About the Poker Hand Probability Calculator
This poker hand probability calculator gives the exact chance of being dealt each poker hand, from a royal flush down to high card. Choose five-card hands (five-card draw before the draw, or five-card stud) or the best five of seven cards (Texas Hold’em by the river, or seven-card stud), pick a hand, and see its probability, its odds as “1 in X” and “X to 1 against”, the number of combinations and the chance of that hand or better. A full table ranks every hand.
Switch to card-draw mode to answer the other common question: what are the chances of hitting one of my outs? Enter how many cards are still unseen, how many of them help you, how many cards you will draw, and how many hits you need. This works for poker draws, other card games and any “draw without replacement” problem.
All figures are exact combinatorics for a standard 52-card deck with no jokers or wild cards, counting each hand by its best five-card category. They are the long-run frequencies of random deals; they do not account for opponents’ cards or folding decisions.
With the default inputs, the probability is 0.1441%. Change any value above to recalculate instantly.
How to use the poker hand probability calculator
- 1Choose whether you want the chance of a poker hand or of drawing your outs.
- 2For hands, pick 5 cards or best 5 of 7, then choose the hand.
- 3For draws, enter unseen cards, outs, cards to be drawn and hits needed.
- 4Read the probability and odds, and use the table to compare every outcome.
Formula and method
Each hand probability is the number of card combinations that make that hand divided by the number of possible hands. For five cards, the counts come straight from combinatorics: for example a full house is 13 ranks × C(4,3) ways for the trips × 12 ranks × C(4,2) ways for the pair = 3,744. Straights and flushes exclude straight flushes, which are counted separately, and the royal flush is shown apart from other straight flushes.
For seven cards each combination is classified by its best five-card hand, which gives the standard 133,784,560-hand breakdown. Card-draw mode uses the hypergeometric distribution: the chance of drawing at least k of your outs when d cards are dealt from N unseen cards without replacement. Odds against = (1 − p) ÷ p.
- C(n, k)
- Number of ways to choose k cards from n
- N
- Unseen cards
- outs
- Unseen cards that help you
- d
- Cards to be drawn
- k
- Minimum number of outs you need
Worked examples
Being dealt a full house in five cards
There are 3,744 full houses among 2,598,960 five-card hands, a probability of 0.1441% — about 1 in 694. Including quads, straight flushes and royals, a full house or better comes up 0.170% of the time.
Royal flush in Texas Hold’em by the river
Among 133,784,560 seven-card combinations, 4,324 contain a royal flush, so the chance is about 0.0032% or 1 in 30,940 — much better than the 1 in 649,740 for five cards.
Flush draw on the flop, seeing turn and river
With 9 flush cards among 47 unseen, you miss on both streets with probability (38 × 37) ÷ (47 × 46) = 65.03%, so you complete the flush 34.97% of the time — roughly 1 in 2.86.
Frequently asked questions
What are the odds of a royal flush?+
In five cards the chance is 4 in 2,598,960, or 1 in 649,740. Using the best five of seven cards (Hold’em by the river), it is 4,324 in 133,784,560, about 1 in 30,940.
What is the probability of a full house?+
A five-card full house occurs 3,744 times in 2,598,960 hands, or 0.144% (about 1 in 694). With seven cards it rises to about 2.60%, roughly 1 in 38.5.
Why is a flush ranked higher than a straight?+
Hand rankings follow rarity. In five cards there are 5,108 flushes but 10,200 straights, so a flush is about half as likely and beats a straight. The same order holds for seven-card hands.
How many possible poker hands are there?+
There are C(52,5) = 2,598,960 distinct five-card hands and C(52,7) = 133,784,560 seven-card combinations from a standard 52-card deck without jokers.
What are the odds of hitting a flush draw?+
With 9 outs and 47 unseen cards on the flop, you hit by the river 34.97% of the time. From the turn, with one card to come, it is 9 ÷ 46 = 19.57%.
Sources