How Many Poker Hands Are in a 52-Card Deck?

There are exactly 2,598,960 possible five-card poker hands in a standard 52-card deck. That figure is the number of ways to pick 5 cards from 52 when the order you receive them in doesn’t matter — and every probability in poker is built on top of it. Understanding where the number comes from makes the hand rankings click into place.

The math: 52 choose 5

The total is the combination “52 choose 5,” written C(52,5):

C(52,5) = (52 x 51 x 50 x 49 x 48) / (5 x 4 x 3 x 2 x 1)
        = 311,875,200 / 120
        = 2,598,960

The top multiplies the 5 cards you draw from a shrinking deck; dividing by 5 factorial (120) removes the duplicate orderings. The result — 2,598,960 — is the denominator of every five-card poker probability.

How many of each hand type exist

Those 2.6 million hands split cleanly across the ten ranking categories. Each count is fixed by the structure of the hand:

Add those ten counts together and you get exactly 2,598,960. The rarer a hand, the higher it ranks — royal flushes number just 4, while high-card hands number over 1.3 million. That inverse relationship is the whole logic behind what beats what in poker.

Two-card starting hands: 1,326 and 169

Before the flop in Hold’em you hold two cards, so a different count applies. The number of two-card combinations is C(52,2):

C(52,2) = (52 x 51) / 2 = 1,326 combinations

Strategically, though, players group these into 169 distinct starting hands, because suits are interchangeable preflop. The 169 breaks down as:

• 13 pocket pairs (like AA, KK) — 6 combos each = 78 combos
• 78 suited hands (like A♠K♠) — 4 combos each = 312 combos
• 78 offsuit hands (like A♠K♦) — 12 combos each = 936 combos

That’s 13 + 78 + 78 = 169 hand types and 78 + 312 + 936 = 1,326 combinations — the two ways of counting the same starting hands.

Why this matters

Every odds figure you’ll ever use — the 0.144% chance of a full house, the 1-in-649,740 shot at a royal flush — is a specific hand count divided by 2,598,960. Knowing the denominator lets you sanity-check any probability you read. For the full breakdown of percentages, see the poker hand probability chart.

Combinations versus permutations

The reason we land on 2,598,960 rather than a much larger number is that poker uses combinations, not permutations. If order did matter, the count would be 52 x 51 x 50 x 49 x 48 = 311,875,200 ordered five-card sequences. But A♠ K♠ Q♠ J♠ 10♠ is the same hand no matter which order those cards arrive, and there are 120 (5 factorial) orderings of any five cards. Dividing 311,875,200 by 120 collapses all those duplicates into a single hand, giving 2,598,960. Getting this distinction right is the difference between a correct probability and one that’s off by a factor of a hundred.

A sanity check you can use

Because every five-card probability is “hand count divided by 2,598,960,” you can verify any figure you read. See a claim that a flush occurs 0.2% of the time? Multiply: 0.002 x 2,598,960 is about 5,198, which is close to the true 5,108 flushes. Told a royal flush is a 1-in-650,000 shot? Divide 2,598,960 by 4 and you get 649,740 — spot on. Anchoring to the denominator turns vague poker “facts” into numbers you can check in your head.

Bottom line

A 52-card deck yields 2,598,960 unique five-card poker hands, and 1,326 two-card starting combinations (169 distinct hands). Those two numbers anchor all of poker math. Explore the frequencies at the probability chart, the ranking logic at the hand rankings hub, and deeper calculations in odds and math.