Poker Hand Odds

How often a Hold'em hand or range wins, ties and loses, against a hand, a range or any two cards.

This prices one side against one other side, each of them a single holding or a range of holdings, if the board is dealt out. It is not a three-way pot and not the question of whether putting money in is correct.

Your equity

Calculating equity…

Opponent · any two cards

Board · Preflop

You · your hand

Deckfills your card 1

What equity counts

Equity is your win % plus half your tie %, your expected share of the pot at showdown. A range is weighted by its combinations rather than by its hands, so AA is 6 of them and AKo is 12, and any card already on the board or in a known hand is removed from both sides before anything is counted. Every hand in a range is counted at full weight: partial frequencies, where a hand only shows up some of the time, are not supported yet. The calculation stays heads-up throughout.

Published heads-up equities, checked against this engine

Four matchups the poker literature quotes a headline figure for, each fully enumerated by this page’s own evaluator rather than taken from a chart. Aces over kings is one matchup with two different answers, depending on the suits.

Aces vs kings of the other two suits

81.26%

Aces vs kings sharing the aces’ suits

82.64%

Kings that share the aces’ two suits cannot make the flush the aces would otherwise still be drawing dead to, which is worth 1.38 points on its own: a single matchup, nominally “aces over kings”, with two different correct answers.

Two further published heads-up matchups, checked against this engine
Matchup	Equity
Suited ace-king vs A pair of queens	46.2%
Ace-king vs A dominated ace-queen	73.9%

Ace-king holds a tie rate of 4.8% against the dominated ace-queen, nearly one hand in twenty, which a win-percentage-only reading of this matchup would hide entirely. These four are exact enumerations, not simulations like the result above: every possible board is counted, so there is no range to print beside them.

Written and reviewed by Alexander Korsager · last reviewed September 28, 2026 · corrections

The idea

Equity is the fraction of the pot a hand wins on average if the board were dealt out many times. Preflop, pocket aces have roughly 85% equity against a single random hand; a hand like 7-2 offsuit has about 35%.

Set your two cards, then either leave the opponent as any two cards or deal them the exact hand you think you are up against.Add a flop, turn or river to watch a matchup move as the board runs out. Both sides of the calculation are heads-up: it compares two holdings, not a multiway pot.
Either side can also be a range rather than a hand, which is closer to what you actually know at the table: you rarely have their exact two cards, you have a set of holdings they could have. Click the 13x13 grid or type standard notation (22+, ATs+, KQo) and the equity is averaged over every matchup that range allows, weighted by combinations, with any card already on the board or in a known hand removed from both sides.
Below the result is the part a single percentage hides.Equity is a long-run rate, so the tool also shows the exact spread of results over 10, 100 or 1,000 repetitions of the same spot: how many pots a favorite really wins over a finite run, and how often that run still finishes behind.

FAQ

Questions players ask

What does poker equity mean?

It is your expected share of the pot: run the hand to showdown thousands of times and equity is the percentage of those runs you win, split pots counted proportionally.

Is a coin flip really 50/50?

Classic flips like a pair versus two overcards are close to 55/45 for the pair, not exactly even. True 50/50 spots are rarer than the nickname suggests.

Can I run my hand against a specific hand instead of a random one?

Yes. Switch the opponent from any two cards to a set hand, deal them the exact holding you are up against, and add a flop, turn or river to see how the matchup changes as cards come. The calculation stays heads-up: it compares two holdings, not a multiway pot.

Can I put my opponent on a range instead of one hand?

Yes, and you can do the same with your own side, so hand against range and range against range are both supported. Select the hands on the 13x13 grid or type them in standard notation such as 22+, ATs+, KQo. Each hand is counted at full weight; partial frequencies, where a holding only appears some of the time, are not supported yet.

How is a range weighted?

By combinations, not by hands. A pocket pair is 6 card combinations, a suited hand is 4 and an offsuit hand is 12, so a range of AA and AKo is one third aces rather than half. Cards already on the board or in a known hand are removed first, which is why a range of AA is 3 combinations rather than 6 when you hold an ace yourself.

