Poker Odds Calculator
Every draw is a fraction: the cards that save you (your outs) over the cards that don’t. Enter your outs and how many cards are still to come, and this calculator returns your exact chance of completing the draw — computed combinatorially, with the famous rule of 4 and 2 shown beside the exact figure it approximates.
Outs: Counting the Cards That Love You
After the flop, you know five cards (your two, the board's three) — leaving 47 unknown, of which some number complete your hand. Those are your outs, and the whole of drawing mathematics is their fraction of the deck. The canonical counts are worth memorising because the calculator's defaults come from them: a flush draw has 9 outs (thirteen of the suit minus the four you can see), an open-ended straight draw has 8 (four cards at each end), a gutshot has 4, and two overcards have about 6 (discounted by the chance they still lose — the craft of "dirty outs"). The exact probabilities then follow from combinatorics, not folklore: with one card to come, your chance is outs ÷ 47; with two, the completion probability is one minus the chance of missing twice, 1 − (47−o)(46−o) ÷ (47×46) — the formula the widget evaluates, exact to the second decimal.
Worked Example: The Flush Draw at the Flop
The defaults run poker's most-studied position: 9 outs, two cards to come. Exact: 1 − (38 × 37) ÷ (47 × 46) = 1 − 1,406 ÷ 2,162 = 1 − 0.6503 = 34.97% — the flush arrives about one time in three, at odds against of about 1.86 to 1. The rule of 4 (outs × 4) estimates 36%, close enough for table talk; switch to one card to come and the exact figure is 9 ÷ 47 = 19.15% against the rule of 2's estimate of 18%. The percentages then meet the pot: facing a bet that asks you to call less than about 35% of the eventual pot, the draw is mathematically self-funding; ask more and you are paying for the privilege of hoping. That comparison — your exact completion percentage against the price the pot is charging — is the entire legitimate content of "pot odds," and this page computes the half of it that lives in the deck.
The Rule of 4 and 2: A Shortcut and Its Error Bars
The famous shortcut (multiply outs by 4 with two cards to come, by 2 with one) survives because its errors are small across the draws that matter most: it overestimates slightly at high out counts (a 15-out monster draw is exactly 54.12%, not the rule's 60% — the calculator's note flags the drift when it grows) and underestimates a hair at low ones. Its genuine virtue is tempo: poker decisions arrive in seconds, and a rule that prices a draw within a point or two at conversational speed beats an exact figure computed after the clock is called. This page's position is the professional one: learn the rule for the table, learn the exact figures for the study — and let this calculator be the study, so that the shortcut you use under pressure is one whose errors you have already met in daylight.
The Turn Card Halves the World
There is a melancholy arithmetic at the centre of draw poker: the flop's generous two-card promise (34.97% for the flush) collapses, on any blank turn, to the single-card truth (19.15%) — and the price of continuing usually does not halve with the probability. This asymmetry disciplines the game's economics: draws are bought most cheaply at the flop, where the two-for-one probability lives, and most dearly at the turn, where players who fell in love with the flop's figure keep paying it. The calculator's two modes exist to make the cliff visible before the chips do; toggle them on the same out count and the 16-point drop is the entire sermon. Professionals internalise the cliff so thoroughly that their flop aggression is partly an arbitrage — buying two cards at prices set by opponents still thinking in one-card terms.
Combination Draws and the Fifteen-Out Ceiling
The draw hierarchy tops out at the combination monster: a flush draw married to an open-ended straight draw shares the two flush-straight cards, for 9 + 8 − 2 = 15 outs — exactly 54.12% over two cards, a mathematical favourite against most made hands, and the calculator note's drift warning made flesh (the rule of 4 says 60%, six points of pure optimism). Add a pair's improvement outs and the count can reach the low twenties, where the "draw" is favoured over everything but sets — the inversion that makes aggressive semi-bluffing with such hands correct rather than cute. The ceiling matters because it bounds the shortcut's error: below about 12 outs the rule of 4 is a rounding error's width from the truth, above it a systematic flattery. The calculator prices the whole ladder exactly, so the shortcut may be used in the region where it deserves trust, and distrusted, with numbers in hand, in the region where it flatters.
Related Tools
More from the Other Calculators hub: the Dice Average Calculator for the other game's distributions, and the Implied Probability Calculator — pot odds are implied probability in a cowboy hat.
Frequently Asked Questions
How do I count outs correctly?
Count every unseen card that makes your hand the likely winner, then discount: outs that complete your draw but improve an opponent more (making a flush on a paired board that may already be a full house) are dirty, and the craft is counting them at a fraction or excluding them. Start from the clean table — flush 9, open-ender 8, two pair to a full house 4, gutshot 4, one overcard 3 — then adjust for the specific board with the suspicion the game teaches. The calculator prices whatever out count you settle on; the settling is the skill, and it is deliberately left where it belongs, with the player.
What are pot odds, exactly?
The ratio the pot offers on your call: if there is 100 in the pot and the bet is 25 to call, you are being offered 4 to 1 on your money, and your draw needs to win more than 20% of the time (25 of the eventual 125) to break even. Compare that breakeven percentage with this calculator's exact figure: call when your chance exceeds the price, fold when it falls short — the entire arithmetic of correct drawing, over which implied odds (the future bets your made hand will win) and reverse implied odds (the future bets your second-best hand will lose) then drape their complications. Cards first, economics immediately after.
Should I count outs I might share with an opponent?
Shared outs are still outs for your completion probability — the deck does not care whose hand a card also helps — but they darken the result when they complete you both and theirs is bigger, which is the domination problem the discounting FAQ describes. The starkest case is drawing to the low end of a straight (the "idiot end"), where your completing card simultaneously makes a higher straight possible for anyone holding one more card. Price the draw with this calculator, then apply the table's context as a discount — the number is the ceiling of your true equity, never the floor.
Why does the two-card figure fall short of doubling the one-card figure?
Because the second card's chance applies only to the worlds where the first card missed: 19.15% on the turn, plus 19.57%-ish of the remaining 80.85% on the river, totalling 34.97% rather than 38.3%. The widget's formula (one minus the product of the miss fractions) is the general shape of "at least once in k tries" probability — the same shape as at-least-one-six in several dice rolls — and meeting it here, where money rides on the answer, is the fastest way to make the shape permanent in a player's intuition.
What about odds before the flop?
Pre-flop equities (pocket aces versus a random hand, about 85%; ace-king versus a pair, a near coin flip shaded by suits) come from enumerating or simulating the full five-card runout between two known hands — a different computation from the draw arithmetic here, which assumes the four-stage information state of a player looking at a flop. Dedicated equity calculators run those millions of runouts; this page owns the flop-and-after territory where outs are countable by hand, and its exactness there is the point: different information, different machinery, no overlap of pretending.
How do implied odds change the call?
Implied odds add the bets you expect to win on later streets when the draw lands: a flush draw that fails the immediate pot-odds test can still be a correct call against an opponent who will pay off large bets when the third flush card falls — you are buying not just the pot but a licence to extract. The discipline is that implied odds are a forecast, easily inflated by hope; the calculator's exact percentage is the anchor that keeps the forecast honest, and the professional sequence is to compute the card odds first (here), the price second (at the table), and only then argue — cautiously, in writing if necessary — about the future.