# 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.

- URL: https://toolstackhub.co.uk/tools/card-draw-probability-calculator/
- Category: Calculators
- Price: free, no sign-up
- Privacy: runs in the browser; input is not uploaded
- Last updated: 2026-10-08

## About
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.

## How to use
1. Enter the total cards in your deck and how many copies of the card you are looking for.
2. Enter how many cards you draw: your opening hand, or the hand plus one draw per turn.
3. Choose how many copies you want to see.
4. 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.

## FAQ
**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, with no sign-up or limits.