Hypergeometric Land Calculator
See the exact probability of drawing the cards you need. This is the math behind Manacove's land count recommendations.
Out of 99 total cards
Cards seen: 12 (7 opening + 4 draws + 1 extra)
99 for Commander, 60 for Standard/Modern
80%
What is the Hypergeometric Distribution?
The hypergeometric distribution calculates the probability of drawing a specific number of "successes" from a finite population, without replacement. Unlike the binomial distribution (coin flips), each draw changes the remaining pool - exactly how drawing cards from a deck works.
The formula is: P(X = x) = C(K, x) · C(N-K, n-x) / C(N, n) where C(a, b) is the binomial coefficient "a choose b." N is the population size, K is the number of successes in the population, n is the sample size, and x is the number of observed successes.
Why Does This Matter for Commander?
Your Commander deck has 99 cards. You draw an opening hand of 7, then one card per turn. How likely are you to hit your land drops? This is not a guess - it is exact math. The hypergeometric distribution tells you the precise probability of drawing any number of lands (or any other card type) by any given turn.
Manacove uses this math to recommend land counts. With 40 lands on the draw, you see 11 cards by turn 4 (7 opening hand + 4 draws), giving a 73% chance of hitting all 4 land drops. Check the "+1 extra draw" box to account for a cantrip or card draw spell (12 cards seen), which pushes it to ~80% - the baseline Manacove uses.
Land Drop Probability Table
Probability of hitting at least N land drops on turn N in a 99-card Commander deck. Assumes one extra card drawn in the first few turns (cantrip, card draw spell). Use the calculator above to explore different land counts and deck sizes.
| Lands | Turn 2 | Turn 3 | Turn 4 | Turn 5 | Turn 6 |
|---|---|---|---|---|---|
| 33 | 91% | 78% | 62% | 45% | 30% |
| 35 | 93% | 82% | 68% | 51% | 36% |
| 37 | 94% | 86% | 73% | 58% | 43% |
| 38 | 95% | 87% | 75% | 61% | 46% |
| 40recommended | 96% | 90% | 80% | 67% | 53% |
| 42 | 97% | 92% | 84% | 73% | 60% |
| 44 | 98% | 94% | 87% | 78% | 66% |
Values assume a vanilla opening hand with no mulligans, cantrips, or card draw effects. Real-game probabilities are typically higher - mulligans let you throw back land-light hands, and most decks include cantrips or draw spells that see additional cards. These numbers are a conservative floor, not a ceiling.
Lands First, Rocks Second
As Sam Black explains, the number of lands you play is a simple math question driven by two things: when you are willing to miss your first land drop, and how many cards you are drawing per turn. Mana rocks should not reduce your land count. Decide how many lands you need first, then add rocks on top of that if your deck wants more than one mana per turn.
Lands are the stickiest resource in Commander. Board wipes reset creatures, artifact removal blows up rocks, but mass land destruction is rare and widely frowned upon. A land you play on turn two is almost certainly still there on turn ten. That makes every land drop one of the most durable investments you can make in a game.
The common counter-argument is "but what about drawing too many lands?" Run the numbers in reverse: with 43 lands (57 spells) and 12 cards seen, you are 81% to have drawn at least 6 spells - more than enough plays for turns two through four. Games are far more forgiving of land-heavy draws than land-light ones. If you flood, you look non-threatening and opponents leave you alone until you draw action. If you miss land drops, you fall behind on mana in a way that is almost impossible to recover from.
Why can we ignore mulligans in this calculator? Because mulligans only push real-game probabilities higher. You mulligan land-light hands, not land-heavy ones, so the vanilla hypergeometric numbers are a conservative floor. If the math says you hit your drops 73% of the time with no mulligans, your actual rate in real games will be higher. This means you can trust these numbers as a worst-case baseline.
Making 40 Lands Work
The math says 43 lands is optimal. Frank Karsten's updated 2024 formula - adjusted for Commander's free mulligan and drawing on the play - arrives at the same number. But nobody wants to run 43 lands, and even Wizards builds precons with 37-39. As Rebell Lily breaks down, 40 is a practical sweet spot: easy to remember, 80% success rate on turn 4, and the gap between 40 and 43 can be hedged with smart card choices.
Spell: Land Cyclers
Spells you discard to search for a basic land type. They live in your spell slots (not your 40 lands), but find a land when you need one. Running 3 makes 40 feel like 43. The LotR cycle is best - only 1 mana to cycle.
Land: Card Draw Cyclers
Actual lands that tap for mana but can also cycle to draw a card. When flooded, cash one in for a fresh draw. Amonkhet duals, New Capenna and Ikoria triomes all have this. Keep tapped lands under 10 total.
MDFCs (Double-Faced Cards)
Spell on one side, land on the other - you choose. Modern Horizons 3 has a full dual-color cycle, and Zendikar Rising covers every color. Every MDFC "land" doubles as a real spell.
Utility Lands
Lands that do more than tap for mana. Clue lands investigate, creature lands attack, and cards like Fountainport and War Room convert late-game mana into resources.
Beyond Lands
The hypergeometric distribution is not just for lands. Use the General Mode above to calculate probabilities for any card type. How likely are you to see at least one piece of removal in your opening hand? What are the odds of drawing your combo piece by turn 6? Switch to General Mode, set the population to your deck size, successes to the number of copies, and sample size to the number of cards you will have seen.