Card draw probability calculator
Work out your chance of drawing at least one copy of a specific card, given your deck size and how many copies you're running.
This computes "at least one copy" odds using the hypergeometric distribution — the standard draw-without-replacement model, not a simulation.
"At least one" includes the chance of drawing multiple copies too, not just exactly one — that's a deliberately broader, more commonly useful question than an exact-count calculation would answer.
Worked example
Say you run 4 copies of a card in a 40-card deck and draw 7 cards (a typical opening hand size). Your chance of seeing at least one copy is about 55.2%.
Compare that to running only 1 copy of the same card in the same deck: with the same 7 cards drawn, your odds drop to about 17.5%. More copies of a card in the deck substantially raises your chance of drawing it early — exactly why deck-builders run multiple copies of their key cards.
FAQ
What math is this based on?
The hypergeometric distribution — the standard way to calculate draw odds from a fixed-size deck without replacement, where each card drawn changes the odds for the next one.
Does this work for any deck-based game?
Yes — it's a generic calculator based only on the numbers you enter, not tied to a specific game's card list.
What if I want the odds for drawing exactly one copy, not at least one?
This calculator only computes "at least one" — the more commonly asked question. "Exactly one" needs a different, more specific formula.
What happens if copies exceed my deck size?
That's rejected as invalid — you can't have more copies of a card than cards in the deck.
What if I draw more cards than are in my deck?
Also rejected — you can't draw more cards than the deck contains.
Does drawing more cards always increase my odds?
Yes — more draws can only increase or maintain your chance of having seen at least one copy, never decrease it.
Does this account for cards I've already seen, like a starting hand plus later draws?
Enter your total cards drawn so far (starting hand plus any draws) as one combined number — the calculator doesn't track draws in stages.
Is 100% possible?
Yes — if the number of cards drawn is high enough relative to the deck and copies, the chance can reach exactly 100%.
Does shuffling affect this?
The formula assumes a properly randomised deck — it doesn't account for stacking, scrying, or other card-order manipulation.
Can I use this for lands or resource cards specifically?
Yes — the calculation is the same regardless of what the card does; it only needs deck size, copies, and cards drawn.