A poker odds calculator does one narrow piece of arithmetic: it turns a count of helpful cards into a percentage, and it turns a bet size into the percentage that bet is charging. Those two numbers are the whole of pot odds. Everything else at a poker table — reading opponents, position, bet sizing, table image — sits outside arithmetic entirely, and no calculator can touch it.
Arb Digital publishes this as part of a free tools library built mostly around probability, measurement and business maths, and this page belongs in that library because the underlying calculation is a clean combinatorics problem. It counts unseen cards, works out how often a draw completes, and compares that frequency with the ratio a bet implies. It is a description of a probability, not a recommendation about money.
What This Poker Odds Calculator Does
You supply an outs count — the number of unseen cards that turn your hand into a winner — and tell the tool how many cards are still to be dealt. It returns the exact probability that at least one of those outs arrives, calculated from the number of unseen cards rather than from a lookup table. Alongside it you get the familiar rule-of-2-and-4 shortcut so you can see how far the mental estimate drifts from the true figure.
The second half of the page handles the price. Enter the pot size and the amount you are being asked to call, and the tool reports the equity that call is demanding, expressed as a percentage. It also reports the largest call that would leave the two figures level, which is the break-even point where the arithmetic stops favouring either side.
The boundary with the adjacent tools on this site matters, because several of them look similar and answer different questions. The probability calculator handles single-event and conditional probability for any event you can describe, with no card-counting built in. The odds probability converter moves between fractional, decimal and percentage forms of the same number. The implied probability calculator extracts the probability baked into a quoted price. The lottery odds calculator works on combinations drawn from a fixed pool, and the dice probability calculator handles dice rather than cards. This page is the only one that models unseen cards in a deck and pairs the result with a pot price.
How to Use It
- Pick your draw type or count outs yourself. The presets cover the common shapes. If your hand is unusual, switch to custom and count the cards that genuinely improve you.
- Choose how many cards are still to come. Two cards from the flop is only realistic when no further betting is possible; otherwise use one card at a time.
- Enter the pot and the call. The pot figure should include every chip already in the middle, including the bet you are being asked to match.
- Compare the two percentages. The hero figure is how often the draw arrives. The price figure is how often it would need to arrive for the call to break even on chips alone.
- Read the break-even call size. It shows where those two numbers meet, which makes the sensitivity to bet sizing obvious.
The Formula and How It Is Calculated
After the flop you can see five cards: your two hole cards and three community cards. That leaves 47 unseen cards from the deck's 52. The calculator works out the chance of missing entirely and subtracts it from one, because "at least one out" is much easier to compute as the complement of "no outs at all".
With two cards to come and o outs, the probability of missing both is the number of ways to choose two non-outs divided by the number of ways to choose any two cards: C(47 − o, 2) ÷ C(47, 2). Worked example with a nine-out flush draw: C(38, 2) = 703 and C(47, 2) = 1,081, so the miss chance is 703 ÷ 1,081 = 0.6503, and the chance of completing is 34.97%. With one card to come the sum collapses to a single division — nine outs out of 46 unseen cards on the turn is 19.57%.
That complement trick is the standard combinatorial approach to card problems. The University of Hawaii mathematics department's reference on 5-card poker hand probabilities runs the same machinery in the other direction, enumerating all 2,598,960 possible five-card hands to derive how often each hand type appears.
The pot side is simpler. The equity a call requires is the call divided by the final pot after that call: with 100 in the middle and 25 to call, that is 25 ÷ 125 = 20%. The break-even call size inverts the same relationship: for a given equity e and pot P, the call at which the two match is P × e ÷ (1 − e). At 34.97% equity into a pot of 100, that break-even call is 53.8.
Why the Rule of 2 and 4 Drifts
The mental shortcut most players learn is to multiply outs by two for one card to come and by four for two cards. It is a linear approximation of a non-linear function, and it is accurate enough at small out counts and increasingly wrong at large ones. Nine outs with one card to come estimates at 18% against a true 19.6% — close. Fifteen outs with two cards to come estimates at 60% against a true 54.1% — a six-point overshoot.
The reason is double counting. Multiplying by four implicitly adds the turn chance and the river chance together, but the two events overlap: some runouts hit on both streets, and those get counted twice. The overlap grows with the square of the out count, which is why the error is invisible with four outs and substantial with fifteen. A common correction is to subtract the amount by which the out count exceeds eight, so fifteen outs becomes 60 − 7 = 53%, which lands within a point of the exact answer. The calculator shows both figures side by side so the gap is never a surprise.
The rule of four has a second, larger problem that has nothing to do with arithmetic. It answers "how often do I hit by the river", but you rarely get to see the river for free. If there is a bet coming on the turn, the honest question is the one-card figure, and using the two-card figure quietly inflates your estimate by roughly double.
