Determine your chances of hitting a playable opening hand in Magic: The Gathering. This calculator uses the Hypergeometric Distribution to find the probability of drawing an exact number of lands, helping you fine-tune your deck ratios for competitive play.
MTG Land Probability Calculator
MTG Land Probability Formula
The calculation uses the Hypergeometric Distribution formula, which is standard for sampling without replacement from a finite population. This is the correct model for opening hands in Magic: The Gathering.
$$P(\text{Exactly } M \text{ Lands}) = \frac{\binom{L}{M} \cdot \binom{T-L}{H-M}}{\binom{T}{H}}$$
Where $\binom{n}{k}$ (n choose k) is the combination formula: $\frac{n!}{k!(n-k)!}$
Formula Source: StatTrek Hypergeometric Distribution | MTG Wiki on Opening Hands
Variables Explained
- Deck Size (T): The total number of cards in your deck (e.g., 60 for Constructed formats).
- Lands in Deck (L): The total number of basic, non-basic, and dual lands you run.
- Opening Hand Size (H): The number of cards you draw to start the game (usually 7).
- Target Lands (M): The exact number of lands you are looking for in your opening hand.
Related Calculators & Resources
Explore other essential tools for optimizing your Magic: The Gathering experience:
- MTG Card Draw Odds Calculator
- Mana Curve Optimizer
- Sideboard Win Percentage Tracker
- Commander Mulligan Probability Tool
What is the MTG Land Probability Calculator?
This tool is a necessity for serious Magic: The Gathering players, moving beyond simple percentages to provide mathematically precise probabilities for drawing specific quantities of lands. Since MTG decks are a finite population that is sampled without replacement (you don’t put the drawn cards back), the Hypergeometric Distribution provides the only correct probability model.
Understanding these probabilities is crucial for deck construction. A deck with too few lands risks “mana screw” (being unable to play spells), while a deck with too many risks “mana flood” (drawing too many lands and no threats). By calculating the odds of drawing 2, 3, or 4 lands, players can make data-driven decisions on their land counts, significantly improving consistency.
How to Calculate Land Probability (Example)
- Define Variables: Assume a Standard 60-card deck (T=60) with 24 lands (L=24). The Opening Hand Size is 7 (H=7). We want exactly 3 lands (M=3).
- Calculate Total Combinations: Find the total number of possible opening hands, $\binom{60}{7}$. This is the denominator.
- Calculate Land Success Combinations: Find the number of ways to choose 3 lands from the 24 available lands, $\binom{24}{3}$.
- Calculate Non-Land Success Combinations: Find the number of ways to choose the remaining 4 cards (7-3) from the 36 non-lands (60-24), $\binom{36}{4}$.
- Find Probability: Multiply the Land and Non-Land Success combinations (Step 3 * Step 4) and divide by the Total Combinations (Step 2). The result is the probability of drawing exactly 3 lands.
Frequently Asked Questions (FAQ)
Binomial distribution assumes sampling with replacement (you put the card back), which is incorrect for MTG. The Hypergeometric Distribution is required because each card drawn changes the composition of the remaining deck, which is the definition of sampling without replacement.
The ideal count depends on your deck’s mana curve. Generally, Aggro decks might run 20-22 lands, Midrange 23-25, and Control 26+. Use the calculator to find a range (e.g., 2 to 4 lands) that gives you a total probability of over 85%.
If you enter an optional probability, the calculator will perform a consistency check. It will calculate the expected probability based on T, L, H, and M, and report if your manually entered probability is within an acceptable margin of error (EPS) of the calculated result.
No, this calculator determines the probability for the initial, un-mulliganed opening hand. Post-mulligan decisions or the Scry mechanic introduce complexity that requires a more advanced simulation model.