Card draw probability (hypergeometric)
Your chances of having a specific card in your opening hand or after a few turns.
How it works
Hypergeometric distribution: P(X = k) = C(copies, k) × C(deck − copies, drawn − k) / C(deck, drawn). We add up from k = "at least" to the maximum.
Results are for guidance only and do not replace professional advice.
Worked example
With the default values:
- Cards in deck60
- Copies of the card you want4
- Cards drawn7
- At least (copies)1
you get:
- Chance of at least 139.95 %
- Exactly 133.63 %
- None at all60.05 %
- Average number in hand0.47
Frequently asked questions
How does the “Card draw probability” tool work?
Hypergeometric distribution: P(X = k) = C(copies, k) × C(deck − copies, drawn − k) / C(deck, drawn). We add up from k = "at least" to the maximum.
What do I need to enter?
Just fill in: cards in deck, copies of the card you want, cards drawn, at least. The result updates as you type.
Can you give an example?
Cards in deck: 60; Copies of the card you want: 4; Cards drawn: 7; At least (copies): 1 → Chance of at least 1: 39.95 %; Exactly 1: 33.63 %.
Is this calculator free, and is my data private?
Yes. HOD Calc is completely free with no sign-up. The calculation runs in your browser: nothing you type is sent or stored.