This guide gives both complete distributions, explains how to reproduce the smaller one, and shows why neither column directly tells you whether your hand will win against a particular opponent. Figures use one ordinary 52-card deck, no jokers or wild cards, uniformly distributed unordered sets, and mutually exclusive highest-hand categories. Wizard of Odds publishes the source counts for both sample spaces; the five-card distribution is also consistent with Pagat's single-deck table.
Name the Experiment Before Quoting a Percentage
There are at least three questions that readers call “poker hand odds.” One is the frequency of a category among five dealt cards, as with five cards dealt before a draw. A second is the frequency of the best five out of seven uniformly random cards. A third is the chance that a particular two-card Hold'em starting hand improves or wins after a known board and opponents' ranges. The first two are unconditional distributions. The third is a conditional problem with known cards, removed cards and an opponent model. Our How to Play Poker guide explains the game sequence; you cannot copy a row from the unconditional table into a decision in that sequence.
For the seven-card column, Hold'em reaches seven available cards by combining two hole cards and five board cards, but a player's two known hole cards and the shared board change the conditional sample space. A random seven-card set has the same unconditional category distribution as the seven-card table; a specific player at a specific flop does not.
Exact Category Counts: Five Dealt Cards and Best Five of Seven
The rows below are exclusive: a royal flush is not counted again in “straight flush,” and a straight flush is not counted again in “flush” or “straight.” “One pair” excludes two pair and stronger categories. We calculate percentages as count / denominator × 100 and round only for display. The printed percentages may not sum to exactly 100% because of rounding; the integer counts must sum exactly.
| Highest category | Five-card count | Five-card probability | Seven-card count | Seven-card probability |
|---|---|---|---|---|
| Royal flush | 4 | 0.000154% | 4,324 | 0.003232% |
| Straight flush, non-royal | 36 | 0.001385% | 37,260 | 0.027851% |
| Four of a kind | 624 | 0.024010% | 224,848 | 0.168067% |
| Full house | 3,744 | 0.144058% | 3,473,184 | 2.596102% |
| Flush, not straight flush | 5,108 | 0.196540% | 4,047,644 | 3.025494% |
| Straight, not straight flush | 10,200 | 0.392465% | 6,180,020 | 4.619382% |
| Three of a kind | 54,912 | 2.112845% | 6,461,620 | 4.829870% |
| Two pair | 123,552 | 4.753902% | 31,433,400 | 23.495536% |
| One pair | 1,098,240 | 42.256903% | 58,627,800 | 43.822546% |
| High card | 1,302,540 | 50.117739% | 23,294,460 | 17.411920% |
| Integer total | 2,598,960 | 100% before display rounding | 133,784,560 | 100% before display rounding |
The five-card royal and non-royal straight-flush rows together make the 40 straight flushes in Pagat's traditional table. The seven-card royal and non-royal rows likewise add to 41,584 straight-flush-category outcomes. A table that merges these rows is not wrong if it says so; a table that compares its merged row to our non-royal row without adjustment is.
Reproduce the Five-Card Denominator and Selected Counts
Order does not distinguish a final poker hand: A♠ K♠ Q♠ J♠ 10♠ is the same five-card set no matter which card came first. That is why the denominator is a combination, not a permutation:
C(52,5) = 52! / (5! × 47!) = 2,598,960.
There are four suits and one ace-high straight flush per suit, so the royal flush count is 4. There are ten possible five-rank straight sequences per suit when the ace-low wheel is included. That gives 10 × 4 = 40 straight flushes in all, of which four are royal, leaving 36 non-royal.
For an exact one-pair hand, choose the pair's rank in 13 ways, choose two of its four suits in C(4,2) = 6 ways, choose three different other ranks in C(12,3) = 220 ways, and choose one of four suits for each of those singletons. The result is 13 × 6 × 220 × 4³ = 1,098,240. The condition that the remaining three ranks differ prevents accidentally counting two pair, trips or a full house. Their suits need no special flush exclusion because a pair uses two suits.
For a flush category, choose a suit and any five of its 13 cards, then remove that suit's ten straight flushes: 4 × (C(13,5) − 10) = 4 × (1,287 − 10) = 5,108. A five-card straight-flush hand would otherwise be counted as a flush as well. Wizard of Odds' poker-math derivations give further category construction, while the full probability table provides the count checksum.
To audit the full table, number the 52 cards, enumerate each five- or seven-card set once in increasing card order, and assign it to its strongest category. Check same-suit rank sequences before ordinary flushes and straights, count rank groups for quads, full houses and pairs, and treat A-2-3-4-5 as a five-high straight. Increment only one row per set, then verify that all ten integer rows sum to C(52,5) or C(52,7). This procedure checks the seven-card best hand, not 21 independent five-card hands.
