Poker odds calculator: a free hand equity tool with pot odds built in
This poker hand odds calculator works out Texas Hold'em equity for two to six hands. Give each player two cards, add a flop, turn and river if you like, and it shows how often every hand wins or splits the pot. The pot odds check underneath tells you whether a call pays in the long run. It is free, needs no account and runs in your browser.
Hand 1
Hand 2
Hand 3
Hand 4
Hand 5
Hand 6
Board, optional: flop, turn and river
Press a slot, then a card. Press a filled slot to clear it.
- Hand 1 A♠K♠ Win 46.02% · Tie 0.39%
- Hand 2 Q♥Q♦ Win 53.59% · Tie 0.39%
Exact before the flop: all 1,712,304 possible boards counted.
How hand 1 finishes by the river
- Straight flush0.06%
- Four of a kind0.14%
- Full house2.44%
- Flush7.26%
- Straight2.14%
- Three of a kind4.56%
- Two pair22.93%
- One pair43.03%
- High card17.43%
Pot odds check
Is a call worth it? Compare the price of calling with your equity.
The pot includes any bet you are facing. Type your own equity to override the calculator's figure.
What a poker odds calculator does
A poker odds calculator answers one question: if the cards still to come were dealt out in every way they could be, how often would each hand end up best? In Texas Hold'em each player holds two private cards and shares five on the board, so once the hole cards are known the only thing left to chance is the board. The calculator deals each possible board, or a large random sample of them, scores every hand on each one and keeps count. Each hand's share of the wins and split pots is its equity.
It cannot see an opponent's cards and it does not tell you what to do. The value is in what you learn by feeding it hands: that jacks are only a modest favourite over ace-king, or that ace-king crushes ace-queen yet trails a pair of twos.
The tool at the top of the page is a poker hand odds calculator for Hold'em with two to six players. It opens on A♠K♠ v Q♥Q♦ before the flop, a classic all-in spot: the suited ace-king wins 46.02% of all boards, the queens win 53.59% and 0.39% end in a split pot. For the chance of being dealt each starting hand or flopping a set, see the poker odds guide.
How the calculator counts: every board, or a large sample
Which method a poker odds calculator uses depends on how much of the board is known. With two hands and a flop showing, 45 cards are unseen, so there are C(45,2) = 990 possible turn and river pairs; on the turn there are just 44 rivers. The calculator deals every one and gives an exact answer, the same every time. This is enumeration, and it is used whenever two board cards or fewer are still to come.
Before the flop, two known hands leave C(48,5) = 1,712,304 possible boards, and each extra hand adds to the work. In the browser the calculator therefore samples 100,000 random boards for two or three hands and 60,000 for four to six, and the note under the result says so. That is Monte Carlo simulation, the method a poker odds calculator falls back on when there are too many boards to count: 100,000 boards land within about 0.3 percentage points of the exact figure 19 times in 20, and 60,000 within about 0.4. The first answer printed above is not sampled; for the default match-up all 1,712,304 boards were counted when the page was built.
A seven-card evaluator picks each player's best five cards, including the low straight from ace to five. When two hands make exactly the same five cards, often because the board itself plays, the pot is split, and heads-up that returns half of it: equity is the win share plus half the tie share. The tables below were re-counted by a separate program with a different method; see how we calculate the odds. Under the results the calculator also shows how the first hand finishes by the river. Ace-king suited, for instance, ends with a flush 7.3% of the time and with no pair at all 17.4% of the time.
Hand equity against pot odds
Equity is your share of the pot if the hand were played out many times with no more betting; pot odds are the price of carrying on. If calling £25.00 gives you a shot at a pot that will then hold £125.00, you are paying 20.0% of the final pot, so you need to win at least 20.0% of the time to break even. Pot odds of 4 to 1 say the same thing.
The pot odds panel runs that sum. With ace-king suited against queens all in, 46.2% beats the 20.0% required: 46.2% of £125.00 is worth £57.75 for a cost of £25.00, a gain of £32.75 a call on average.
