MTG Deck Probability Calculator
Deck / Hand Probability Calculator
Uses the hypergeometric distribution to calculate the exact probability of drawing specific cards. Works for Magic: The Gathering, Pokemon TCG, Yu-Gi-Oh!, and any other card game with a fixed deck.
Probability of Drawing Target
Standard Deck Configurations
| Game | Deck Size | Opening Hand | Max Copies |
|---|---|---|---|
| Magic: The Gathering | 60 (standard), 100 (Commander) | 7 | 4 (1 in Commander) |
| Pokemon TCG | 60 | 7 | 4 |
| Yu-Gi-Oh! | 40–60 | 5 | 3 |
| Flesh & Blood | 60 | 4 | 3 |
| Lorcana | 60 | 7 | 4 |
A 4-of in a 60-card deck has a ~39.9% chance to appear in your opening 7. A 24-land deck has a ~39.9% chance to have exactly 3 lands in hand.
References & Methodology
- Hypergeometric Distribution — NIST/SEMATECH e-Handbook of Statistical Methods (6.3.3.1) — Exact formula for sampling without replacement from a finite population; foundational model for card draw probability.
- Reid Duke — "Level One: Mana" (Wizards of the Coast, 2014) — Practical application of hypergeometric probability to Magic: The Gathering deck construction and mana base theory.
- Frank Karsten — "How Many Lands Do You Need to Consistently Hit Your Land Drops?" (Channel Fireball, 2022) — Standard reference for competitive MTG deck math using hypergeometric simulation over 10M trials.
References
- Jeff Orkin, "Three States and a Plan: The A.I. of F.E.A.R." — MIT
- Neller, T. & Presser, C. (2004). "Optimal Play of the Dice Game Pig" — The UMAP Journal, Vol. 25
- MDA: A Formal Approach to Game Design and Game Research — Hunicke, LeBlanc, Zubek (2004)
- Cornell University — Department of Mathematics: Game Theory and Card Games
- Neller, T. & Presser, C., "Optimal Play of the Dice Game Pig" (The UMAP Journal, 2004)
- Smithsonian Institution — The Art of Video Games Exhibition Documentation
- Smithsonian Institution — National Museum of the American Indian
- Cornell University College of Agriculture and Life Sciences — Tree Fruit Resources