MCPCalc

Card Odds Calculator

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

Scratchpad (not saved)

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(≥1)=1−(N−Kn)(Nn)P(\ge1)=1-\frac{\binom{N-K}{n}}{\binom{N}{n}} where NN is deck size, KK desired cards, nn cards drawn. Exactly one: P(=1)=(K1)(N−Kn−1)(Nn)P(=1)=\frac{\binom{K}{1}\binom{N-K}{n-1}}{\binom{N}{n}}.

Notation used in the formulas: RR = Chance of At Least One; x1x_{1} = Deck Size; x2x_{2} = Desired Cards in Deck; x3x_{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.

Reference Book

Games, Gambling, and Probability

An Introduction to Mathematics

David G. Taylor · Chapman and Hall/CRC

A natural reference for odds, card draws, poker-style counting, gambling expectations, and game probability.

View Book

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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