MTG Land Draw Probability Calculator
Calculate land-draw probabilities without replacement, inspect the complete supported distribution, and compare entered land counts for the same library.
Interactive calculator · Method MTG_LAND-1.0 · Last reviewed: 2026-11-05
Calculate your scenario
P(X=k) = C(K,k) × C(N−K,n−k) / C(N,n), with max(0,n−(N−K)) ≤ k ≤ min(K,n).
Your inputs
Default worked example. Edit the inputs to calculate your scenario.
Default worked example
Uniform sampling without replacement: N=60, K=24, n=7; count 2 through 4 lands inclusively. All 7 cards are counted directly; no turn or mulligan rules are assumed.
How to use the calculator
Enter library size, lands, and the total cards actually counted. Select exact, at-least or inclusive range; optionally enter comparison land counts separated by commas.
What the result means
Read the requested range probability alongside the exact and at-least probabilities, then compare alternative land counts without changing the sample size.
Formula and units
P(X=k) = C(K,k) × C(N−K,n−k) / C(N,n), with max(0,n−(N−K)) ≤ k ≤ min(K,n). Expected lands = nK/N. A stable recurrence centered at the mode constructs and normalizes the full supported distribution; sum tolerance is 1e−12.
Worked examples
60-card library example, 24 lands, 7 cards counted: Library size N (60 is an editable example): 60 cards; Lands K: 24 cards; Cards counted in sample n: 7 cards; Lower / exact land count: 2 lands; Upper land count (range mode): 4 lands; Optional comparison land counts (comma separated): 22,26; Requested probability: range.
Example result: Requested probability: 77.456704297%; Exactly lower count: 26.941462364%; At least lower count: 85.734412009%; Expected lands: 2.8; Distribution probability sum: 1.
10-card reference library with exactly two lands drawn: Library size N (60 is an editable example): 10 cards; Lands K: 4 cards; Cards counted in sample n: 3 cards; Lower / exact land count: 2 lands; Upper land count (range mode): 2 lands; Optional comparison land counts (comma separated): 3,5; Requested probability: exact.
Example result: Requested probability: 30%; Exactly lower count: 30%; At least lower count: 33.333333333%; Expected lands: 1.2; Distribution probability sum: 1.
Limitations and common mistakes
Uniform finite-library sampling without replacement. Library sizes 60 and 99 are editable examples. No mulligan optimization, colored mana, ramp, tutors, card database, deck legality or optimal land-count advice. Independent of and not endorsed by Wizards of the Coast. Up to 1,000 cards and 12 comparison counts; tiny tail probabilities can underflow below floating-point precision.
Treating draws as independent replacement trials or assuming cards counted automatically equals a particular turn.
Sources and assumptions
Method MTG_LAND-1.0; last formula review 2026-11-05. Sources and their supported claims. Calculation methodology.
SciPy: scipy.stats.hypergeom. Hypergeometric PMF and support model draws without replacement.