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.
- Setting Maximum Copies = 0 means no upper limit (you just want at least the minimum).
- References: Frank Karsten, How Many Lands Do You Need to Consistently Hit Your Land Drops? (Channel Fireball, 2022); Hypergeometric distribution (Wikipedia).