Card Probability Calculator
Works for any deck or any draw without replacement, including raffles and sampling from a small batch.
Exactly this many
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
This many or more —
This many or fewer —
None at all —
At least one —
Reading this —
The formula
P(k) = C(K, k) × C(N − K, n − k) ÷ C(N, n)
This is the hypergeometric distribution: N cards, K of the kind you want, n drawn.
What to watch out for
A full deck has 52 cards, with 4 of each rank and 13 of each suit. To work out a specific poker hand, use the combination calculator, as many hands involve several conditions at once.
Frequently Asked Questions
What is the chance of exactly one ace in 5 cards?
29.95% (1 in 3.34).
What is the chance of at least one ace in 5 cards?
34.12% (1 in 2.93).
What is the chance of 5 hearts in 5 cards?
0.04952% (1 in 2,019).