Enter your deck size, number of copies of the desired card, cards drawn, and desired successes to calculate the exact probability of drawing what you need. The Card Probability Calculator uses the hypergeometric distribution to give you precise odds — including the chance to draw exactly k, at least k, or at most k copies of your target card.
Chance to Draw Exactly k
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Chance to Draw At Least k
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Chance to Draw At Most k
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Chance to Draw None (0 copies)
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The hypergeometric distribution calculates the probability of drawing a specific number of successes from a finite population without replacement. It's perfect for card games because each card drawn reduces the deck size, changing the odds with every draw — unlike a coin flip where probabilities stay constant.
Population Size is the total number of cards in your deck. Sample Size is how many cards you draw (e.g. 7 for an opening hand). Successes in Population is how many copies of the card you want exist in the deck. Successes in Sample (k) is how many copies you hope to draw.
For MTG, set the deck size to 60 (or 100 for Commander), enter the number of copies of the card you're interested in (max 4 for most cards), set the sample size to 7 for an opening hand, and choose how many copies you want to see. The calculator instantly shows your exact odds.
Yu-Gi-Oh decks are typically 40–60 cards, and players draw 5 cards to start. Set your deck size and copies accordingly, and use k=1 or k=2 to find out how likely you are to open with a key combo piece in your starting hand.
'Exactly k' is the probability of drawing precisely that many copies. 'At least k' sums the probability of drawing k or more copies — useful when any number above k is fine. 'At most k' sums the probability of drawing k or fewer copies — useful for checking the chance you won't be flooded with a card.
A larger deck dilutes your copies of the desired card, reducing the probability of drawing one in a given hand size. Keeping a lower deck size (closer to the minimum) maximizes consistency by keeping the ratio of desired cards to total cards higher.
Yes — the hypergeometric formula is universal. Just enter the correct deck size for that game (e.g. 60 for Pokémon), your card copies, and your draw size. The math works for any card game where you draw from a shuffled finite deck without replacement.
The calculator will guard against invalid inputs. The number of copies in the deck cannot exceed the deck size, and your desired successes cannot exceed the number drawn or the copies available. Invalid combinations will return 0% probability.