Draws show why the cards to come matter. You hold four hearts after the flop, the pot is £60 and an opponent bets £20. The pot is now £80.00 and a call costs £20.00, so you need 20.0%. With one card to come your nine hearts give 19.1%, just short: the call loses about £0.85 on average. If the opponent is all in and you will see both cards, the same draw is worth 35.0% and the call pays well.
Pot odds leave out money still to come. Implied odds count what you expect to win later when a draw lands, which can justify a call slightly short on price; reverse implied odds count what you lose when you make your hand and still lose, such as a small flush against a bigger one. Neither changes the equity.
Outs and the rule of 2 and 4, checked against the exact odds
An out is an unseen card that improves your hand to one you expect to win: nine for a flush draw, eight for an open-ended straight draw such as 9-8 on a 7-6-2 flop. The rule of 2 and 4 turns outs into a percentage: double them for the next card, or multiply by four on the flop for the chance by the river. The exact figures come from the 47 unseen cards after the flop: outs ÷ 47 for the turn, and 1 − C(47 − outs, 2) ÷ C(47, 2) by the river.
| Outs | Typical draw | Next card, exact | Rule of 2 | By the river, exact | Rule of 4 |
|---|---|---|---|---|---|
| 2 | Pocket pair to a set | 4.3% | 4% | 8.4% | 8% |
| 4 | Inside straight (gutshot) | 8.5% | 8% | 16.5% | 16% |
| 5 | One pair to two pair or trips | 10.6% | 10% | 20.4% | 20% |
| 6 | Two overcards | 12.8% | 12% | 24.1% | 24% |
| 8 | Open-ended straight draw | 17.0% | 16% | 31.5% | 32% |
| 9 | Flush draw | 19.1% | 18% | 35.0% | 36% |
| 12 | Flush draw and a gutshot | 25.5% | 24% | 45.0% | 48% |
| 15 | Flush draw and open-ended | 31.9% | 30% | 54.1% | 60% |
The rule of 2 holds up because it is close to outs ÷ 50 against the true outs ÷ 47. The rule of 4 drifts high as outs grow, since it counts hitting on both cards twice: with 4 outs it gives 16% against an exact 16.5%, with 15 outs 60% against 54.1%. Subtracting a point for every out above eight fixes most of the gap. Rules of thumb also assume every out wins, while a heart that completes your flush can pair the board and fill someone's full house. The calculator scores every hand on every card, so such tainted outs count only when they really win.
Preflop match-ups worth knowing
These match-ups come up again and again. Each was counted exactly over all 1,712,304 boards with the suits shown; other suit combinations can move a figure by a point or so.
| Match-up | Type | First hand wins | Second hand wins | Split pot |
|---|---|---|---|---|
| A♠A♥ v K♦K♣ | Pair over a lower pair | 81.06% | 18.55% | 0.38% |
| A♠K♠ v Q♥Q♦ | Two suited overcards v a pair | 46.02% | 53.59% | 0.39% |
| J♠J♣ v A♥K♦ | Pair v two overcards | 57.09% | 42.58% | 0.33% |
| 2♠2♥ v A♦K♣ | Small pair v two overcards | 52.75% | 46.67% | 0.58% |
| A♠K♦ v A♥Q♣ | Dominated: shared ace, lower kicker | 71.72% | 23.69% | 4.59% |
| K♠K♥ v A♦K♣ | Pair v a hand holding one of its cards | 69.61% | 29.60% | 0.79% |
| A♣K♦ v 8♠7♠ | Two overcards v suited connectors | 57.91% | 41.71% | 0.38% |
A pair against two higher cards is the famous coin flip, and it is not quite even: J♠J♣ v A♥K♦ wins 57.09% for the jacks, and even 2♠2♥ v A♦K♣ wins 52.75%. A pair against a lower pair is another matter: A♠A♥ v K♦K♣ leaves the kings 18.55%. Domination is where hands that look close are not. In A♠K♦ v A♥Q♣ the queen has to pair for the second hand to win, which happens 23.69% of the time, and 4.59% of boards split. In K♠K♥ v A♦K♣ ace-king wins 29.60%, with only one king left in the deck to pair. Suited connectors do better than they look: A♣K♦ v 8♠7♠ gives the small cards 41.71%.
