iGaming Journalist & Crypto Casino Analyst
Almost every poker probability quoted online traces back to the same handful of numbers, and most articles repeat them without showing the arithmetic. This reference does the opposite. Every figure below was computed from scratch by exhaustive enumeration — all 2,598,960 five-card hands, all 133,784,560 seven-card hands, and every one of the 1,712,304 possible boards for each heads-up matchup listed. Nothing here is simulated, rounded from memory or copied from another site. The numbers are exact, and the method is described in full at the bottom so you can reproduce them.
Key Findings
A royal flush appears once in 649,740 five-card deals but once in 30,940 seven-card Hold'em hands — 21 times more often. Pocket aces arrive once in 221 hands, and at a nine-handed table someone holds them once every 24.6 deals. Aces beat kings 82.6% of the time. A flopped flush draw completes by the river 35.0% of the time, or 1.86 to 1 against.
Five-Card Hand Frequencies
The foundation of every poker probability is the 52-card deck's 2,598,960 distinct five-card combinations. The table below gives the exact count and probability of each hand category, with categories defined so that they do not overlap: a flush count excludes straight flushes, and a straight count excludes straight flushes.
| Hand | Combinations | Probability | Odds against |
|---|---|---|---|
| Royal flush | 4 | 0.000154% | 1 in 649,740 |
| Straight flush (non-royal) | 36 | 0.001385% | 1 in 72,193 |
| Four of a kind | 624 | 0.024010% | 1 in 4,165 |
| Full house | 3,744 | 0.144058% | 1 in 694 |
| Flush | 5,108 | 0.196540% | 1 in 509 |
| Straight | 10,200 | 0.392465% | 1 in 255 |
| Three of a kind | 54,912 | 2.112845% | 1 in 47.3 |
| Two pair | 123,552 | 4.753902% | 1 in 21.0 |
| One pair | 1,098,240 | 42.256903% | 1 in 2.37 |
| High card | 1,302,540 | 50.117739% | 1 in 2.00 |
These are the numbers that determine poker hand rankings. The ordering is not arbitrary — each hand outranks the one below it precisely because it is rarer. Note that in five-card poker, half of all hands are nothing at all, and 92% are a pair or worse.
Seven-Card Hand Frequencies
Texas Hold'em and Seven Card Stud do not deal five cards. They give you seven and let you make the best five, which changes everything. The 133,784,560 seven-card combinations produce a dramatically different distribution, and this is the table most players actually need.
| Best five-card hand | Combinations | Probability | Odds against |
|---|---|---|---|
| Royal flush | 4,324 | 0.0032% | 1 in 30,940 |
| Straight flush (non-royal) | 37,260 | 0.0279% | 1 in 3,591 |
| Four of a kind | 224,848 | 0.1681% | 1 in 595 |
| Full house | 3,473,184 | 2.5961% | 1 in 38.5 |
| Flush | 4,047,644 | 3.0255% | 1 in 33.1 |
| Straight | 6,180,020 | 4.6194% | 1 in 21.6 |
| Three of a kind | 6,461,620 | 4.8299% | 1 in 20.7 |
| Two pair | 31,433,400 | 23.4955% | 1 in 4.26 |
| One pair | 58,627,800 | 43.8225% | 1 in 2.28 |
| High card | 23,294,460 | 17.4119% | 1 in 5.74 |
Three comparisons are worth drawing out. First, a royal flush is 21 times more likely across seven cards than five. Second, two pair jumps from 4.75% to 23.50%, making it by far the biggest structural difference between the two formats. Third, high card collapses from 50.1% to 17.4% — with seven cards, making nothing at all is uncommon.
This is why hand values compress in Hold'em. If almost a quarter of seven-card holdings reach two pair by the river, then two pair is a much weaker relative holding at showdown than a five-card frequency table would suggest. Understanding that gap is a prerequisite for the range-based thinking covered in our poker strategy section.
Starting Hand Probabilities
There are 1,326 distinct two-card starting hands in Hold'em. The table below gives exact frequencies for the categories that come up most in discussion and analysis.
| Starting hand category | Probability | Frequency |
|---|---|---|
| A specific pocket pair (e.g. aces) | 0.4525% | 1 in 221 |
| Aces, kings or queens | 1.3575% | 1 in 73.7 |
| Any pocket pair | 5.8824% | 1 in 17.0 |
| Ace-king suited | 0.3017% | 1 in 331.5 |
| Ace-king (any) | 1.2066% | 1 in 82.9 |
| Premium (JJ+ or AK) | 3.0166% | 1 in 33.1 |
| Any two Broadway cards (T or better) | 14.3288% | 1 in 7.0 |
| Any ace | 14.9321% | 1 in 6.7 |
| Any suited hand | 23.5294% | 1 in 4.25 |
The 1-in-221 figure for aces is the most repeated number in poker, and it is worth extending to the table level. At a nine-handed table, the probability that at least one player holds pocket aces on any given deal is 4.06%, or once every 24.6 hands. The probability that one player holds aces and another simultaneously holds kings is 0.159%, or roughly once in every 631 deals — a useful benchmark for players who suspect their site is dealing "action flops".
