Free entry
Card Odds
Estimate the chance of a card event. Compete on the accuracy of your probability judgment.
MO STATS · FREE CALCULATOR
Card Draw Probability Calculator
Calculate the probability of drawing at least a specified number of target cards from a known deck.
No account to calculateNo real-money wageringTransparent assumptions
CALCULATOR
Card draw odds
Find the chance of drawing matching cards from a finite deck without replacement.
Start with your assumptions
Enter values and calculate to see the result, method, and assumptions.
PUT YOUR JUDGMENT TO WORK
Compete on decisions.
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Bankroll Arena
Choose a stake for a simulated opportunity. Compete on the quality of the decision under stated odds.
Games award nonredeemable MO Chips and decision scores. Chips cannot be bought, transferred or exchanged, and game results never earn anything of monetary value. Subscribing gives no competitive advantage.
Worked example
- At least one ace in five cards
- 34.1158%
- No aces in five cards
- 65.8842%
For a standard 52-card deck with four aces, five draws without replacement have probability 1 − C(48,5)/C(52,5) = 34.1158% of containing at least one ace.
Example inputs
- N:
52 - K:
4 - n:
5 - k:
1
Method
For deck size N, target-card count K and n draws, P(X = x) = C(K,x)C(N − K,n − x)/C(N,n). Sum this distribution from the requested minimum count upward. Cards are not replaced between draws.
Assumptions
All remaining cards are equally likely to be drawn. Enter the remaining deck and target-card counts after known removals. This calculator handles a target-card category; it does not evaluate full poker hand strength or opponents’ strategies.
Related
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