MTG Mulligan Probability
Hypergeometric probability of drawing N+ lands in a Magic: the Gathering opening hand.
Overview
The MTG Mulligan Probability calculator uses the hypergeometric distribution to compute the chance of drawing a target number of lands (or any "good" card type) in your Magic: the Gathering opening hand. Tell it your deck size, land count, opening-hand size, and the threshold you consider "keepable", and it returns the probability of meeting that threshold plus the breakdown by exact land count.
It is purpose-built for the question every Magic player asks: "Should I keep this hand?" The math says you'd see exactly 3 lands in a 7-card opener from a 60-card 24-land deck about 31 percent of the time, and 2-or-3 lands about 56 percent of the time. Knowing the curve makes the mulligan decision data-driven rather than gut-based.
How it works
Drawing n cards from a deck of N containing K lands is the canonical hypergeometric problem. The probability of exactly k lands in the opener is C(K, k) * C(N - K, n - k) / C(N, n), where C denotes the binomial coefficient. Summing this from your minimum acceptable land count to your maximum gives the "keepable" probability.
For mulligan analysis under the London Mulligan, the model also reports the chance of acceptable opening hands across 7, 6, and 5 card sizes by recomputing with smaller n. Each mulligan effectively trades one card for another fresh draw from the same composition, so the per-mulligan probability stays the same but the bottom-of-deck cost of the mulligan grows.
Examples
- 60-card, 24-land deck, 7-card opener: chance of 2-5 lands (the usual "keepable" range) is about 84 percent.
- Same deck, chance of fewer than 2 lands (a likely mulligan): about 9.5 percent.
- 60-card, 22-land deck, 7-card opener: chance of 2-5 lands drops to about 80 percent.
- A 17-land Limited deck with 7-card opener: chance of 2-4 lands is about 73 percent; mulligans become noticeably more frequent.
FAQ
What's the right land count for a 60-card deck?
24 is the common starting point for an average-curve deck. Aggro decks often run 22; control runs 25-27.
Should I mulligan a one-land hand?
Usually yes, unless the hand has cheap card draw or a strong curve that works around it.
How does the London Mulligan affect the math?
You draw 7 every mulligan but put N cards on the bottom for the N-th mulligan, so the effective hand size drops.
Does this account for non-land mana sources?
No, only literal lands. For decks with mana rocks or dorks, increase the land count by the count of those sources.
What about the play-vs-draw difference?
The calculator handles opening hand. On the draw, you see one extra card by turn 2, which slightly improves any "land by turn 2" probability.