The premium category matters for anyone thinking about opening ranges. Only 3.02% of hands are JJ or better or ace-king. Any strategy that requires a premium holding to continue will be folding well over 90% of the time, which is why the beginner ranges in our introduction to poker extend considerably wider than the top 3%.
Flop Probabilities
Once you hold two cards, 50 remain, producing 19,600 possible flops. These are the numbers that determine whether a speculative hand is worth playing.
| Flop event | Probability | Odds against |
|---|---|---|
| Pocket pair flops a set or better | 11.755% | 1 in 8.5 |
| Pocket pair flops exactly a set | 11.510% | 1 in 8.7 |
| Pocket pair flops a full house | 0.735% | 1 in 136 |
| Pocket pair flops quads | 0.245% | 1 in 408 |
| Unpaired hand flops a pair or better | 32.429% | 1 in 3.08 |
| Unpaired hand flops trips or better | 1.357% | 1 in 73.7 |
| Suited hand flops a flush draw | 10.944% | 1 in 9.1 |
| Suited hand flops a made flush | 0.842% | 1 in 118.8 |
| Suited hand flops a backdoor flush draw | 41.587% | 1 in 2.4 |
| Flop comes all one suit | 5.177% | 1 in 19.3 |
| Flop is paired | 16.941% | 1 in 5.9 |
The set-mining figure of 11.76% is the basis of the widely cited rule that you need roughly 10 to 15 times the call amount in implied odds to profitably call a raise with a small pocket pair. The exact odds are 7.5 to 1 against flopping a set, and since you will not win every time you do flop one, the practical requirement is higher.
The suited-hand numbers deserve attention because they are routinely overestimated. A suited hand flops a made flush only once in 119 attempts, and a flush draw once in 9.1. Suitedness adds roughly 2 to 3 percentage points of equity against a typical range — real, but nowhere near enough to justify playing a hand you would otherwise fold. The 41.6% backdoor figure is the more valuable one, because backdoor equity is what makes many continuation bets profitable.
Outs to Equity: The Complete Conversion Table
The most practical table in this article converts a count of outs into an exact probability of improving. All figures assume no cards are dead beyond your two hole cards and the three flop cards, leaving 47 unseen.
| Outs | Hit on turn | Hit by river | Odds against by river | Typical draw |
|---|---|---|---|---|
| 2 | 4.3% | 8.4% | 10.9 : 1 | Pocket pair to a set |
| 3 | 6.4% | 12.5% | 7.0 : 1 | One overcard |
| 4 | 8.5% | 16.5% | 5.1 : 1 | Inside straight draw |
| 5 | 10.6% | 20.4% | 3.9 : 1 | Pair to two pair or trips |
| 6 | 12.8% | 24.1% | 3.1 : 1 | Two overcards |
| 7 | 14.9% | 27.8% | 2.6 : 1 | Set to full house or quads |
| 8 | 17.0% | 31.5% | 2.2 : 1 | Open-ended straight draw |
| 9 | 19.1% | 35.0% | 1.9 : 1 | Flush draw |
| 10 | 21.3% | 38.4% | 1.6 : 1 | Inside straight plus overcard |
| 12 | 25.5% | 45.0% | 1.2 : 1 | Flush draw plus inside straight |
| 15 | 31.9% | 54.1% | 0.85 : 1 | Flush draw plus open-ended straight |
These figures show exactly where the popular "rule of four and two" goes wrong. Multiplying outs by four to estimate river equity works well at low out counts: eight outs gives an estimate of 32% against a true 31.5%. At fifteen outs the shortcut estimates 60% against a true 54.1%, an error of nearly six percentage points. The shortcut overstates because it double-counts boards where you hit on both streets.
The multi-street figures only apply when you are certain to see both cards, which in practice means an all-in situation. Facing a bet on the flop with more betting to come, the single-street number is the honest one. To check specific holdings against ranges rather than raw out counts, use our poker equity calculator.
All-In Matchup Equities
The following equities were computed by enumerating all 1,712,304 five-card boards for each matchup. Split pots are counted as half a win for each side, which is the standard convention.
| Matchup | Favourite equity | Underdog equity | Split |
|---|---|---|---|
| AA vs KK | 82.64% | 17.36% | 0.54% |
| AA vs KQ suited | 82.32% | 17.68% | 0.38% |
| AA vs AK suited | 87.86% | 12.14% | 1.26% |
| AA vs 72 offsuit | 88.19% | 11.81% | 0.40% |
| QQ vs AK offsuit | 56.76% | 43.24% | 0.42% |
| QQ vs AK suited | 53.79% | 46.21% | 0.39% |
| 88 vs AK offsuit | 55.16% | 44.84% | 0.38% |
| AK offsuit vs JT suited | 58.82% | 41.18% | 0.42% |
| AK offsuit vs QJ offsuit | 64.84% | 35.16% | 0.47% |
Several results here contradict common assumptions. Aces are a bigger favourite over 72 offsuit (88.19%) than over ace-king suited (87.86%) — but the margin is small, because holding an ace blocks the opponent's outs so severely. Aces against kings, at 82.64%, is a smaller edge than most players expect for the best possible preflop confrontation.
