Hypergeometric Card Draw Calculator
Reviewed by Hamza Gujjar, Algorithm Architect & Software Developer
Last updated: July 27, 2026Why card draws need a different formula than dice
Unlike independent dice rolls, drawing cards from a deck changes the odds for every subsequent draw, since cards aren't replaced - the hypergeometric distribution correctly models this "without replacement" behavior.
Worked example
For drawing 5 cards from a standard 52-card deck (13 cards of one suit), wanting exactly 1 of that suit:
Result = 41.142%
This matches the well-known real probability of drawing exactly one card of a specific suit in a standard 5-card poker hand, confirming the calculation - this same formula applies broadly to any card or tile-drawing game mechanic, not just standard playing cards.