Playing Card Probability Calculator
Exact probabilities for drawing cards: aces in a poker hand, hearts in a draw, any target cards in any hand size — counted with combinations from a 52-card deck.
Example — Exactly 2 aces in a 5-card hand3.993% — about 1 in 25
Standard 52-card deck, drawn without putting cards back. Example in the defaults: exactly 2 aces in a 5-card hand.
How we got it — the example, step by step
- Ways to choose the hand: C(52,5) = 2,598,960 equally likely hands.
- Winning hands: choose 2 of the 4 aces (C(4,2) = 6) and fill the other 3 places from the 48 non-aces (C(48,3) = 17,296): 6 × 17,296 = 103,776.
- Probability = 103,776 ÷ 2,598,960 = 0.039930 = 3.993%.
Check it backwards
The probabilities of drawing 0, 1, 2, 3 or 4 aces in 5 cards add to exactly 100% — this answer is the '2' slice of that whole.
Questions people also ask
Does it assume the cards are replaced?
No — this is drawing without replacement, the way real card games work: each card drawn shrinks the deck, and the combinations count exactly that.