Does 62% equity mean I win 62 of the next 100 hands?

No, and the spread under the result is there to show it. 62% is a long-run rate, and a run of 100 hands lands somewhere in a distribution around it: the middle stops of that distribution, and the chance of finishing with fewer than half the pots, are both shown for 10, 100 and 1,000 repetitions of the spot.

Why does the number move slightly when I re-run it?

Because that answer was simulated rather than enumerated. Where the number of board run-outs is small enough, the tool counts every one of them and says so, and re-running cannot change the answer. Where it is not, preflop above all, it samples 25,000 run-outs instead: one standard error is about 0.3 of a percentage point, so the last printed digit should be read as noise rather than precision. You do not have to take that on trust, because a sampled figure carries the range the run pins it to, printed under the number as a 95% interval, and an enumerated one carries no range at all. The tool always states which of the two produced the figure you are looking at.

Methodology

How this is calculated

Figures on this page come from one of two engines, and the page says which one produced the number in front of you. Where the board run-outs left to deal fit inside a measured budget, every one of them is counted against every possible matchup and the answer is exact: re-running cannot change it.

Where they do not, preflop above all, the page samples 25,000 random completions instead. Either way the deck has your cards, the opponent's cards and any board cards already removed, each side's best five of seven are scored, and wins, ties and losses are tallied.

Nothing is transcribed from a published odds chart: the evaluator is the ranking rules of poker written as a comparison, so the numbers are derived here rather than looked up.

Equity, the figure labeled as such, is wins outright plus half of every tie, which is your expected share of the pot at showdown and the only one of the four figures that is comparable across matchups.

A sampled answer carries sampling error, so each sampled figure prints the range its own run pins it to and an exact one prints nothing.

Those ranges are two-sided 95% intervals on the normal approximation, the figure plus or minus 1.96 standard errors, computed from the run in front of you rather than measured once at the default matchup.

Win, tie and lose are each a share of trials, so the binomial standard error is theirs: the square root of p times one minus p, over the trial count. Equity is not a share of trials and is not computed that way.

A run-out pays it 1, 0.5 or 0, so its variance is the win rate plus a quarter of the tie rate, less the equity squared, which is strictly smaller than the binomial figure whenever the matchup can chop and identical to it when it cannot.

Handing equity to the binomial formula would print a range wider than the sample supports on exactly the matchups where ties are the interesting part.

Every range is clamped at 0% and 100%, because the normal approximation runs past both ends on a hand already drawing dead or already unbeatable, and a range whose ends round together at the figure's own precision prints as that single value rather than as a range of zero width.

One standard error at the worst case, a win rate of a half over 25,000 run-outs, is 0.316 of a percentage point, which is why the last digit of a simulated figure should be read as noise and why Re-run moves it slightly. An exact answer has no such error and the page does not offer a Re-run for it.

Common misreadings5

Equity is a long-run rate, not a forecast for the hand you are looking at. An 85% favorite loses roughly one time in seven, and it will feel like more than that.
A correct read of your equity does not make a losing game a winning one. These are the odds of the cards, and they say nothing about the rake, the stakes or whether you should be sitting there.
Equity is not pot odds. A hand can be well ahead and still be a bad call at the price offered, and a hand can be a clear underdog and still be a correct one. Compare the two on the pot odds tool rather than reading a decision off this page.
The win percentage and the equity figure are different numbers, and the gap between them is the tie rate. Quoting a win percentage as your share of the pot understates every matchup where the board can play, which is most of them.
Re-running until a number looks better does not make it truer. The spread between runs is the measurement error, not new information.

