Updated
Using Card draw probability calculator
Find hypergeometric probabilities for drawing exactly k marked cards without replacement.
P(k) = C(marked,k) × C(unmarked,draws − k) ÷ C(total,draws). All cards are equally likely and draws are uniformly shuffled. No game strategy, replacement, pity counter or guaranteed pack distribution is assumed.
A worked example
Example inputs: cards in population = 52, matching cards in population = 4, cards drawn without replacement = 5, matches wanted (k) = 1. Probability of exactly k matches (%) = 29.9473635608.
Before you use the result
P(k) = C(marked,k) × C(unmarked,draws − k) ÷ C(total,draws). All cards are equally likely and draws are uniformly shuffled. No game strategy, replacement, pity counter or guaranteed pack distribution is assumed.
Example results for cards in population
These examples use Matching cards in population: 4; Cards drawn without replacement: 5; Matches wanted (k): 1. They are reference calculations, not recommended settings.
| Cards in population | Probability of exactly k matches (%) |
|---|---|
| 26 | 44.4816053512 |
| 52 | 29.9473635608 |
| 104 | 17.0557527132 |
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ToolOctopus. “Card draw probability calculator.” Updated 2026-09-26. https://tooloctopus.com/card-draw-probability-calculator.
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