Poker Odds Calculator – Outs to Percentages, Exact
Count the cards that complete your hand — your outs — and this page turns them into your real chances: the exact combinatorics for the next card and for both cards to come, with the famous rule of 4 and 2 sitting right beside the exact figures so you can see how close the shortcut lands. Add the pot and the call, and it also prices the bet for you: the equity the call demands, against the equity your draw actually has.
Your draw
The price: pot odds
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Your chances
The draw, three ways
The price of the call
Ahead of the price
Your draw lands 35.0% of the time; the call demands only 16.7%. On the arithmetic alone, calling this bet earns money over the long run — the gap is 18.3 points. What the arithmetic cannot see: future bets, implied odds and the cards your opponents hold.
- One card: outs ÷ unseen cards; two cards: 1 − C(unseen − outs, 2) ÷ C(unseen, 2) — a 9-out flush draw on the flop is 19.15% on the next card, 35.0% by the river.
- The rule of 4 and 2 is a shortcut, not the exact figure: it gives 36% where the exact two-card figure is 35.0%.
- Only count cards that genuinely help: a card that completes your draw while giving an opponent a stronger hand is a dirty out.
- The shortcut, checked
- The outs table
- Pairs well with this calculation
- From outs to a decision in three steps
- How the poker odds calculator works
- Going deeper
- The outs table, exact, and where the shortcut bends
- Pot odds and the break-even line, at several prices
- Dirty outs, blockers and why the count is a judgment
- Implied odds, fold equity and the limits of pot-odds arithmetic
- Frequently asked questions
The shortcut, checked
Every bar below is drawn to the same 0–100% scale. Players quote the rule of 4 and 2 because it is fast — here is how far it actually lands from the exact combinatorics, on your numbers.
The shortcut bars sit close to the exact ones for small draws — that closeness, not magic, is why the rule survives. Watch it drift on a 15-out combo draw (try the chip above): the rule of 4 promises 60%, the exact figure is 54.12%.
The one idea underneath all of it
A draw is a fraction. The cards that save you, divided by the cards you cannot see — that is the whole subject. Two cards to come makes the fraction kinder, because missing once still leaves a second chance; the exact formula is just the careful bookkeeping of both chances at once. Everything on this page, the rules of thumb included, is that one fraction wearing different coats.
The outs table
Exact percentages for every draw size worth memorising — computed from the same combinatorics as the calculator, not rounded from the shortcut.
Read the drift, not just the numbers: up to about 8 outs the rule of 4 stays within a point of the exact figure. Past that it inflates — 60% promised against 54.12% delivered at 15 outs, and 80% against 67.53% at 20. The bigger the draw, the more the shortcut flatters it.
Pairs well with this calculation
Odds in their other costumes — prices, probabilities and percentages.
From outs to a decision in three steps
Count your outs, honestly
List every unseen card that improves your hand to the one you are drawing to. You know five cards — your two and the board — so the deck you are drawing from is the 47 you cannot see. Count only cards that genuinely help: a card that completes your draw but hands an opponent something better is a dirty out, and counting it flatters the maths.
Pick the street
On the flop, two cards are coming, and your chance is the chance of hitting on either — that is the 1 − C(miss, 2) ÷ C(47, 2) figure. On the turn, one card remains and the maths shrinks to a single division: outs ÷ 46. The stage button above picks the right deck size for you.
Compare with the price
A call is a purchase: you pay the call to win the pot. The equity it demands is call ÷ (pot + call) — pay $20 into a $100 pot and you need just 16.7% to break even. If your draw lands more often than that, the arithmetic of the call is profitable over the long run, whatever happens this once.
How the poker odds calculator works
one card: outs ÷ unseen cards · two cards: 1 − C(unseen − outs, 2) ÷ C(unseen, 2)
The example on this page. A flush draw on the flop: four of your suit are visible, nine remain — 9 outs among 47 unseen cards. One card: 9 ÷ 47 = 19.15%. Both cards: the draw misses only when both new cards come from the 38 that do not help, and that happens C(38, 2) ÷ C(47, 2) = 703/1081 = 65.03% of the time — so it lands 1 − 65.03% = 34.97% of the time, displayed as 35.0%.
A gutshot against the same price. Four outs by the river is 16.47%. Put the same $20 call into the same $100 pot — the call demands 16.7% — and the gutshot falls short by a fifth of a point. Same pot, same price, different draw, different answer: at the margin, exact figures are what separate the two.
