Gaming calculators

MTG Probability Calculator

Updated Jul 27, 2026 By Jehan Wadia
Rate Formulas
Draw Setup
How many cards are in your library right now.
How many cards you're drawing (e.g., opening hand).
How many copies of the target card are in your deck.
How many copies you want to see in your draw.
Current setting: On the Play — the player on the play skips their turn-1 draw (rule 103.8a). This drives the turn-by-turn table below.
Exact
33.63%
P(exactly 1 copy)
At Least
39.95%
P(1 or more copies)
At Most
93.68%
P(1 or fewer copies)
Step-by-Step Solution
Exact Probability Distribution
Full Probability Distribution
Chance of each possible number of copies appearing in your draw. The highlighted row is your "Copies Needed" target.
Copies Drawn Exact P(X = k) At Least P(X ≥ k) At Most P(X ≤ k)
Turn-by-Turn Progression
Assumes a 7-card opening hand and one draw per turn.
Turn Cards Seen Chance of Finding Your Target
Draw Setup
How many cards are in your library right now.
Total cards seen in the draw you're testing.
Sets "Cards Drawn" for you from the turn and the play/draw switch.
Current setting: On the Play
Card Groups You Need
All Requirements Met
Joint probability
Odds
Roughly 1 in this many draws
Miss Chance
At least one requirement not met
Step-by-Step Solution
Requirement Breakdown
Each group's chance on its own, ignoring the other requirements.
Card Group Copies in Deck Minimum Needed Expected Copies Drawn Chance On Its Own
Individual vs. Combined Odds
Deck & Guild Counts
Library size when Niv-Mizzet Reborn resolves.
Enter how many cards of exactly those two colors you run for each guild. Cards with one color, three colors, or no colors are not hit by the reveal.
White / Blue
Blue / Black
Black / Red
Red / Green
Green / White
White / Black
Blue / Red
Black / Green
Red / White
Green / Blue
Expected Cards Drawn
Average guilds hit in the reveal
Most Likely Result
Peak of the distribution
Chance of 5+ Cards
Five or more guilds represented
Step-by-Step Solution
Distribution of Cards Drawn
Probability of drawing exactly this many cards off the Niv-Mizzet Reborn reveal.
Cards Drawn Exact Probability At Least This Many
Per-Guild Hit Chance
Chance that at least one card of each guild shows up in the reveal.
Guild Colors Copies in Deck Expected Revealed Chance of a Hit

Introduction

This MTG probability calculator tells you how likely you are to draw the cards you need. Type in your deck size, how many cards you draw, and how many copies you run. You get the exact odds right away.

The tool has three modes:

  • Single Card — Find the chance of drawing one card, like a land or a bomb. See the odds for your opening hand and for each turn after.
  • Combo Draw — Need two or more pieces at once? Set up card groups and see the chance of getting all of them together.
  • Niv-Mizzet Reborn — Enter your guild card counts and see how many cards Niv is likely to draw you.

Every answer comes with a step-by-step breakdown, a chart, and a full table, so you can see the math behind the number. Use it to test a deck list, pick the right number of copies, or settle a debate about your mulligan. If you play other card games, the same engine powers our general card draw calculator and our Yugioh probability calculator.

How to use our MTG Probability Calculator

Pick a tab, type in your deck size and card counts, and the calculator shows your draw odds as a percent, plus step-by-step math, charts, and tables.

Cards in Deck (Single Card tab): Type how many cards are left in your library. Use 60 for Standard or Modern, 40 for Limited, and 99 for Commander. Quick buttons fill this in for you.

Cards Drawn: Type how many cards you will see. Use 7 for an opening hand, or add one card for each turn you draw.

Copies in Deck: Type how many copies of the card you want are in your deck. Most decks run 1 to 4.

Copies Needed: Type how many copies you want in hand. Use 1 for most cards, or 2 if you need a pair.

On the Draw switch: Turn it on if you draw first. Leave it off if you are on the play, since that player skips the turn-one draw. This changes the turn-by-turn table.

Cards in Deck (Combo Draw tab): Type your library size for the multi-card check, such as 60 or 99.

Cards Drawn (Combo Draw tab): Type the total cards you will see in that draw.

Turn number: Type a turn instead, and the tool fills in Cards Drawn for you using the play or draw switch.

Card group name: Name each group you need, like Lands, Removal, or Combo Piece.

Copies in deck (group): Type how many cards are in that group, like 24 lands.

Minimum needed (group): Type how many of that group you must draw. Add up to six groups with the Add Requirement button.

Cards in Deck (Niv-Mizzet Reborn tab): Type your library size when Niv-Mizzet Reborn resolves.

Guild counts: For each of the ten guilds, type how many cards you run in exactly those two colors. One-color, three-color, and colorless cards do not count, so leave them out.

MTG Draw Probability: What It Means

Every game of Magic: The Gathering starts with a shuffled deck. You cannot pick your cards, but you can know your odds. Draw probability tells you how likely you are to see a card in your opening hand or by a certain turn. Deck builders use these odds to choose how many lands, removal spells, and combo pieces to run.

The Math Behind It

Card draws use the hypergeometric distribution. That is a fancy name for a simple idea: you pull cards out of a deck and never put them back. Each card you draw changes the odds for the next one. This is different from rolling dice, where the odds stay the same every roll — see our dice probability calculator for that kind of independent event, or the general probability calculator for single-event math.

Four numbers drive the math:

  • Cards in deck – your library size, like 60 for Standard or 99 for Commander.
  • Cards drawn – how many cards you have seen so far.
  • Copies in deck – how many of that card (or that type of card) you play.
  • Copies needed – how many you want in hand.

