Calculate Poker Hand Combinations
Use this tool to compute how many unique hands are possible from a deck, and optionally view the classic 5-card poker hand distribution.
Why poker combinations matter
Poker is a game of incomplete information, but the mathematics of card combinations is exact. If you know how many possible hands exist and how often each hand rank appears, you make better decisions about bets, calls, folds, and bluffs.
A combinations calculator helps you quickly answer questions like:
- How many unique 5-card hands can be dealt from a 52-card deck?
- How rare is a full house compared to a straight?
- How do hand counts change if deck size or hand size changes?
The core formula: combinations (n choose k)
For poker-style hand counting, order does not matter. The hand A♠ K♠ Q♠ J♠ 10♠ is the same hand no matter the deal sequence. That means we use combinations, not permutations.
where n = total cards in deck, and k = cards drawn.
For standard 5-card poker, this becomes C(52, 5) = 2,598,960 total distinct hands.
Standard 5-card poker hand frequencies
When you use n=52 and k=5, the calculator displays exact counts and probabilities for all classic hand categories:
- Royal Flush
- Straight Flush (excluding royal)
- Four of a Kind
- Full House
- Flush
- Straight
- Three of a Kind
- Two Pair
- One Pair
- High Card
This is useful for both new players learning relative hand strength and experienced players reviewing long-run expectations.
How to use this calculator
1) Enter deck size
Use 52 for standard poker. You can also test custom deck sizes for variants or educational exercises.
2) Enter hand size
Use 5 for classic hand comparisons. Other values show the total combination count C(n, k).
3) Click Calculate
You’ll get the total unique hands instantly. If you selected 52 and 5, you also get the full odds breakdown table.
Quick examples
- Texas Hold'em hole cards: C(52, 2) = 1,326 possible starting combinations.
- Five-card draw total hands: C(52, 5) = 2,598,960.
- Seven-card selections: C(52, 7) = 133,784,560.
Common mistakes this tool helps avoid
- Confusing permutations with combinations.
- Underestimating how rare premium hands really are.
- Comparing hands by gut feeling instead of frequency.
- Ignoring the baseline odds when evaluating results over small samples.
Final takeaway
A poker combinations calculator does not replace table skill, but it strengthens your foundation. Better math means better intuition over time. Use this page to study hand rarity, improve strategic thinking, and build confidence in probability-driven decisions.