The turn. One card is gone from the deck and one chance remains, so 9 outs is simply 9 ÷ 46 = 19.57%. Notice the turn figure for a flush draw is a touch kinder than the flop’s single-card figure (19.15%) — the deck is one card smaller, and none of the missing cards was one of yours.
Where the rule of 4 and 2 fits. One card gives each out about a 2% chance (1 ÷ 47 = 2.13%), so outs × 2 estimates one card. Two cards is not quite twice that — missing twice is likelier than the naive doubling allows — but outs × 4 still lands within about a point for draws up to 8 outs. This page keeps the shortcut visible next to the exact answer so its error is never hidden.
How the numbers are rounded. Percentages are carried unrounded through every step and rounded only for display: one decimal in the headline, two in the exact figure. Percentages that appear inside sentences are the same values, so the page cannot disagree with itself between the table and the text.
Going deeper
The rule of 4 pretends the two cards are independent chances of about 2% per out each. They are not quite: the second card is drawn from a deck one card smaller, and the chances of the two cards overlap — a card that arrives on the turn cannot also arrive on the river. For small draws the overlap is a rounding error. For big ones it compounds: at 15 outs the true figure is 54.12% while the rule promises 60%, and at 20 outs it promises 80% against a real 67.53%.
There is a standard repair. For draws with more than 8 outs, multiply by 4 as usual and then subtract the number of outs above 8: at 15 outs, 60 − 7 = 53%, within a point of the exact 54.12%; at 12 outs, 48 − 4 = 44% against an exact 44.96%. This page shows the plain rule, unedited, beside the exact figure — but if you only ever memorise one correction, memorise that subtraction.
Pot odds answer a narrow question: what share of the time must this call succeed for it to pay for itself? Pay $20 to win a $100 pot and the answer is 20 ÷ 120 = 16.7%. Anything that lands more often than that is, on the bare arithmetic, a profitable purchase repeated over a career — the result of any single hand is still luck, and this page’s comparison says nothing about the cards you cannot see.
Two honest caveats. Implied odds: if hitting your draw will win extra bets on later streets, the effective price is kinder than the raw pot odds — real, but a forecast, not a fact. Reverse implied odds run the other way: a draw that completes into a second-best hand can cost more after it hits. Both live outside this calculator on purpose. What is inside it — the outs, the percentages and the price — is the part that can be computed exactly, and it is the part worth getting right first.
The outs table, exact, and where the shortcut bends
The guide above works one draw in full, the nine-out flush draw. The table below works the whole family of common draws the same way, with exact figures computed from the 47-card unseen deck on the flop, so you can see both the pattern and the point where the rule of 4 stops being a harmless shortcut and starts being a misleading one. The one-card column is outs divided by 47. The two-card column is one minus the chance that both new cards miss, which is one minus combinations of non-outs taken two at a time divided by combinations of 47 taken two at a time. The rule-of-4 column is simply outs times four, and the error column is the shortcut minus the exact two-card figure.
| Draw (outs) | Next card only | By the river, exact | Rule of 4 | Shortcut error |
|---|---|---|---|---|
| Gutshot (4) | 8.51% | 16.47% | 16% | −0.47 points |
| Open-ended straight (8) | 17.02% | 31.45% | 32% | +0.55 points |
| Flush draw (9) | 19.15% | 34.97% | 36% | +1.03 points |
| Flush draw plus gutshot (12) | 25.53% | 44.96% | 48% | +3.04 points |
| Combo draw (15) | 31.91% | 54.12% | 60% | +5.88 points |
| Big combo draw (20) | 42.55% | 67.53% | 80% | +12.47 points |
The pattern in the error column is the lesson. Up to about eight outs the shortcut is within roughly half a point of the exact figure, which is why generations of players have used it without harm. At nine outs it is already a full point high, at twelve outs it is three points high, and at twenty outs it promises 80 percent for a draw that lands 67.53 percent of the time, an error of more than twelve points. The reason is not mysterious: the rule of 4 treats each out as worth about two percent per card and adds those values, but the two cards cannot both be outs in the way addition assumes, because the second card is drawn from a smaller deck after the first card has missed. The overlap grows with the number of outs, so the shortcut’s error grows with it. The FAQ above gives the standard correction for large draws, subtracting the outs above eight from the rule-of-4 result, which at fifteen outs gives 60 minus 7, or 53 percent, much closer to the exact 54.12 percent than the uncorrected 60. On this page you never need the correction, because the calculator shows the exact figure beside the shortcut, but at a live table, where there is no calculator, the correction is the difference between a shortcut and a self-deception.
