Tabletop and Board Game Calculators
Card draw probability calculator.
Enter the size of your deck, how many copies of a card it holds and how many cards you draw. You get the exact chance of seeing at least, exactly or at most the number you need. Runs in your browser.
Deck and draw
Odds
Enter your numbers above.
Answer
In a 60-card deck with 4 copies of a card, the chance of at least one copy in a 7-card opening hand is 39.95%. After 4 more draws (11 cards seen) it rises to 56.55%. The chance of two or more copies in the opening hand is 6.32%.
Worked example
60 cards, 4 copies, 7 drawn. The chance of drawing none is C(56, 7) / C(60, 7) = 60.05%, so at least one copy is 1 - 60.05% = 39.95%. To see it by your fifth turn on the play you have seen 7 + 4 = 11 cards, which gives 56.55%.
How it works
Hypergeometric distribution. Cards are drawn without replacement, so each draw changes the deck. With N cards, K copies of the card and n cards drawn, the chance of exactly x copies is C(K, x) x C(N - K, n - x) / C(N, n). This is the hypergeometric distribution, which describes successes in draws without replacement from a finite population.
At least and at most. The chance of at least k copies sums the exact chances for x from k up to n. The expected number of copies is n x K / N.
Counting draws. Enter every card you have seen: the opening hand plus each card drawn since, and any extra cards you have drawn from effects. The tool treats the deck as shuffled randomly and does not model searching, mulligans or putting cards back.
Sources and basis (opened 2026-10-08): Hypergeometric distribution (Wikipedia) for the distribution of successes in draws without replacement.
FAQ
How do I calculate the odds of drawing a card in my opening hand?
Enter your deck size, the number of copies and the hand size as cards drawn, and read the At least line for 1 copy.
Why not just multiply the chance of each draw?
Because cards are not replaced the chances change after each draw. The hypergeometric formula accounts for that exactly.
How do I find the chance of drawing a card by a certain turn?
Add the cards drawn so far to the opening hand size. If you start with 7 cards and have drawn 4 more, enter 11.
What is the chance of drawing no copies?
For 4 copies in a 60-card deck with 7 cards drawn it is 60.05%.
Does it work for something other than card games?
Yes. It fits any draw without replacement from a finite pool, such as drawing raffle tickets or picking items from a bag.
Disclaimer
Fan-made math tool, not affiliated with or endorsed by the publishers of any game named on this page.