Work out card draw probability instantly with clear inputs, formula shown and shareable results.
With replacement the draws are independent so the miss chance is (1 - K/N) to the power of the draws; without replacement the hypergeometric form C(N-K, d) / C(N, d) applies. The two models diverge fast on a small deck, which is why deck-building games are analysed hypergeometrically rather than with simple independent probabilities.
With replacement
P(no hit) = (1 - K / N) ^ draws
Without replacement
P(no hit) = C(N - K, draws) / C(N, draws)
P(no hit) = (1 - K / N) ^ draws. With replacement the draws are independent so the miss chance is (1 - K/N) to the power of the draws; without replacement the hypergeometric form C(N-K, d) / C(N, d) applies.
The two models diverge fast on a small deck, which is why deck-building games are analysed hypergeometrically rather than with simple independent probabilities.
Enter cards in the deck, cards that count as a hit, cards drawn, return each card before the next draw. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.