Fold Equity Calculator

Leave Bet Size at $50, Pot Size at $120 and Fold percent at 50. You are firing a $50 bluff into $120. Half the time, on this assumption, the opponent folds and you win the $120 without showdown. The other half, you get called and, because this is a pure-bluff model, you lose the $50 with no showdown value. Expected value is foldRate × pot − (1 − foldRate) × bet = 0.50 × 120 − 0.50 × 50 = 60 − 25 = $35.00. A plus-$35 bluff at 50 percent folds is a print if the fold frequency is honest and your hand really is air.

The break-even fold rate for a pure bluff is bet / (pot + bet) = 50 / 170 ≈ 29.41 percent. If villains fold more often than that, the bluff has positive EV even with zero equity when called; if they fold less, you need showdown value or a cheaper size. The default 50 percent is comfortably above 29.41 percent, which is why the EV lands at +$35 rather than zero. Change Fold percent to 29 and the EV collapses toward zero; change it to 20 and the bluff is a leaking $10-ish every time you fire.

Common mistakes: treating Fold percent as “he looks weak” without a sample; ignoring that a $50 bet into $120 is 41.7 percent of pot, a size that gets called more often than a small stab; and forgetting this engine awards you nothing when called. Real bluffs with six-out or nine-out backup have extra EV when they get called, which this page refuses to add. If you want combined EV, compute fold equity here and equity-when-called elsewhere, then weight them: foldRate × pot + (1 − foldRate) × (equity × (pot + bet) − bet).

Worked next steps. Raise the bet to $120 (pot-sized) and keep 50 percent folds: EV = 0.5 × 120 − 0.5 × 120 = 0, so a pot-sized pure bluff needs more than 50 percent folds to print, specifically bet/(pot+bet) = 120/240 = 50 percent exactly at break-even. Drop the bet to $30: break-even fold falls to 30/150 = 20 percent, EV at 50 percent folds is 0.5×120 − 0.5×30 = $45. Smaller bluffs need fewer folds but win a worse price when they work. None of these numbers say the next player will fold. They price a frequency you still have to estimate from history, not from hope.

Fold equity is the slice of expected value that comes from making someone quit. This calculator isolates that slice for a pure bluff: you win the pot when they fold, you lose the bet when they do not, and you are assumed to have zero chips at showdown. Tournament grinders live on this identity at the bubble, where a 30 percent fold is worth more than the same fold in a cash game because ICM punishes calling stations. Cash players use it to sanity-check whether a river air-ball is priced. Coaches use it to kill the myth that every missed draw “has to fire.”

The phrase fold equity circulated in English-language strategy through the 1990s and early 2000s — Harrington on Hold’em made it vocabulary for MTT regulars — but the EV identity is older than the slogan. Any game-theory bluff frequency starts from the same trade: pot captured versus chips risked. Solvers later mixed in equity-when-called so that “pure air” is a boundary case, not the typical river polarisation. This page stays on the boundary on purpose. If you want a merged number, you must bring equity from another tool.

What it does not do: estimate Fold percent for you, model multi-street barrels, or award you a share of the pot when called. There is no field for outs, no field for ICM, no field for the chance of a raise. A three-bet bluff that can be four-bet has a worse distribution than the two-outcome model here. Blockers matter in real bluffs (you hold the ace of hearts, so flush calls decrease) and are invisible here.

Limitations. Fold percent is an input, not an output. Using 50 percent because it is the default is circular. Live tells, HUD fold-to-cbet stats, and solver frequencies are all estimates with error bars; a 10-point miss in Fold percent flips the sign of a thin bluff. Stack depth caps the bet. If the bet is an all-in, pot and bet must reflect effective stacks, not the chip pile in the middle plus a fantasy of more behind.

This tool will not tell you to bluff. A +$35 figure at 50 percent folds is only as good as the 50. If the true fold rate is 25 percent, the same $50 into $120 is EV = 0.25×120 − 0.75×50 = 30 − 37.50 = −$7.50. Educational EV, not a prediction that they fold, not financial advice.

Fold equity isolates the slice of expected value that comes from forcing a fold, under the austere hypothesis of zero showdown equity when called. Write B for the bluff size, P for the pot, and f for the fold probability. Pure-bluff value is then a two-outcome lottery. After that sentence the displayed identity is EV = f × P − (1 − f) × B. Defaults B = 50, P = 120 and f = 50 percent give EV = 0.5 × 120 − 0.5 × 50 = 35 dollars. Half the time the 120 is captured without showdown; half the time the 50 is lost as air.

Break-even fold frequency solves the same trade with value set to zero. From fP = (1 − f)B one obtains f* = B / (P + B) = 50 / 170 ≈ 0.2941, or about 29.41 percent. Above that threshold a pure bluff is profitable even with nothing at showdown; below it, equity when called is required to justify the 50. The default 50 percent sits comfortably above 29.41 percent, which is why the worked value lands at +35 rather than at zero. A pot-sized 120 into 120 would have f* = 50 percent exactly; a smaller 30 into 120 would need only 20 percent folds.

Derivation is ordinary decision theory on a two-action game, not a private invention. With probability f the opponent folds and the accounting credits P relative to giving up. With probability 1 − f the bet is called and, by the zero showdown equity assumption, B is lost in full. Linearity of expectation delivers EV = 0.5 × 120 − 0.5 × 50 = 35 dollars on the defaults. If instead there is equity e when called, the second term becomes (1 − f)(e(P + B) − B). That backup is omitted here on purpose so that fold equity can be studied in isolation.

Chen and Ankenman, in The Mathematics of Poker (2006), placed this trade inside equilibrium bluff ratios: the frequency of bluffs is chosen so that the opponent is indifferent between calling and folding. Sklansky had already priced bluffs as pot captured versus chips risked; Harrington applied the same identity to tournament pressure. Nobody discovered fP − (1 − f)B any more than anyone discovered pP − (1 − p)C for calls. Game theory of bluffs starts from this accounting and then adds range construction, blockers, and the threat of a raise, none of which appear in the two-outcome model.

Assumptions close the lecture and they are strict. A single decision to bet or check, no raise possible, no further streets, f estimated independently of the precise cards except insofar as the estimate used them, zero showdown equity, no rake, chip expected value rather than tournament-dollar concavity. The 35-dollar figure is only as good as the 50 percent fold input. If the true fold rate is 25 percent, the same 50 into 120 yields 0.25 × 120 − 0.75 × 50 = −7.50 dollars. Fold frequency is not a physical constant of the table. The 29.41 percent break-even and the +35 default are prices of a frequency, not a prediction that the next opponent folds.