MTG Card Draw Probability Calculator
Calculate the probability of drawing at least a certain number of specific cards from your deck using the hypergeometric distribution.
Total number of cards in your deck (Standard: 60, Commander: 99)
How many copies of the target card are in your deck
Number of cards drawn (opening hand = 7, after 1 draw = 8, etc.)
Minimum number of copies you want to draw
Enter values and click Calculate.
Formula
This calculator uses the Hypergeometric Distribution:
P(X = k) = C(K, k) × C(N−K, n−k) / C(N, n)
P(X ≥ k) = ∑i=kmin(K,n) P(X = i)
Where:
- N = total deck size (population size)
- K = copies of target card in deck (success states in population)
- n = number of cards drawn (draws)
- k = desired number of copies in hand (observed successes)
- C(a, b) = binomial coefficient = a! / (b! × (a−b)!)
- Expected value E[X] = n × (K / N)
Logarithms of factorials are used internally to avoid numerical overflow for large deck sizes.
Assumptions & References
- The deck is perfectly shuffled (each card equally likely to appear in any position — uniform random sampling without replacement).
- No mulligans, scrying, or tutoring effects are modeled; this reflects a pure opening hand or draw probability.
- Standard MTG deck: 60 cards, up to 4 copies of any non-basic card. Commander: 99 cards, 1 copy per card.
- The hypergeometric distribution is the mathematically correct model for drawing without replacement (unlike the binomial, which assumes replacement).
- Reference: Hypergeometric Distribution — Probability and Statistics, DeGroot & Schervish; also documented at mtg.wtf and Frank Karsten's coverage on ChannelFireball.
- Frank Karsten's landmark article "How Many Sources Do You Need to Consistently Cast Your Spells?" (ChannelFireball, 2022) uses this exact distribution for mana base analysis.