Pot odds and the break-even line, at several prices
A call is a purchase, and the price of the purchase is the call divided by the pot plus the call. The table below prices several common situations, so the comparison the calculator performs for your numbers can be felt as a habit rather than a calculation. The break-even figure is the hit rate at which calling neither wins nor loses money over the long run, before any consideration of future betting. If your draw lands more often than the break-even figure, the arithmetic of the call is profitable; if it lands less often, folding is, on the arithmetic alone.
| Pot before your call | Call demanded | Break-even hit rate | Flush draw (35.0%) | Gutshot (16.5%) |
|---|---|---|---|---|
| $50 | $20 | 28.6% | Call | Fold |
| $100 | $20 | 16.7% | Call | Fold, by 0.2 points |
| $100 | $50 | 33.3% | Call | Fold |
| $200 | $20 | 9.1% | Call | Call |
| $100 | $100 | 50.0% | Fold | Fold |
Two rows deserve attention. The second row is the page’s own example, and the gutshot’s fate in it is a lesson in margins: at 16.47 percent against a break-even of 16.7 percent, the gutshot falls short by barely two tenths of a point, which is why the guide above says that at the margin, exact figures are what separate a good call from a bad one. A player using the rule of 4 would call, because the shortcut says 16 percent, which rounds in the mind to about even; a player using the rule of 2 for one card would face a different question entirely. The fourth row shows the opposite trap: a small call into a large pot makes almost any draw callable on the arithmetic, including the gutshot, and the mistake there is not calling but calling for the wrong reason, as if a cheap call were a free one. It is not free; it is a small losing or winning investment like any other, and over hundreds of hands the small edges compound exactly as the large ones do.
The fifth row is the boundary every player should memorise. A pot-sized call demands 50 percent, and no single draw on the flop reaches it: even the twenty-out combo draw lands 67.53 percent of the time by the river, which beats it, but that is a rare monster draw, and most draws a player actually holds sit well below 50 percent. When the call equals the pot, the question stops being about your draw’s raw chance and becomes about what else the call buys: future bets you can win if you hit, the chance your opponent folds to a later bet, and the strength of the hand you already hold. Those are the subjects of the next two sections, and none of them are in the pot-odds figure.
Dirty outs, blockers and why the count is a judgment
The calculator counts exactly what you tell it to count, and the hardest part of using it well is deciding what to tell it. An out is only an out if the card genuinely improves your hand to the one you are drawing to, and improves it enough to win. A card that completes your flush while also completing a possible full house for an opponent who has been betting strongly is a dirty out: it looks like help and it may be a trap, and counting it at full value overstates your chances. The standard practice is to discount dirty outs, counting them as half an out or excluding them entirely when the opponent’s betting tells a consistent story of a stronger hand. The calculator has no way to know which of your outs are dirty, because it cannot see the betting or the opponent; the discount is a judgment you apply before you type the number in, not a calculation the page performs for you.
Blockers work in the opposite direction and are equally invisible to the calculator. If you hold two cards of a suit, fewer cards of that suit remain for anyone else, and if an opponent’s likely range includes hands that block your outs, the effective number of outs is smaller than the nominal count. The page’s arithmetic assumes all 47 unseen cards are equally available, which includes your opponents’ hole cards and the burn cards as unknown cards, and that assumption is correct as a statement about what you know. But a player who can narrow an opponent’s range, for example an opponent who raised before the flop and bet strongly on a board with an ace, may reasonably conclude that some of their outs are already in the opponent’s hand. The honest response is not to change the deck size in the calculator, which would break the arithmetic, but to reduce the outs you enter, and to say so when you discuss the hand afterwards.
The practical discipline that follows is to enter outs in ranges, not points. If your flush draw is clean, enter 9. If one of the nine cards also pairs the board in a way that could give an opponent a full house, try 8 and 9 and see whether the decision changes. If it does not change, the dirty out did not matter and you can stop worrying about it. If it does change, the hand is genuinely close, and close hands are where bankroll discipline matters more than arithmetic: a decision that flips on one discounted out is a decision whose expected value is near zero either way, and the cost of getting it wrong is small. The players who lose money on outs are not the ones who miscount by one; they are the ones who count every card that helps their hand and none that helps their opponent’s.
Implied odds, fold equity and the limits of pot-odds arithmetic
Pot odds answer one question: is this call profitable if nothing else happens after it? In real poker, something else almost always happens after it, and the two most important somethings have names. Implied odds are the future bets you expect to win if your draw lands. A flush draw that misses the pot-odds test by a point can still be a profitable call if, when it hits, your opponent will pay off a substantial further bet, because the effective pot for the decision includes those future winnings, not just the money already in the middle. The reverse also holds: a draw that passes the pot-odds test can be a losing call if your opponent will fold whenever the draw lands, so that you win only the current pot and never the implied extra. The calculator does not model implied odds, because it cannot know your opponent, and any page that claimed to price them exactly would be inventing a number.