Poker hand rankings and how often each hand is made
Every result a poker odds calculator gives rests on the standard hand rankings. How rare each hand is depends on how many cards you choose from. Dealt five cards, there are C(52,5) = 2,598,960 possible hands, each count following from a short formula.
| Hand | Combinations | Chance | How it is counted |
|---|---|---|---|
| Royal flush | 4 | 0.00015% | 4 suits |
| Straight flush | 36 | 0.0014% | 9 straights below the royal × 4 suits |
| Four of a kind | 624 | 0.024% | 13 ranks × 48 kickers |
| Full house | 3,744 | 0.14% | 13 × C(4,3) × 12 × C(4,2) |
| Flush | 5,108 | 0.20% | 4 suits × (C(13,5) − 10 straights) |
| Straight | 10,200 | 0.39% | 10 straights × 4⁵ suit patterns − 40 straight flushes |
| Three of a kind | 54,912 | 2.11% | 13 × C(4,3) × C(12,2) × 4² |
| Two pair | 123,552 | 4.75% | C(13,2) × C(4,2)² × 44 |
| One pair | 1,098,240 | 42.26% | 13 × C(4,2) × C(12,3) × 4³ |
| High card | 1,302,540 | 50.12% | 1,277 rank sets × (4⁵ − 4) non-flush suit patterns |
Hold'em gives each player seven cards, two in the hand and five on the board: C(52,7) = 133,784,560 sets. We counted them by grouping the sets by how many cards of each rank they hold, then dealing every set with five or more cards of one suit separately to find the flushes.
| Hand | Combinations | Chance | Odds |
|---|---|---|---|
| Royal flush | 4,324 | 0.0032% | 1 in 30,940 |
| Straight flush | 37,260 | 0.028% | 1 in 3,591 |
| Four of a kind | 224,848 | 0.17% | 1 in 595 |
| Full house | 3,473,184 | 2.60% | 1 in 39 |
| Flush | 4,047,644 | 3.03% | 1 in 33 |
| Straight | 6,180,020 | 4.62% | 1 in 22 |
| Three of a kind | 6,461,620 | 4.83% | 1 in 21 |
| Two pair | 31,433,400 | 23.50% | 1 in 4.3 |
| One pair | 58,627,800 | 43.82% | 1 in 2.3 |
| High card | 23,294,460 | 17.41% | 1 in 5.7 |
With seven cards, one pair (43.8%) is the most likely result, and two pair (23.5%) is more common than nothing at all (17.4%). A flush goes from 0.20% in five cards to 3.0% in seven, and three of a kind (4.8%) and a straight (4.6%) end up almost level.
Omaha and other games
This calculator is for Texas Hold'em only. In Omaha each player holds four cards and must use exactly two of them with exactly three from the board, so hands connect with far more boards and preflop equities run much closer together. Entering two of your four Omaha cards here would give a wrong answer. Other variants, such as short-deck Hold'em or seven-card stud, need counts of their own too.
Using a free poker odds calculator fairly
This is a free study tool, and study is the only way to use a poker odds calculator without putting an account at risk. Many online poker sites ban real-time assistance software, meaning any program that works out odds or suggests plays while a hand is in progress, and their terms set out the consequences, up to closing the account and keeping winnings. The rules differ from site to site, so read the terms wherever you play.
Away from the table, a poker odds calculator is one of the best teachers poker has. Enter a hand you played and the cards you think your opponent held, and check whether the price you paid was right. Guess the equity before you press Calculate; after a few dozen hands the guesses get close.
