MTG Hypergeometric Calculator

This MTG hypergeometric calculator tells you how often your deck actually does what you built it to do. Twenty-four lands in sixty cards gives you two to five lands in your opening seven 84% of the time. Run a four-of and you see it in your opener 40% of the time, rising to 49% by turn 3 on the play. Pick the turn and play or draw above and the free calculator counts the cards you’ve seen for you.

How the MTG hypergeometric calculator counts cards

You see seven cards, then one more each turn. On the play you skip the turn-1 draw, so by turn 3 you’ve seen nine cards on the play and ten on the draw. The calculator uses that number as the sample and runs the standard hypergeometric sum:

P(exactly k) = C(copies, k) × C(deck − copies, seen − k) ÷ C(deck, seen)

“At least 1” is what you want for a key card. “At least 2” is the right question for colour requirements, like having two sources of blue by turn 2.

Numbers worth knowing

• 60 cards, 24 lands: at least four lands by turn 4 on the play, 63%. That’s why curve-topping four-drops feel unreliable.
• 40-card Limited deck, 17 lands: two to five lands in the opener 88% of the time.
• One-of tutor target with no tutors: by turn 5 on the draw you’ve seen 12 cards, so 20%. Plan around it, don’t rely on it.

It ignores mulligans, scry and card draw, which all help. Treat the result as the floor, then think about how much your smoothing spells add.

The general hypergeometric calculator handles any deck, and the Yu-Gi-Oh probability calculator is set up for 40-card Main Decks and 5-card hands.