Fold equity is the chance that a bet or raise wins the pot immediately, without any draw landing at all, and it is the reason strong players sometimes raise a draw rather than call with it. A raise that wins the pot outright some fraction of the time, and otherwise leaves you with the same draw you had, can be profitable even when a call is not, because the raise adds a second way to win. Neither implied odds nor fold equity appears in the pot-odds figure, and both depend on reads, stack sizes and table dynamics that no calculator can see. Treat the pot-odds verdict as the floor of the analysis: if the arithmetic alone says call, the call is sound before any of these considerations; if it says fold by a wide margin, only a strong, specific reason about future betting should overturn it; if it says fold by a fraction of a point, the hand is close enough that the unmodelled factors decide it.
One final limit deserves stating plainly, because odds pages are sometimes read as promises. Nothing on this page is a winning system, and no pattern of calls derived from pot odds guarantees profit in any session. Pot-odds arithmetic describes long-run expectation over many repetitions of the same decision; in a single evening, variance dominates, and a player can make every correct decision and still lose. The responsible way to use these figures is as a discipline for decision-making and a check against the most expensive mistakes, such as chasing a gutshot into a pot-sized bet, while keeping stakes at a level where a run of bad variance is an annoyance rather than a harm. If poker stops being enjoyable at the stakes you play, the correct response is to lower the stakes, not to look for a better odds table.
Pot odds in one division
Pot odds are one division: the amount you must call divided by the pot plus the call. If the pot holds $80 and the call is $20, the pot odds are 20 divided by 100, which is 20 percent. That percentage is the break-even line: if your chance of winning the hand is above 20 percent, calling is profitable in the long run, and if it is below, calling loses money on average no matter how the hand feels.
The comparison is what makes pot odds useful, because hand odds alone do not decide anything. A flush draw with 9 outs has about a 19.6 percent chance of hitting on the next card, which is just below the 20 percent break-even line in the example above, so the call is marginally unprofitable on pot odds alone. Implied odds — money you expect to win on later streets if you hit — can rescue such a call, but they must be estimated honestly, not assumed.
The Rule of 4 and 2, and where it bends
The Rule of 4 and 2 is a shortcut: multiply your outs by 4 on the flop for the chance of hitting by the river, and by 2 on the turn for the chance on the next card. Nine outs on the flop give about 36 percent by the rule, against an exact 35.0 percent; nine outs on the turn give about 18 percent by the rule, against an exact 19.6 percent. The shortcut is close enough to decide most calls at the table, and that is its purpose.
Exact chances for common out counts. The rule overstates large out counts on the flop and understates on the turn.
| Outs | Flop to river (exact) | Rule of 4 | Turn to river (exact) | Rule of 2 |
|---|---|---|---|---|
| 4 | 16.5% | 16% | 8.7% | 8% |
| 9 | 35.0% | 36% | 19.6% | 18% |
| 15 | 54.1% | 60% | 32.6% | 30% |
Where the rule bends is at large out counts on the flop, where multiplying by 4 overshoots because the two cards are not independent draws: the first card changes the deck for the second. Fifteen outs give 54.1 percent exactly, not 60 percent. At the table the rule is fine; when the money is large and the out count is high, use the calculator’s exact figure instead.
Frequently asked questions
What are outs in poker?
Outs are the unseen cards that improve your hand to the hand you are drawing to. If you hold four hearts, the nine hearts still in the deck are your outs — any of them completes the flush. Only count cards that genuinely help: a card that finishes your draw while giving an opponent a stronger hand is a dirty out, and counting it overstates your chances.
How do I work out my chances on the flop?
Two cards are coming, so count your outs and take one minus the chance that both cards miss. For a flush draw that is 1 − C(38, 2) ÷ C(47, 2) = 34.97%, about 35 times in 100. For the very next card alone it is just outs divided by unseen cards: 9 ÷ 47 = 19.15%. Enter your outs above with the stage set to Flop and both figures appear, exact and shortcut side by side.
What is the rule of 4 and 2, and how accurate is it?