Counting Outs Honestly: Discounted and Dead Outs
Everything on this page depends on the outs number being right, and the number is where most errors live. An out is only an out if the card wins the hand. Four cards that make your straight are not four outs if two of them also put a third suit on the board and complete a flush for someone who is representing exactly that. Experienced players discount those cards — counting them as half an out, or not at all — long before touching a calculator.
Dead outs work the other way. A card you need that is already visible in a face-up hand or an exposed card is not in the deck at all, and the unseen-card denominator changes too. That is what the exposed-cards field handles: it removes cards from the unseen pool, which slightly raises the chance that a remaining out arrives. In normal play you never have that information and the field should stay at zero.
There is also the case of outs that improve you to a hand that is still second best. A pair of overcards has six outs to a pair, but if an opponent already holds a set, none of those six cards wins. The calculator cannot see the opponent's hand and does not try to guess it. It computes what you tell it.
Pot Odds, Implied Odds and What This Tool Does Not Model
The price figure on this page is pure pot odds: the chips in front of you right now against the chips you must put in right now. It ignores every chip that might enter the pot later. In deep-stacked play those future chips can be the larger part of the equation, and players call them implied odds — the extra money you expect to win on later streets when the draw completes, against the extra money you expect to lose when it does not.
Implied odds are an estimate, not a calculation, because they depend on how an opponent will behave on a street that has not happened yet. Nothing on this page attempts to model that, and any tool that claims to is guessing. Similarly, this page computes equity against an unspecified opponent range rather than against a specific hand. Full range-versus-range equity requires enumerating every combination on both sides, which is a different and much heavier calculation than counting outs.
Finally, the whole comparison assumes you will actually see the card you are paying for. If you call a bet on the flop with one card to come and then face another bet on the turn, the price you agreed to was not the price you ended up paying.
Equity Is a Frequency, Not a Forecast
The single most common misreading of a poker odds figure is treating it as a statement about the hand in front of you. It is not. A 35% equity figure means that across a very large number of identically shaped situations, the draw completes roughly 35 times in 100. In the hand you are currently playing, the card is either coming or it is not, and the percentage has no opinion about which.
The mathematics behind that distinction is the same law of large numbers that governs coin flips, and the coin flip probability calculator shows how slowly short samples converge on their expected proportion. Over a hundred trials, outcomes scatter widely around the average. Sequences of results that look like patterns are ordinary variance, and the conditional probability calculator is a good place to see why updating on new information changes a probability while past outcomes do not.
Arb Digital's free tools library covers probability, conversion and forecasting arithmetic across dozens of calculators, and our team is happy to talk through anything the tools cannot answer.
Browse Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using the two-card figure when a bet is coming — it roughly doubles the estimate for a card you have not yet paid to see.
- Counting outs that complete a better hand elsewhere — a card that makes your straight and someone else's flush is not a clean out.
- Leaving the current bet out of the pot figure — the pot you compare against must include the chips being wagered into it.
- Reading equity as a prediction — it describes a long-run frequency across many hands, never the card that is about to be dealt.
- Trusting the rule of 4 at high out counts — it overstates fifteen-out draws by about six percentage points because it double counts overlapping runouts.
Related Free Tools From Arb Digital
Use the probability calculator for general event probability, the odds probability converter to move between odds formats, the implied probability calculator to read the probability inside a quoted price, the lottery odds calculator for draws from a numbered pool, and the dice probability calculator for dice outcomes. Everything else sits in the free online tools hub.
Frequently Asked Questions
Forty-seven. You can see your own two hole cards and the three community cards, which is five of the deck's fifty-two, leaving forty-seven unknown cards from your point of view regardless of how many opponents are still in the hand.
The shortcut is a linear approximation. Multiplying by four adds the turn and river chances together without removing the runouts that hit on both streets, so it overstates the answer, and the overstatement grows as the out count rises.
Yes. Pot odds compare the chips you must add against the size of the pot you would win, and that pot already contains the bet your opponent has just made.
No. It works from an outs count you supply, which describes cards that improve your hand rather than a full comparison of two known hands. Range-versus-range equity requires enumerating every combination on both sides.
An out that improves your hand but may still lose. A card that completes your straight while also putting a third flush card on the board is often counted as half an out or ignored, because it can hand an opponent a stronger hand at the same time.
No. Equity is a long-run frequency across a very large number of similar situations. In any single hand the outcome is determined by the cards, and a hand with high equity still loses a predictable share of the time.
Implied odds are the additional chips you expect to win on later streets if your draw completes. They are an estimate of future behaviour rather than a calculation, and this tool deliberately excludes them.
This page describes a probability calculation only. It is not gambling advice, it does not evaluate whether any wager is worthwhile, and it makes no claim about outcomes. Gambling carries a risk of financial loss and can become harmful; in the United States the National Council on Problem Gambling operates a confidential helpline at 1-800-MY-RESET.