The pair-versus-two-overcards matchups are near coinflips by design. Queens beat ace-king offsuit only 56.76% of the time, and suitedness alone swings that matchup by almost three percentage points, to 53.79%. Eights against ace-king, at 55.16%, is barely worse for the pair than queens are — the pair's advantage comes from being made, not from being high.
The final row shows why dominated hands are so costly. Ace-king against queen-jack offsuit is a 64.84% favourite, a far larger edge than any pair-versus-overcards spot, because the underdog's best cards are outranked rather than merely behind. Terminology used throughout this section is defined in our poker glossary.
Scale Check: What These Numbers Mean in Practice
Probability tables can feel abstract until they meet real field sizes. The 2026 WSOP Main Event drew 9,208 entrants and built an $85,634,400 prize pool, with 1,382 players cashing. At 9,208 entrants each playing hundreds of hands, the rare events in these tables stop being rare in aggregate. A 1-in-30,940 royal flush becomes an expected daily occurrence in a field that size.
This is the practical value of exact probabilities: they tell you not just what is likely in one hand, but what to expect across a population of hands. A player logging 50,000 hands a year should expect roughly 1.6 royal flushes, about 226 sets from pocket pairs held to the flop, and around 2,026 hands where at least one opponent at a full table was dealt aces.
Methodology
Every probability in this article was computed by exhaustive enumeration rather than simulation, so all figures are exact rather than estimated.
The five-card frequency table was produced by classifying all 2,598,960 combinations of five cards from a standard 52-card deck. The seven-card table was produced by classifying all 133,784,560 seven-card combinations, taking the best available five-card hand from each, using a bitmask-based evaluator written in C for speed. Category definitions are mutually exclusive: royal flushes are excluded from the straight flush count, straight flushes from the flush and straight counts, and so on.
Starting hand and flop probabilities were computed combinatorially from binomial coefficients on the reduced deck remaining after each stage. Table-level figures for pocket aces were computed by inclusion-exclusion over the possible placements of the four aces among the dealt hands.
All-in equities were computed by enumerating every one of the 1,712,304 possible five-card boards for each two-hand matchup using a full seven-card evaluator with complete kicker resolution, then scoring wins, losses and ties. Split pots are credited as half a win to each player. Outs-to-equity figures assume 47 unseen cards after the flop and no dead cards beyond the five known to the player. The seven-card frequency counts reproduce the values published in the combinatorics literature exactly, which serves as an independent verification of the evaluator.
Frequently Asked Questions
What are the odds of a royal flush in Texas Hold'em?
1 in 30,940 across all seven cards, or 0.0032%. This is very different from the 1 in 649,740 figure usually quoted, which applies to a five-card deal. Because Hold'em lets you make your best five from seven, royals occur roughly 21 times more often than the five-card figure suggests.
How often will I be dealt pocket aces?
Once in every 221 hands, or 0.4525% of the time. At a nine-handed table, someone at the table holds aces once every 24.6 hands, and an aces-versus-kings confrontation occurs roughly once in 631 deals.
What are the odds of flopping a set with a pocket pair?
11.755% to flop a set or better, which is 7.5 to 1 against. Flopping exactly a set is 11.510%, a full house 0.735% and quads 0.245%. This is the calculation behind the standard implied odds guidance for set mining.
Is the rule of four and two accurate?
It is accurate at low out counts and increasingly wrong at high ones. With eight outs it estimates 32% against a true 31.5%. With fifteen outs it estimates 60% against a true 54.1%. It also only applies when both remaining cards are guaranteed, which usually means an all-in.
How much of a favourite is AA against KK?
82.64%, with 0.54% of boards splitting the pot. That is a smaller edge than most players assume for the best possible preflop matchup, and it means the underdog wins roughly one time in six.
Sources
- arXiv — Big Two and n-card poker probabilities (combinatorial reference)
- PokerNews — 2026 WSOP Main Event field size and prize pool
- WSOP.com — 2026 Main Event updates and payout data
All probability figures are original calculations by DeucesCracked, produced with the enumeration method described in the Methodology section. The external sources above are cited for the real-world field size data used in the scale-check section and as an independent cross-check on the seven-card frequency counts.
Cite This Article
If you use data from this article, please link back to https://www.deucescracked.com/blog/poker-probability-reference-odds-data — the figures may be reproduced with attribution. More reference tables and training material are available at DeucesCracked.
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