Assumptions7

The matchup is heads-up. Two sides, not a multiway pot, and each side is either an exact holding you deal it or a range of holdings, with any two cards being the range of every hand.
A range is weighted by its card combinations rather than by its hands: a pocket pair is 6 of them, a suited hand 4 and an offsuit hand 12. Every matchup the two ranges allow is counted once and the result is their average, so a range of aces and offsuit ace-king is one third aces rather than half.
Every hand in a range counts at full weight. Partial frequencies, where a holding appears only some of the time, are not supported, so a range you would really play at 30% is priced here as though you always had it.
Every card you have not entered is unseen rather than gone, and each is equally likely to come. That is what makes this a probability and not a reading of a real table.
The board always runs to five cards. Nobody folds, so this is a showdown figure and not the value of playing the hand.
An opponent set to any two cards is drawn uniformly from the remaining deck, which includes every hand a real player would have folded before the flop. Against a range that has already been narrowed by betting, your equity is usually lower than the random-hand figure.
Suits matter and are not cosmetic. The same two ranks give a different answer depending on which suits are already dead, which is why the card picker asks for a suit rather than just a rank.

Limits6

Where the answer is a sample, the range printed under each figure is how much of it the run actually pins down, and a gap narrower than those ranges are wide, between two runs or between two similar matchups, is inside the noise rather than a result. Run it again before treating a small gap as real. Where the page says the answer is exact, this does not apply and the figure is the figure.
The range under a sampled figure says where the true number sits, not where the next Re-run will land. The spread between two runs is the wider of the two quantities, because each of them carries its own error: two independent estimates differ by about 1.4 times as much as one estimate sits from the truth. So a Re-run landing a little outside the range you were just shown is ordinary rather than a contradiction, and separating two sampled matchups by eye needs more daylight between them than either range on its own suggests.
A range is a set of holdings, not a strategy. Selecting the hands someone might have does not say how often they bet, check or fold with each, and a range that has been narrowed by betting is not the same object as the one you drew on the grid.
Multiway pots are not modeled at all. Three-handed equity is not a hand-versus-hand number and cannot be estimated by combining two of them.
No betting, no fold equity, no stack sizes. Equity is one input to a decision and this tool computes only that input.
Preflop is always sampled and always will be. With neither side fixed there are 2,598,960 boards to walk before the matchups are counted, which is not a walk a browser can afford, so the exact engine is reserved for the streets where it fits: a hand against a range from the turn on and usually on the flop, two ranges on the river.

Evidence

The evaluator is pinned first, on hand-built rankings for every category, on the low-ace cases, on kickers inside each category, and on the requirement that no tiebreaker can carry into the category above it.

It is then checked against an outside source, reproducing every published seven-card category frequency (Wikipedia, Poker probability) within sampling error.

Equity itself is validated against a complete enumeration of every remaining run-out, which the test module uses as ground truth and cross-checks against the heads-up equities the poker literature publishes for well-known matchups, rendered in full on the panel below the calculator rather than restated here.

The simulation this page runs is then required to land within three standard errors of that enumeration, preflop and on a flop, so the stated precision is asserted in the tests rather than promised in prose.

The range engine is a separate implementation from that enumeration on purpose, so the check does not share code with the thing it checks: it is asserted to reproduce the two-hand enumeration wherever both can answer the same spot, and its combination weighting is verified by computing the same answer the long way round, one enumeration per opponent combination.

The ranges printed under the sampled figures are pinned there too, and the equity one hardest, because it is the figure whose arithmetic differs from the other three: the tests require it to agree with the binomial interval to twelve places when the matchup cannot chop, to be strictly narrower at the same equity once it can, to collapse to no width on a hand that is drawing dead or unbeatable, and to cover the enumerated truth about 95% of the time measured over 60 independent seeds rather than asserted on the one seed that happened to land inside.

The spread shown under the result is not simulated at all: the number of pots won over a run of hands is a closed-form discrete distribution, checked in the tests against a binomial computed from first principles.

A passing suite means the simulation matches the enumeration and this page matches the code; it does not turn a sampled number into an exact one.

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Published heads-up equities, checked against this engine

What this tool shows

Questions players ask

How this is calculated

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