Card Odds Calculator

Compute odds of drawing specific cards from a deck without replacement.

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What This Calculator Does

Compute odds of drawing specific cards from a deck without replacement.

It combines Deck Size, Desired Cards in Deck, Cards Drawn to estimate Chance of At Least One, Chance of Exactly One, Chance of None.

Formula & Method

Using combinations, chance of at least one desired card is P(\ge1)=1-\frac{\binom{N-K}{n}}{\binom{N}{n}} where N is deck size, K desired cards, n cards drawn. Exactly one: P(=1)=\frac{\binom{K}{1}\binom{N-K}{n-1}}{\binom{N}{n}}.

Notation used in the formulas: R = Chance of At Least One; x_{1} = Deck Size; x_{2} = Desired Cards in Deck; x_{3} = Cards Drawn.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

Deck Size: Used directly in the calculation.
Desired Cards in Deck: Used directly in the calculation.
Cards Drawn: Used directly in the calculation.

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