Card Game Odds Calculator

Work out card game odds instantly with clear inputs, formula shown and shareable results.

About Card Game Odds Calculator

This is the hypergeometric model: the chance of no hit is C(deck - outs, drawn) / C(deck, drawn), and at least one hit is one minus that. Drawing without replacement changes the odds after every card, so multiplying single-card chances overstates your outs; the combinations form is exact.

Formulas

No hit

P(none) = C(N - K, d) / C(N, d), with N cards, K outs and d drawn

At least one

P(at least one) = 1 - P(none)

Worked example

With the default values below, Card Game Odds Calculator returns Chance of at least one hit of 34.116%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Cards in the deckminimum 2: 52
Cards that count as a hitminimum 1: 4
Cards drawnminimum 1: 5

Results

Chance of at least one hit: 34.116%
Chance of exactly one hit: 29.947%
Chance of missing entirely: 65.884%
Odds of at least one hit: 1 in 2.93

Step by step

1Values used
2No hit
3At least one
4Chance of at least one hit= 34.116
5Chance of exactly one hit= 29.947
6Chance of missing entirely= 65.884
7Odds of at least one hit= 1 in 2.93

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Card Game Odds figure worked out?

P(none) = C(N - K, d) / C(N, d), with N cards, K outs and d drawn. This is the hypergeometric model: the chance of no hit is C(deck - outs, drawn) / C(deck, drawn), and at least one hit is one minus that.

Why does this matter?

Drawing without replacement changes the odds after every card, so multiplying single-card chances overstates your outs; the combinations form is exact.

What do I need to enter?

Enter cards in the deck, cards that count as a hit, cards drawn. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.