Why Seven Cards Are Not Seven Times the Five-Card Odds
Seven available cards contain C(7,5) = 21 five-card subsets, but those subsets overlap heavily. The same seven-card set may contain several pairs, a flush and a straight, while its highest category is recorded once. Multiplying a five-card probability by 21 would count overlapping outcomes repeatedly and could exceed one. Instead, classify each of the 133,784,560 seven-card sets by its best five. The seven-card count column above follows Wizard of Odds' published seven-card distribution; its integer rows add to the stated denominator.
This also explains the large change in high card. A random five-card set has no pair or better in 1,302,540 cases, about 50.12%. Among random seven-card sets, 23,294,460 have no pair or better as their best hand, about 17.41%. The values describe category frequency, not the chance that an ace-high hand beats a live opponent.
A Known Hand Creates a New Sample Space
Suppose you hold A♠ K♠ and the flop is Q♠ 7♠ 2♦. Five cards are known, leaving 47 unseen cards before the turn. There are nine remaining spades, so the chance that the turn card is a spade is 9 / 47 ≈ 19.15%. The chance that at least one of the next two cards is a spade is 1 − (38/47 × 37/46) ≈ 34.97% if two distinct cards are dealt uniformly without replacement and no other cards become known. A spade completes your flush here, but it does not guarantee the pot: some runouts let an opponent make a full house or straight flush. You can also win on a runout with no spade.
The arithmetic changes if the known cards or event change. If you specify an opponent's hand, those cards leave the unseen deck too. If you want the probability of winning, you must define opponents' holdings or ranges, possible future boards, ties and whether you are comparing raw showdown equity or an in-game decision with betting. A draw-completion percentage is not interchangeable with realized equity or the price of a call.
In an actual hand, write down the board, action and assumptions before calculating. The hand-review guide provides that record; it does not turn this unconditional frequency table into a win estimate.
| Question | Correct denominator in this example | What is counted |
|---|---|---|
| Next card is a spade | 47 | Nine remaining spades on the turn. |
| At least one spade across turn and river | C(47,2) unordered runouts, or sequential 47 × 46 | Complement of drawing two of 38 non-spades. |
| Best category from seven random cards before any cards are known | C(52,7) | Highest five-card category across all seven-card sets. |
| Win versus a specified opponent | Depends on removed cards and range weights | Showdown outcomes including ties. |
Common Errors When Reading a Probability Chart
Confusing frequency with strength. A rare hand category ranks highly in standard high poker, but a category's unconditional frequency does not say how much it wins against a specific range. The poker hand rankings guide answers the category-order question; this table answers how often categories occur under two specified deals.
Calling a five-card deal a Hold'em river result. The five-card column samples five random cards. A Hold'em river gives a player seven available cards. A known hole-card pair narrows the possibilities further.
Combining overlapping categories. A straight flush is also a flush in ordinary language, but the table assigns each set to its highest category only. Check whether another chart combines royal and other straight flushes.
Confusing outs with equity. Nine remaining spades are an event count. They do not account for an opponent's hand, redraws or a shared board that helps both players.
Comparing rounded totals. Rounded display percentages can miss exactly 100% by a few units in the last decimal place. Compare integer counts to the combinatorial denominator first.
Quick Answers
What is the probability of a royal flush in five dealt cards? Exactly 4 / 2,598,960, about 0.000154%, or one five-card set in 649,740. That assumes a uniformly random set from one standard deck and no draws or wild cards.
Is a royal flush equally rare among seven available cards? No. Exactly 4,324 of 133,784,560 seven-card sets contain a royal flush, about 0.003232%. Do not apply either number to a board and hole cards already seen.
Does 34.97% to hit a spade by the river mean a 34.97% chance to win? No. It means at least one spade appears across two future cards under the stated known-card model. Winning depends on the opponent and the final board.
Sources and Calculation Boundary
The five- and seven-card category counts are from Wizard of Odds' Poker Probabilities and cross-checked at the five-card category level against Pagat's public-domain single-deck table. The five-card royal, straight-flush, pair and flush formulas and the conditional spade example are recalculated above. An exhaustive enumeration of all 2,598,960 five-card and 133,784,560 seven-card sets reproduces every one of the ten category counts. No claim here is a measured win rate or an operator-specific strategy recommendation.
About the Editorial Team
The Poker-Eye Editorial Team researches, checks, and maintains product and educational content. Sources and product boundaries are reviewed before publication.