5-Card Poker Probability Calculator
Probability Chart
Example Data Table
| Hand Rank | Combinations | Probability | Percentage | Approx Odds Against |
|---|---|---|---|---|
| Royal Flush | 4 | 0.000001539 | 0.000154% | 649,739.00 to 1 |
| Straight Flush | 36 | 0.000013852 | 0.001385% | 72,192.33 to 1 |
| Four of a Kind | 624 | 0.000240096 | 0.024010% | 4,164.00 to 1 |
| Full House | 3,744 | 0.001440576 | 0.144058% | 693.17 to 1 |
| Flush | 5,108 | 0.001965402 | 0.196540% | 507.80 to 1 |
| Straight | 10,200 | 0.003924647 | 0.392465% | 253.80 to 1 |
| Three of a Kind | 54,912 | 0.021128451 | 2.112845% | 46.33 to 1 |
| Two Pair | 123,552 | 0.047539016 | 4.753902% | 20.04 to 1 |
| One Pair | 1,098,240 | 0.422569028 | 42.256903% | 1.37 to 1 |
| High Card | 1,302,540 | 0.501177394 | 50.117739% | 1.00 to 1 |
Formula Used
The total number of five card poker hands is:
C(52,5) = 52! / (5! × 47!) = 2,598,960
The probability of any hand rank is:
Probability = Matching hand combinations / 2,598,960
The percentage chance is:
Percentage = Probability × 100
The odds against the hand are:
Odds Against = (1 / Probability) - 1
The chance of at least one target hand after many deals is:
At least one = 1 - (1 - Probability)^Number of hands
How to Use This Calculator
Select the poker hand rank you want to study. Enter the number of hands dealt. Add a sample size if you want an expected count for a study group. Enter a stake and payout multiplier if you want a basic return estimate. Choose decimal places for cleaner reporting. Press the calculate button. The result appears above the form and below the header section. Use the CSV button for spreadsheet work. Use the PDF button for a simple report.
Understanding 5-Card Poker Probabilities
Why Combinations Matter
Five card poker probability starts with combinations. A standard deck has 52 cards. A hand contains five cards. Order does not matter. So the total number of possible hands is C(52,5). This equals 2,598,960 unique hands. Every hand rank is counted inside this total.
Rare Hands Have Small Counts
A royal flush has only four possible combinations. Each suit has one royal sequence. This makes it the rarest standard five card hand. A straight flush is also rare. Four of a kind is more common, but still unusual. These hands have strong value because their combination counts are very small.
Common Hands Dominate Results
One pair and high card results appear far more often. Their combination counts are large. This is why most random hands are not premium hands. The calculator shows this clearly with percentages, odds, and expected hits.
Using Expected Frequency
Expected frequency helps with planning. For example, if a hand has a probability of 0.001, then 10,000 deals may produce about 10 hits. This is not a guarantee. Random variation can create more or fewer results. Still, expected frequency is useful for simulations, teaching, and game analysis.
Interpreting Odds Against
Odds against show how many misses are expected for each hit. A higher value means a rarer hand. This format is easy to understand for players. It also helps compare different ranks quickly.
Using the Chart
The chart compares hand rank percentages. Large bars represent common hands. Small bars represent rare hands. This visual view helps users see the full probability spread without reading every number.
Practical Use
This tool is useful for statistics lessons, game design, probability checks, and poker study. It uses exact combinatorial counts, not guesses. That makes the output stable and repeatable for standard five card poker.
FAQs
What does this calculator measure?
It measures exact probabilities for standard five card poker hands. It also shows combinations, percentages, odds against, and expected hits for repeated deals.
Does card order matter?
No. Five card poker hand probability uses combinations. The same five cards count as one hand, regardless of the order in which they appear.
What is the total number of hands?
A standard 52-card deck creates 2,598,960 unique five card hands. This value comes from C(52,5).
Why is royal flush so rare?
Only four royal flushes exist in a deck. There is one for each suit, so its probability is extremely small.
What does odds against mean?
Odds against estimate how many losing outcomes occur for each successful target hand. Larger odds mean the hand is less likely.
Are jokers included?
No. This calculator assumes a standard 52-card deck without jokers, wild cards, or replacement cards.
Can this predict real game results?
It gives mathematical expectations. Real deals can vary because random outcomes do not always match expected averages over small samples.
Why add expected hits?
Expected hits help estimate how often a selected hand may appear across many deals, simulations, lessons, or probability experiments.