What this calculator does
This poker probability calculator answers a specific, fixed question: dealt five cards at random from a standard 52-card deck, what is the chance of getting a particular hand type, such as a flush, full house or two pair? These are not estimates, they are exact combinatorial results, the same figures found in any poker probability table, worked out here from first principles so you can see where each one comes from.
That makes this a different tool from an in-play odds calculator. Poker hand probability, in the sense used here, is about the one-off deal from a full, unseen deck. Once a hand is partway dealt and you know your outs, the relevant question becomes your chance of improving on the cards still to come, which is a different calculation covered separately.
The formula
Every 5-card hand from a 52-card deck is equally likely, and there are C(52,5) = 2,598,960 of them in total. Each hand type has a known number of card combinations that produce it, worked out by counting choices of rank, suit and kicker cards. Probability is that count divided by 2,598,960, and odds against are the remaining hands compared to the winning ones.
| Term | Meaning |
|---|---|
| C(52,5) | The total number of distinct 5-card hands from a 52-card deck: 2,598,960. |
| Combinations | The number of distinct 5-card hands that count as the chosen hand type. |
| Odds against | How many losing hands there are for every winning one, written as a ratio. |
The inputs explained
| Field | What to enter |
|---|---|
| Hand type | The poker hand type to check, from a royal flush down to no pair at all. Each category excludes the rarer hands above it in the standard ranking, so a flush here means a flush that is not also a straight flush. |
When to use it
Settling an argument about hand rarity
People often misjudge how much rarer a full house is than three of a kind, or how much more common one pair is than everything else combined. Running each hand type through gives the exact figures to compare side by side.
Understanding starting-hand odds before any betting
Before any cards are exchanged or community cards revealed, these are the true baseline odds of the five cards you are dealt, independent of any strategy.
Teaching or checking combinatorics
The poker deck is a standard worked example in combinatorics courses precisely because the counting argument for each hand type is instructive but easy to get wrong, particularly the flush and straight counts which must exclude straight flushes.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Probability of each standard poker hand
Every standard hand ranking, run through the same calculator, from rarest to most common.
| Hand type | Probability | Odds against |
|---|---|---|
| Royal flush | 0.000154% | 649,739.0 : 1 |
| Straight flush | 0.001385% | 72,192.3 : 1 |
| Four of a kind | 0.024010% | 4,164.0 : 1 |
| Full house | 0.144058% | 693.2 : 1 |
| Flush | 0.196540% | 507.8 : 1 |
| Straight | 0.392465% | 253.8 : 1 |
| Three of a kind | 2.1128% | 46.3 : 1 |
| Two pair | 4.7539% | 20.0 : 1 |
| One pair | 42.2569% | 1.4 : 1 |
| No pair | 50.1177% | 1.0 : 1 |
Questions
What is the probability of being dealt a flush?
About 0.1965%, or roughly 1 in 509 hands, counting only flushes that are not also straight flushes. There are 5,108 such hands out of 2,598,960 possible 5-card hands.
Is a flush rarer than a full house?
No, it is the other way around: a full house occurs in roughly 1 in 694 hands, while a flush occurs in roughly 1 in 509 hands, making the full house the rarer of the two, which is why it outranks a flush. See the table above for the exact figures for both.
Does this account for cards other players are holding?
No. This is the probability from a full, unseen 52-card deck for a single 5-card deal, which is the standard reference figure. Once cards are visible on the table or in your hand, the relevant question shifts to your specific outs, which the poker odds calculator handles.
Why do the flush and straight counts subtract 40?
Counting flushes by choosing any 5 cards of the same suit, or straights by choosing any run of 5 ranks in any suits, both accidentally include straight flushes and royal flushes. Those 40 hands (36 straight flushes plus 4 royal flushes) are subtracted so flush and straight refer only to hands that are not also a straight flush.
For odds once a hand is partway dealt and outs are known, see the poker odds calculator. To rank a specific 5-card hand you already hold, use the poker hand strength calculator.