Poker Hand Probability Calculator
Exact odds of being dealt any 5-card poker hand from a standard 52-card deck.
Your hand equity
Pick your hole cards and any community cards to see the probability of making each hand.
How this is calculated
There are 2,598,960 possible 5-card hands from a 52-card deck. Each hand type's exact count is computed by standard combinatorics — choosing the qualifying ranks, then the qualifying suits within them — and dividing by that total gives the exact probability, with no simulation or estimation involved.
That 2,598,960 figure is C(52,5) — the number of ways to choose 5 cards from 52 when order doesn't matter, calculated as 52! / (5! × 47!). Every hand rank's probability is simply its own combination count divided into that same denominator: a royal flush has just 4 ways to occur (1 per suit) out of those 2,598,960, while a single pair — the most common made hand — has 1,098,240 ways, over a quarter of a million times more likely. This is the same combinatorial reasoning that makes the Birthday Paradox counterintuitive: comparing many possible combinations rather than a single specific outcome changes probabilities dramatically. For probability calculations that update based on new evidence rather than a fixed combinatorial count, see the Bayes' Theorem calculator.
Frequently asked questions
- Where do these numbers come from?
- There are exactly 2,598,960 possible 5-card hands from a standard 52-card deck (52 choose 5). Each hand type's count comes from standard combinatorics — for example, a full house is 13 ranks for the triple × 4 ways to pick which 3 of that rank × 12 remaining ranks for the pair × 6 ways to pick which 2 of that rank. These are fixed, exact values, not estimates.
- Why is "One Pair" ranked below "High Card" in rarity but more useful in a game?
- Rarity and hand strength aren't the same thing here — this rarity ranking is purely about how many ways each hand can occur out of all possible hands. In most poker variants, One Pair does beat High Card despite being slightly more common, because hand rankings are based on strategic value, not raw frequency.
- Does this account for community cards or multiple players?
- The hand equity calculator above does account for community cards — enter your hole cards and any known community cards to see your probability of making each hand over all possible board completions. The static probability table below it shows the fixed odds of a single random 5-card hand from a fresh 52-card deck. Neither tool accounts for opponents' holdings — that would require a full multi-player equity calculation.
- How do I use the hand equity calculator?
- Pick your two hole cards, then optionally add 0–5 community cards to reflect where you are in the hand (pre-flop, flop, turn, or river). Click Calculate equity to see the probability of your hand ending up as each type. The probability shown is over all possible completions of the board — so pre-flop shows how likely each outcome is across all possible runouts.
- Why do the pre-flop probabilities vary between runs?
- Pre-flop (and after just one community card), there are too many possible board completions to enumerate exhaustively in real time, so the calculator uses Monte Carlo simulation — randomly sampling 100,000 possible runouts. The result is accurate to within about 0.1–0.3 percentage points and will vary very slightly between runs. Once three or more community cards are known, the calculator switches to full enumeration and the result is exact.
- Can I use this in my own app?
- Yes — every calculator on Stupidly Clever has a matching REST API and MCP tool that runs the same underlying logic.
- What is the probability of being dealt a royal flush?
- There are exactly 4 ways to make a royal flush (one for each suit) out of 2,598,960 total possible hands — a probability of about 0.000154%, or odds of roughly 1 in 649,740. It is the rarest of the standard hand rankings.
- How does the number of players affect the odds?
- Your own individual odds of being dealt a specific hand from a fresh 5-card deal don't change based on how many other players are at the table. What does change is the probability that at least one player somewhere at the table has a strong hand — with more players in, it becomes more likely someone holds a good hand even though any single player's odds are unchanged.
- How is 'ways to make' different from probability?
- "Ways to make" is the raw count of distinct 5-card combinations that qualify as that hand type — a fixed integer from combinatorics. Probability divides that count by the total 2,598,960 possible hands to express it as a percentage or an "odds of 1 in N" figure — the two numbers describe the same underlying fact in different units.