Card Draw Probability Calculator
Probability of drawing specific cards from a standard deck.
Enter your values
Enter the matching cards in deck you are working with.
Enter the cards drawn you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Probability of drawing specific cards from a standard deck. |
|---|---|
| Category | Statistics |
| Inputs needed | Matching cards in deck, Cards drawn |
| Main output | P(at least 1 match) |
| Formula | P(>=1 match) = 1 - C(52-k,n)/C(52,n) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Matching cards in deck
- Enter the matching cards in deck you are working with.
- Cards drawn
- Enter the cards drawn you are working with.
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.
What do I need to enter into the Card Draw Probability Calculator?
Just 2 values: matching cards in deck, cards drawn. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Card Draw Probability Calculator work out the answer?
Uses the hypergeometric idea: probability of at least one match is 1 minus the probability of drawing zero matches. It applies the formula P(>=1 match) = 1 - C(52-k,n)/C(52,n) and shows the working so you can check each step by hand.
Is the Card Draw Probability Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.