About this tool
The Hypergeometric Draw Calculator tells you how likely you are to draw the cards you need from a deck, the exact maths behind every Magic: The Gathering or trading-card-game consistency question. Everything runs in your browser — no data leaves your device. Enter the deck size, how many copies of the card it contains, how many cards you will draw, and how many you want.
The probability of drawing exactly k copies is P(X = k) = C(K, k)·C(N − K, n − k) / C(N, n), the hypergeometric distribution, where N is the deck, K the copies, and n the cards drawn. To stay accurate for large decks it evaluates every binomial coefficient with log-factorials — lnC(n, k) = lnΓ(n+1) − lnΓ(k+1) − lnΓ(n−k+1) — then exponentiates, so nothing overflows. From the same terms it derives P(at least k), P(at most k), P(at least one) = 1 − P(0), and the expected number of copies drawn, n·K/N.
For an opening hand draw 7 cards; on the play by turn t you will have seen 7 + t cards, so set the drawn field accordingly. The copies wanted cannot exceed the copies in the deck, and you cannot draw more cards than the deck holds — those cases are flagged rather than guessed.