Work out card game odds instantly with clear inputs, formula shown and shareable results.
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.
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)
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.
Drawing without replacement changes the odds after every card, so multiplying single-card chances overstates your outs; the combinations form is exact.
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.