Card Draw Probability Calculator (Opening Hand Odds)
Find the chance of drawing a card, or several copies, in your opening hand or by a given turn, for any deck size. Free, private and instant.
How to use the Card Draw Probability Calculator (Opening Hand Odds)
- Enter the total cards in your deck and how many copies of the card you are looking for.
- Enter how many cards you draw: your opening hand, or the hand plus one draw per turn.
- Choose how many copies you want to see.
- Read the chance of drawing at least that many, exactly that many, or none, and use the table to see how the chance climbs with each draw.
Example
Worked example (a fictional 20-card deck with 2 copies of a card, run through this tool)
- Opening hand of 5 cards: Chance of at least one copy: 44.74% (1 − 8,568 ÷ 15,504)
- None in the opening hand: 55.26%
- Both copies in the opening hand: 5.26%
- After 10 cards drawn: At least one copy: 76.32%
Limitations
- Assumes a fully shuffled deck, with no search, redraw or mulligan effects.
- Counts one card type at a time. Chances of drawing a combination of different cards need separate calculation.
- It cannot say whether drawing the card is good for your plan, only how likely it is.
- Deck size, hand size and copies are whatever you enter. Check your game’s rules for the numbers allowed.
- This is an unofficial maths tool. It is not affiliated with any game or publisher.
Sources
About this tool
The Card Draw Probability Calculator uses the hypergeometric distribution to give your odds of drawing a card from a deck without replacement. Enter the deck size, how many copies of the card are in it and how many cards you draw, and it shows the chance of at least the number of copies you want, exactly that number and none, plus a table of how the chance grows with each extra card drawn. It works for any card game, including trading card games, poker decks and custom decks.
Also searched for as: opening hand calculator, hypergeometric calculator, deck probability calculator, chance to draw a card, tcg draw odds, mulligan calculator.
Card Draw Probability Calculator (Opening Hand Odds) is part of ToolStack Hub's Calculators. It runs entirely in your browser, which keeps your data private and makes results instant. There is nothing to install and no account to create. There is no usage limit.
Guides about this tool
Frequently asked questions
How do I calculate the chance of drawing a card?
Use the hypergeometric distribution. The chance of drawing none is C(N−K, d) ÷ C(N, d), and the chance of at least one is 1 minus that. The calculator does the sum for you.
What are the odds of drawing a card in a 20-card deck?
With two copies and a five-card hand the chance of at least one is 44.74%. With one copy it is 25%, which is simply 5 ÷ 20.
Why is this not a binomial calculation?
Cards are not put back after being drawn, so each draw changes the odds of the next. The hypergeometric distribution accounts for that.
How many copies should I include?
More copies raise the chance of drawing the card but use up deck space. Try different numbers and see the effect on the chance.
Is the tool specific to one game?
No. It works for any deck of any size.
Is the Card Draw Probability Calculator (Opening Hand Odds) free?
Yes. Card Draw Probability Calculator (Opening Hand Odds) is completely free with no sign-up, limits or watermarks.
Is my data private when I use the Card Draw Probability Calculator (Opening Hand Odds)?
Yes. It runs in your browser, so your input is not uploaded to our servers.
Does it work on mobile?
Yes. ToolStack Hub tools work on phones, tablets and desktop browsers.
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