16.67%	20.00%
One-third pot	20.00%	25.00%
Half pot	25.00%	33.33%
Two-thirds pot	28.57%	40.00%
Three-quarters pot	30.00%	42.86%
Pot	33.33%	50.00%
One-and-a-half pot	37.50%	60.00%
Twice pot	40.00%	66.67%

Pure-bluff threshold = risk / (risk + reward). In the 120-pot example, risking 90 to win 120 requires 90 / 210 = 42.86% folds to break even. That is different from the caller's 30% equity threshold. At higher fold rates the zero-equity bluff has positive chip EV under the stated assumptions.

MDF is not your hand's required equity.

The complementary first-bet minimum defense frequency is P / (P + B). For the example, it is 120 / 210 = 57.14%. It is a simplified benchmark for the frequency with which a range continues against a zero-equity bluff. It does not say that every hand needs 57.14% equity, or that you must personally call at that rate in every game.

Raises, later betting, multiway pots, payout effects and the opponent's actual strategy change the problem. Do not give every player in a multiway pot the same heads-up defense quota. GTO Wizard's mathematical-misconceptions article explains why the simplified labels need these boundaries.

Pot-limit: call first in the calculation, then raise the resulting pot.

Using the same fictional 120 pot and 90 bet, a player with no wager already committed on this street would call 90 to make 300, then raise by up to 300. That makes a maximum 390 total wager for that player, not 300 or 480. This is the accounting calculation, not an instruction to physically make a two-motion raise.

With chips already committed, separate the new chips from the total street wager. Short stacks or action-reopening questions need additional checks. The official Omaha explanation describes pot-limit betting; the rules guide explains where procedural rulings belong.

Two other calculations worth keeping straight.

Stack in BB = stack / current big blind. A 28,500 stack at a 1,000 big blind is 28.5 BB. State when the stack was measured. SPR = effective chips remaining / pot at the same decision. Heads-up, 450 effective chips behind a 150 pot gives SPR 3. It is a situation descriptor, not a promise that a particular hand should commit its stack.

An out must improve you to a winner for the question you are answering. Completing a flush is not enough when the opponent can have a better hand or redraw. The flush-and-redraw lab checks that distinction. Do not turn a two-card probability into a one-street calling rule.

Check the denominator before the result.

Against a half-pot first bet, is the call threshold 25% or 33.33%?

25% under the table's assumptions. With P = 100 and B = 50, the final pot is 200. The 33.33% figure is the bettor's zero-equity bluff fold threshold, 50 / 150.

Does a pot-size raise use the same bluff threshold as a pot-size first bet?

Not automatically. Recalculate incremental risk and reward. In the worked pot-limit example, a zero-equity bluff risking 390 to win the current 210 requires 390 / 600 = 65% folds, under the no-further-action assumptions.

Does a positive chip-EV call guarantee a profitable tournament decision?

No. Prize structure and remaining stacks can change the objective. Use the tournament-equity guide; this table does not model prizes or bounties.

Go to the source

These selections retain the directory's access labels, individual review dates and limitations. Public-page reading is not a product accuracy test.

Prepared with AI assistance. Published October 8, 2026. Worked examples are fictional, not Nolan's hands or results. This is educational material for before or after play, not live assistance.