Poker Hand Rankings and the Math Behind Five-Card Odds

Every poker player learns that a flush beats a straight and that a full house beats both. The ranking is not arbitrary: it follows how often each hand shows up. The rarer a hand is, the higher it ranks. This article walks through the ten categories and the counting behind them. It is meant for readers 18 and older and is educational only.

How many five-card hands exist?

A standard deck has 52 cards, and the number of different five-card hands is 52 choose 5, which equals 2,598,960. Each of those hands is equally likely when the deck is shuffled fairly, so the probability of any category is its number of hands divided by 2,598,960.

The rankings from rarest to most common

Here are the categories, with the number of combinations and the approximate probability:

1. Royal flush: 4 hands, about 0.00015%. It is the ace-high straight flush in one suit.
2. Straight flush (excluding royal): 36 hands, about 0.0014%.
3. Four of a kind: 624 hands, about 0.024%.
4. Full house: 3,744 hands, about 0.14%.
5. Flush (not a straight flush): 5,108 hands, about 0.20%.
6. Straight (not a straight flush): 10,200 hands, about 0.39%.
7. Three of a kind: 54,912 hands, about 2.11%.
8. Two pair: 123,552 hands, about 4.75%.
9. One pair: 1,098,240 hands, about 42.26%.
10. High card: 1,302,540 hands, about 50.12%.

Add them up and you get 2,598,960, which confirms the list is complete. Roughly nine out of ten five-card hands are a pair or nothing at all.

Counting one category: the full house

A full house has three cards of one rank and two of another. To count them:

1. Choose the rank for the three of a kind: 13 options.
2. Choose which three of its four suits: 4 options.
3. Choose a different rank for the pair: 12 options.
4. Choose which two of its four suits: 6 options.

Multiply: 13 × 4 × 12 × 6 = 3,744. That is a small slice of 2.6 million hands, which is why a full house beats a flush.

Why a flush outranks a straight

In five-card poker a flush (5,108 hands) is rarer than a straight (10,200 hands), so the flush ranks higher. This logic can change in variants that use different decks or wild cards, because the counts change. When a game departs from the standard 52-card deck, the traditional ranking may not follow the probabilities, and the rules of that game will say which order applies.

Five cards versus Texas Hold'em

The table above applies to a five-card hand dealt from a full deck. In Texas Hold'em, you make your best five-card hand from seven cards (two hole cards plus five community cards), so the odds of each category are different and better hands appear more often. Learning the five-card odds is still a helpful foundation, because the ranking order is the same.

What the odds do and do not tell you

Knowing the odds helps you judge how impressive a hand is and how likely an opponent is to hold something strong. It does not tell you what the next card will be, and it does not remove the luck of the deal. In games played against the house, the payouts are set so that the casino keeps an edge, a point we covered when explaining how to read American odds and what a price means. For the same reason, anyone who promises a sure way to win at cards deserves your skepticism.

A quick study tip

If you want to remember the order, think about how many ways each hand can be built. A hand with fewer ways to form is stronger. You can test yourself by counting a different category, such as a flush: choose a suit (4 options), choose 5 of its 13 ranks (1,287 options), then subtract the 10 straight flushes in that suit, giving 4 × (1,287 − 10) = 5,108.

Frequently asked questions

Do suits have a rank in standard poker? Not in most games. Two hands that differ only by suit usually tie, though some variants use suits to break ties.

What are the odds of being dealt a pair in the first two cards of Hold'em? The chance of a pocket pair is 3 in 51, or about 5.9%, because after your first card, three of the 51 remaining cards match its rank.

Does knowing probabilities make me a winning player? It is a helpful start, but poker also involves opponents, position and decisions under uncertainty. Play for enjoyment, set limits and never rely on it as income.