MTG Hypergeometric Calculator

Deckbuilding in Magic often comes down to a simple but important question. How often will this package actually show up when I need it. A hypergeometric calculator answers that without guessing. It models a real deck draw where cards leave the library after you see them, so later draws are affected by earlier ones. That makes it far more useful than a loose intuition or a coin-flip style estimate.

Commander players use this kind of math constantly, even if they never say the word hypergeometric. You use it when deciding whether 36 lands is enough, when checking how often an opening hand contains two early mana sources, or when asking if a combo package is truly reliable by turn five or six. The number does not replace playtesting. It gives you a better baseline before playtesting starts.

Example. If you play a 99 card Commander deck with 36 lands and want the chance of opening at least three lands, use 99 for deck size, 7 for cards drawn, 36 for successful cards in deck, and 3 for hits wanted. The at least result is usually the keep-decision number players care about most.

The exact result means you draw precisely the number of hits you entered. The at least result adds that case plus every better case above it. The at most result is useful when you are worried about flood, clunky openers, or too many copies of a narrow card. Zero hits is the clean fail-state number. It is especially useful for questions like no lands, no ramp, or no combo access.

The sample size changes the question you are asking. Seven cards usually means opening hand math. A larger number means total cards seen by a later turn. If you want to know the chance of seeing at least one board wipe by turn ten, sample size should match the total cards you expect to have seen by then, not just the seven you opened with.

If the main question is land drops, the mana base calculator turns the same logic into a more deckbuilder-friendly mana view. If the question is really about opening hands under London mulligans, the mulligan calculator frames it in a more game-ready way. For a turn-by-turn cEDH check against mulligans and tutors, including whether your deck casts Rhystic Study by turn two, try the cEDH Goldfish Simulator.

Imagine your deck has ten cards that count as early acceleration. That might be Sol Ring, Arcane Signet, Nature's Lore, Three Visits, mana dorks, and similar cards. If you want the chance of opening with at least one accelerator, set the deck size to 99, cards drawn to 7, successful cards to 10, and hits wanted to 1. The at least number tells you how often the opener contains that kind of start before mulligans.

Now change cards drawn from 7 to 10. That answers a different but often better question. What is the chance of seeing one accelerator by the time you have seen ten total cards. That reflects whether the early game plan is reliable over the first few turns, not only whether the first seven happened to line up perfectly.

The same logic helps with combo packages. If five cards are one side of a combo and four more find or duplicate it, you can test those nine practical hits together. If the result is lower than expected, the deck may need another tutor, another redundant payoff, or simply more draw.

Start with one clear question at a time. Do not ask whether the whole deck is good. Ask whether one package shows up often enough for the role you want it to play. Good inputs produce useful decisions. If you compare two versions of a list, change only one number at a time so you can see what the extra land, tutor, or payoff is actually buying you.

It also helps to check the output against real play patterns. If a combo line needs two different card types, run separate checks for both pieces instead of assuming one big percentage solves the entire problem. If your land count looks mathematically fine but games still stall, the real issue may be color balance, tapped lands, sequencing, or ramp density. This page is a fast tuning tool, not the only source of truth.