Poker has no house edge in the usual sense, since you play other people; the room takes a rake from each pot instead, as the house edge guide explains. Skill wins over a long run, but the cards decide any single night. Casino games are different: the blackjack calculator and the roulette odds calculator show the edge you play against there. If poker has stopped being fun, or you find yourself chasing losses, our responsible gambling page lists free, confidential help in the UK.
Poker odds calculator: questions people ask
How do I use a poker odds calculator?
Choose how many hands, press an empty card slot and pick a card from the deck. Fill both cards for every hand, then leave the board empty for preflop odds or add a flop, turn and river. The odds update after every card; pressing a filled slot clears it.
What do I need to enter into a poker odds calculator?
Two hole cards for each hand and whatever part of the board has been dealt. Stacks, position and bets matter for decisions, but the chance of each hand winning depends only on which cards are known.
Can a poker odds calculator guarantee I win a hand?
No. It tells you how often a hand wins over every possible run-out, not what the next board will be. Even A♠A♥ v K♦K♣ before the flop loses 18.55% of the time.
Can I use a poker odds calculator during a live game?
Treat the answer as no. Many online poker sites ban software that helps in real time while a hand is in play, and card rooms generally do not allow devices during a hand. Use it before or after a session.
Does this calculator work for Pot-Limit Omaha?
No, it is for Texas Hold'em only. Omaha players hold four cards and must use exactly two, so the counting is different and entering two of your four cards here would mislead you.
What is the difference between pot odds and equity?
Equity is your share of the pot if all the cards were dealt out. Pot odds are the price of a call. A call pays in the long run when your equity is higher than the share of the final pot your call makes up.
How can I use the calculator to study away from the table?
Enter hands you played and check whether your calls were priced right, run a draw on several flops, and guess each answer before you look. The gap between guess and answer shrinks quickly.
Are poker odds tools allowed on UK-licensed poker sites?
Each site's own terms decide, and they differ. Many prohibit tools that calculate odds or advise during a hand, and some publish lists of permitted and banned programs. Read the terms before running any software alongside a game.
Could an odds tool break a poker site's terms and lead to a ban?
Yes, if you use it while playing on a site that forbids real-time assistance. Terms usually allow the site to close the account and may let it keep winnings. Studying hands afterwards is the use this tool is built for.
Does the calculator work on a phone or tablet?
Yes. It runs in the browser and the card picker rearranges itself on small screens. Preflop estimates with five or six hands take a moment longer on an older phone.
Why does the preflop answer move a little when I recalculate?
Before the flop the browser samples random boards instead of counting them all, so two runs differ in the second decimal place, by about 0.3 points at most 19 times in 20. From the flop on, every run-out is counted and the answer is fixed.
What does a tie mean in the results?
A split pot: two or more hands finish with exactly the same best five cards, often because the board plays. Heads-up each gets half the pot, so equity adds half the tie share to the win share.
How many outs does a flush draw have, and is the rule of 2 and 4 accurate?
Nine, which gives 19.1% on the turn and 35.0% by the river. The rule of 4 says 36%: close for a flush draw, but it overstates bigger draws, giving 60% for 15 outs against an exact 54.1%.
What are the odds of pocket aces beating pocket kings?
With A♠A♥ v K♦K♣ the aces win 81.06% of all 1,712,304 boards, the kings 18.55%, and 0.38% split. The kings do slightly worse when they share a suit with the aces, because the ace of that suit beats any flush they make in it.
Why is a pair against two overcards called a coin flip?
Because it is close to even: J♠J♣ v A♥K♦ gives the jacks 57.09% and the overcards 42.58%. The spot comes up so often in tournaments that the name stuck.
How does a poker odds calculator fit with safer gambling?
Knowing the odds is useful, but it does not remove the risk of losing money, and the rake is taken whoever wins. Set your limits before you play; our responsible gambling page lists free, confidential UK help.