Poker Hand Probability Calculator
Calculate the probability of being dealt any classic poker hand from a standard 52-card deck. Great for learning poker math or verifying hand rankings.
About this calculator
A standard 52-card deck produces C(52,5) = 2,598,960 distinct five-card hands. Each poker hand type (e.g., flush, full house, straight) corresponds to a fixed count of those combinations. The probability of being dealt a particular hand is: P = (number of ways to make that hand / 2,598,960) × 100%. For instance, there are exactly 4 Royal Flushes, giving a probability of 4/2,598,960 ≈ 0.000154%. The rarer the hand, the fewer combinations produce it — hand rankings in poker directly reflect these mathematical probabilities, with rarer hands beating more common ones.
How to use
Select 'Flush' as your hand type. A flush (five cards of the same suit, excluding straight flushes) has 5,108 possible combinations. The calculator computes: 5108 / 2,598,960 × 100 = 0.1965%. So you can expect a flush roughly once every 509 hands dealt. Compare that to a pair, which appears in 1,098,240 combinations — about 42.26% of hands — illustrating the vast gap in rarity.
Frequently asked questions
What is the probability of being dealt a royal flush in five-card poker?
There are exactly 4 Royal Flushes in a 52-card deck (one per suit), out of 2,598,960 possible five-card hands. That gives a probability of 4/2,598,960 ≈ 0.000154%, or roughly 1 in 649,740 hands. It is the rarest standard hand in poker, which is why it beats every other combination and is often the top prize in video poker pay tables.
How are poker hand rankings determined by probability?
Poker hand rankings are ordered strictly by mathematical rarity — the harder a hand is to obtain by random deal, the higher it ranks. Combinations are counted using combinatorics: for each hand type, mathematicians enumerate every subset of 52 cards that qualifies. Hands with fewer qualifying combinations are ranked above those with more. This ensures the game rewards statistical improbability, making the ranking system both fair and mathematically precise.
Why does a flush beat a straight in standard poker hand rankings?
A flush (5,108 combinations) is rarer than a straight (10,200 combinations), so it ranks higher. Many beginners find this counterintuitive because a straight visually seems more structured, but the numbers are clear: there are nearly twice as many straights as flushes in a 52-card deck. Poker rankings were designed around these exact counts, which is why every reputable hand-ranking chart places the flush above the straight.