A table shortcut: multiply your outs by 4 on the flop for your chance across both cards, and by 2 for one card. It works because each out is worth about 2% per card (1 in 47). For draws up to about 8 outs it lands within roughly a point of the exact answer. It bends on big draws — at 15 outs it promises 60% against an exact 54.12% — so on combo draws, subtract the outs above 8 from the rule-of-4 result, or use the exact figure this page gives.
What are pot odds, in plain terms?
Pot odds are the price of one more card, expressed as the equity a call demands. If the pot is $100 and you must call $20, you are paying 20 to be in a 120 pot, so the call breaks even when your draw lands 20 ÷ 120 = 16.7% of the time. Land more often than that and the call is profitable on the arithmetic over the long run; land less often and folding is. The pot box above does this comparison for your numbers.
How many outs do the common draws have?
A flush draw has 9 outs — thirteen cards of the suit, four already visible. An open-ended straight draw has 8, four at each end. A gutshot has 4. Two overcards have 6, and a hand with both a flush draw and an open-ended straight draw has 15, not 17 — two of the straight cards are already counted among the flush cards. The chips above the outs box load each of these into the calculator.
Why does this calculator draw from 47 cards, not 52?
Because five cards are already known: your two hole cards and the three flop cards. They cannot arrive again, so the deck you are drawing from is the 47 cards you cannot see — which includes your opponents’ hole cards and the burn cards, all equally unknown from where you sit. On the turn a sixth card is known and the unseen deck is 46. Odds computed any other way would quietly pretend you could redraw cards already on the table.
What changes on the turn?
Two things: the number of cards still to come, and the size of the unseen deck. On the flop two cards are coming from 47 unseen cards, so a nine-out flush draw lands 34.97 percent of the time by the river. On the turn one card remains, a sixth card is now known, and the unseen deck is 46, so the same nine outs give 9 divided by 46, which is 19.57 percent for that single card. The rule of 2 estimates it at 18 percent, about one and a half points low. The practical consequence is that a draw that was callable on the flop can become a fold on the turn at the same price, because the price has not changed but the chance has roughly halved; set the stage to Turn above before deciding, rather than carrying the flop figure forward.
How do I count outs for an open-ended straight draw?
Eight: four cards at each end of the straight. If you hold 6-7 on a board of 8-9-2, any 5 or any 10 completes the straight, and there are four of each still unseen, assuming none is already visible. That is the draw the table in the guide above prices at 31.45 percent by the river. The common miscount is to add the flush cards as well when two of your straight cards share a suit with cards you hold; a hand with both a flush draw and an open-ended straight draw has 15 outs, not 17, because two of the straight cards are already counted among the nine flush cards. The chips above the outs box load each standard draw, including the 15-out combo, so you can check a count before trusting it.
Can I use this calculator for multi-way pots?
For the draw arithmetic, yes; for the whole decision, only partly. Your chance of hitting the draw depends on the unseen deck, not on how many opponents are in the pot, so the outs and pot-odds figures remain correct. What changes with more opponents is everything the calculator does not model: the chance that one of them already holds a hand your draw cannot beat, the chance that the pot odds you face are not the odds you will actually pay if someone raises behind you, and the value of hitting your draw against several players who may all pay you off. In a multi-way pot, treat the pot-odds verdict as necessary but not sufficient, and discount dirty outs more aggressively than you would heads-up.
Does a bigger pot always mean I should call?
No. A bigger pot lowers the break-even hit rate, which makes more draws callable, but the comparison is always between that break-even rate and your draw’s actual chance. A gutshot at 16.47 percent is a call into a $200 pot facing a $20 bet, where the break-even is 9.1 percent, and a fold into a $100 pot facing a $100 bet, where the break-even is 50 percent. The pot’s size never makes a draw itself more likely; it only changes the price of chasing it. When the pot grows because opponents keep betting into it, ask whether the growth reflects strength that also dirties your outs, rather than treating every extra dollar as a reason to stay in the hand.
How do I calculate pot odds?
Divide the call by the pot plus the call. A $20 call into an $80 pot gives 20 divided by 100, which is 20 percent. Call when your chance of winning exceeds that break-even percentage.
What is the Rule of 4 and 2?
Multiply outs by 4 on the flop for the chance by the river, and by 2 on the turn for the next card. Nine outs give about 36% by the rule on the flop, against 35.0% exact, and about 18% on the turn, against 19.6% exact.
When does the Rule of 4 and 2 break down?
At large out counts on the flop, where it overshoots: 15 outs give 54.1% exactly, not 60%. The rule is a table shortcut; the exact figure is what the calculator gives.
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How to Calculate Poker Odds
The Rule of 4 and 2, pot odds, and hand odds — with the exact figures.