Knowing the real probability that your opening hand delivers what you need turns the keep-or-mulligan decision from a gut call into a math call. This calculator uses the hypergeometric distribution to tell you exactly how often your opening 7 — and the smaller hands you keep after mulliganing — will contain enough copies of a key card.
How it works
For a single hand the math is exact. With a deck of N cards containing K copies of your key card,
the probability that a hand of h cards holds at least need copies is:
P(X >= need) = 1 - sum over i from 0 to need-1 of [ C(K, i) * C(N - K, h - i) / C(N, h) ]where C(a, b) is the number of ways to choose b items from a. The tool evaluates this for
hands of 7, 6, and 5 cards, matching the London mulligan where you keep progressively fewer cards.
For the by-turn-1 figure, being on the draw means you have effectively seen eight cards by your
first turn, so the calculator draws one extra card for that estimate. The multi-mulligan numbers
(finding a keepable hand within two or three tries) use the familiar 1 - (1 - p)^attempts model,
which is a small overstatement because mulligans are not perfectly independent events.
Example and notes
Imagine a 60-card deck with 24 lands, and you decide a hand is keepable only if it has at least two lands. Enter deck size 60, copies 24, copies needed 2. The opening-7 keep chance comes out around 84%, the 6-card hand drops to about 78%, and the 5-card hand to roughly 70% — a concrete picture of how much consistency you trade away each time you mulligan.
A few things to keep in mind:
- The single-hand figures are exact; only the across-multiple-mulligans figures are estimates.
- Pre-game library manipulation, scry, and surveil effects are not modelled — they only improve your real odds.
- Pair this with the MTG Hypergeometric Draw Calculator when you want the full distribution rather than just the at-least-one threshold.