MTG Mulligan Probability Calculator
Calculate the probability of having at least a certain number of key cards (e.g., lands, combo pieces) in your opening hand, accounting for multiple mulligans using the London Mulligan rule.
Results will appear here.
Formula
Each draw uses the Hypergeometric Distribution:
P(X = k) = C(K, k) × C(N−K, n−k) / C(N, n)
- N = deck size
- K = number of key cards in deck
- n = hand size drawn (7 − mulligans taken)
- k = number of key cards in hand
A hand is "good" if minCopies ≤ X ≤ maxCopies.
Under the London Mulligan, after m mulligans you draw 7 cards and keep 7−m (bottoming m cards). For probability modeling, each attempt is treated as drawing from a freshly shuffled full deck of size n = 7−m.
Total probability of a good hand:
P(good) = Σi=0..m [ P(bad)i × P(good | hand size 7−i) ]
where P(bad)i is the probability of reaching attempt i (all prior hands were bad).
Assumptions & References
- Uses the London Mulligan rule (draw 7, keep 7−m, bottom m cards), introduced in Magic: The Gathering in 2019.
- Each mulligan attempt is modeled as drawing from a freshly shuffled full deck — a standard approximation that slightly overestimates probability but is widely accepted for deck-building analysis.
- "Key cards" can represent lands, combo pieces, removal spells, or any card type you want to track.
- Setting Maximum Copies = 0 means no upper limit (you just want at least the minimum).
- The model does not account for scry effects, partial information, or strategic mulligan decisions beyond the count threshold.
- On the play, the first player draws 7 cards and does not draw on turn 1. On the draw, the second player draws 8 cards total (7 + 1 on turn 1) — this calculator evaluates the opening 7-card hand only.
- References: Frank Karsten, How Many Lands Do You Need to Consistently Hit Your Land Drops? (Channel Fireball, 2022); Hypergeometric distribution (Wikipedia).