Any specific pair class
Six concrete combinations represent one named pocket pair among 1,326 starting hands.
Poker Probability Chart
Inspect card, starting-hand, and five-card frequencies with each sample space stated. This poker probability chart is generated from project code: exact tables use combinations, while simulated estimates record the seed and iteration count.
| Five-card category | Exact combinations | Probability |
|---|---|---|
| High card | 1,302,540 | 50.117739% |
| One pair | 1,098,240 | 42.256903% |
| Two pair | 123,552 | 4.753902% |
| Three of a kind | 54,912 | 2.112845% |
| Straight | 10,200 | 0.392465% |
| Flush | 5,108 | 0.196540% |
| Full house | 3,744 | 0.144058% |
| Four of a kind | 624 | 0.024010% |
| Straight flush | 36 | 0.001385% |
| Royal flush | 4 | 0.000154% |
Generated and verified from C(52,5) = 2,598,960. SHA-256 cc37d36dff48894f76ab18e57489c0e10315aed2affef28edcc23dfc3c68d562.
How the result is built
Poker Probabilities Depend on the Sample Space
Concrete unordered card combinations and abstract starting-hand classes answer different counting questions. They must not share a denominator.
- Physical deck52 cards
- Unordered two-card combinationsC(52,2) = 1,326
- Abstract starting-hand classes169
Five-card combinations2,598,960C(52,5)
Two-card combinations1,326physical deals
Starting-hand classes169abstract labels
Different questions use different denominators
There are 1,326 unordered two-card combinations but 169 abstract starting-hand classes. Five-card category frequencies use 2,598,960 distinct five-card subsets.
Classes are not equally frequent
Concrete frequencies differ by cell: pairs represent six physical holdings, above-diagonal suited entries represent four, and below-diagonal offsuit entries represent twelve. Selecting a grid label uniformly would therefore not sample two-card deals uniformly.
Generation is reproducible
Exact frequencies come from the same five-card evaluator tested by the interactive tools. Metadata records the algorithm version and checksum.
Separate hand frequency from winning chance
Five-card combination frequency answers how often a category appears in a uniformly random five-card sample. It does not equal showdown equity, because Texas Hold'em uses seven available cards, visible blockers, opponents, and the best five-card subset. Use exact probability as a deck baseline, then model the actual game state separately.
Worked examples
Suited versus offsuit
A non-pair has four suited and twelve offsuit combinations before blockers.
Frequently asked questions
Why are there 169 starting-hand classes?
The 13 ranks form 13 pairs plus 78 suited and 78 offsuit non-pairs.
Are all grid cells equally likely?
No. Their concrete combination counts differ.
What is the five-card sample space?
There are C(52,5), or 2,598,960, unordered five-card hands.
Were frequencies copied from another chart?
No. The repository contains the generator and validation tests.