Card Draw Probability Calculator
Probability of drawing specific cards from a standard deck.
Enter your values
ⓘ Live results
Results
- P(at least 1 match)
- 34.116%
- P(zero matches)
- 65.884%
- Total ways to draw n cards
- 2,598,960
Quick answer
Uses the hypergeometric idea: probability of at least one match is 1 minus the probability of drawing zero matches.
P(>=1 match) = 1 - C(52-k,n)/C(52,n)
How to use the Card Draw Probability Calculator
- 1Enter how many cards in the 52-card deck count as a 'match' (e.g. 4 aces).
- 2Enter how many cards you draw without replacement.
- 3The probability of zero matches is subtracted from 1 to get at least one match.
Worked example
Using the values the calculator loads with:
Inputs
- Matching cards in deck4
- Cards drawn5
Results
- P(at least 1 match)34.116%
- P(zero matches)65.884%
- Total ways to draw n cards2,598,960
Frequently asked questions
What if k=0?
There are no matching cards, so the probability of a match is 0%.
Does order of drawing matter?
No, this uses combinations, so the order the cards are drawn in doesn't matter.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.