Under the hood, each answer is a ratio of card combinations. If you want to see how those counts are built, try the combination calculator, the permutation calculator, or the factorial calculator.

Numbers Worth Remembering

In a 60-card deck, 4 copies of a card show up in your 7-card opening hand about 40% of the time. One copy shows up only about 11% of the time. In a 99-card Commander deck, a single copy appears in your opener about 7% of the time. That is why singleton decks lean on tutors and card draw.

On the Play vs. On the Draw

The player who goes first skips their first draw step. So on the play you have seen 7 cards on turn 1, and on the draw you have seen 8. That one extra card raises your odds a little every turn, which matters for finding lands and answers.

Combo and Multi-Card Odds

Some plans need two or more things at once, like a land drop plus a two-drop, or both halves of a combo. Those odds are not just one chance times another. The cards share the same hand, so they compete for slots. Combined odds are always lower than each piece on its own. If you want to price out whether a risky line is worth it, the expected value calculator helps you compare payoffs.

Niv-Mizzet Reborn

Niv-Mizzet Reborn reveals the top 10 cards of your library and lets you draw one card of each two-color pair — up to 10 guilds: Azorius, Dimir, Rakdos, Gruul, Selesnya, Orzhov, Izzet, Golgari, Boros, and Simic. Mono-color cards, three-color cards, and lands do nothing here. The more evenly you spread your gold cards across all ten guilds, the more cards you draw on average.

How to Use These Odds

Use them to test real choices. Should you run 3 or 4 copies? Is 24 lands enough? How fast do you find your win condition? Check the numbers, then adjust your deck list. Good odds will not win every game, but over many games they win more.

More Gaming Odds Tools

Card odds show up all over tabletop and video games. Try our poker odds calculator or Texas Hold'em odds calculator for hold'em hands, the blackjack calculator for hit-or-stand math, the Balatro calculator for joker scoring, and the DnD encounter calculator for tabletop night. Chasing a rare pull instead? The Genshin pity calculator and shiny odds calculator run the same kind of math.


Formulas used

Hypergeometric probability of exactly k copies
P(X = k) = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}
At least k copies (cumulative upper tail)
P(X \ge k) = \sum_{j=k}^{\min(K,n)} \frac{\binom{K}{j}\binom{N-K}{n-j}}{\binom{N}{n}}
At most k copies (cumulative lower tail)
P(X \le k) = \sum_{j=0}^{k} \frac{\binom{K}{j}\binom{N-K}{n-j}}{\binom{N}{n}}
Cards seen by a given turn (play vs. draw)
n_{\text{seen}} = \min\left(N,\; 7 + (t-1) + d\right), \quad d = \begin{cases} 1 & \text{on the draw} \\ 0 & \text{on the play} \end{cases}
Combined probability that all card-group minimums are met
P(\text{all}) = \frac{1}{\binom{N}{n}} \sum_{\substack{k_1 \ge m_1, \ldots, k_g \ge m_g \\ k_1 + \cdots + k_g \le n}} \left[ \prod_{i=1}^{g} \binom{K_i}{k_i} \right] \binom{N - \sum_i K_i}{\; n - \sum_i k_i}
Chance at least one card of a guild is in the reveal
P(\text{guild } i) = 1 - \frac{\binom{N-K_i}{s}}{\binom{N}{s}}, \quad s = \min(10, N)
Expected cards drawn from the Niv-Mizzet reveal
E[\text{cards}] = \sum_{i=1}^{10} \left( 1 - \frac{\binom{N-K_i}{s}}{\binom{N}{s}} \right)
Probability exactly r guilds are represented (inclusion-exclusion)
P(R = r) = \sum_{\substack{A \subseteq G \\ |A| = 10 - r}} \; \sum_{S \subseteq G \setminus A} (-1)^{|S|} \frac{\binom{N - \sum_{i \in A \cup S} K_i}{s}}{\binom{N}{s}}

Frequently asked questions

What is the difference between Exact, At Least, and At Most?

They answer three different questions about the same draw.

  • Exact — you draw that number of copies and no more. Example: exactly 1 land in your hand.
  • At Least — you draw that many or more. This is the number most players want, since one extra copy is fine.
  • At Most — you draw that many or fewer. Use it to check flood risk, like the chance of holding 4 or fewer lands.

Does the calculator include mulligans?

No. It shows the odds for one clean draw off the top of a shuffled deck. Mulligans give you extra tries, so your real chance of starting with a card is higher than the number shown. To guess at a London mulligan, run the 7-card number, then remember you can shuffle back and look again.

My deck already lost cards during the game. What deck size do I type?

Type the number of cards still in your library, and the copies still in there too. If you started with 60 cards and drew 10, type 50. If one copy of your card is already in hand, drop the copies count by one. Fresh numbers give real odds.

Why are my combo odds lower than each piece multiplied together?

Because both pieces have to fit in the same hand. Every slot used by piece one is a slot piece two cannot have. The cards also come out of the same shrinking library, so the draws are linked. The Combo Draw tab counts every valid way to split your drawn cards, so the joint number is correct.

How do I find the odds of drawing any land instead of one named card?

Treat the whole group as one card. Put your total land count in Copies in Deck. For 24 lands in a 60-card deck, type 24. The same trick works for any group: removal spells, creatures, cheap ramp, or all your win conditions together.

What percentage is good enough for a deck?

It depends on the job.

  • Lands and mana: aim for 85% or better. Missing land drops loses games.
  • Key answers: 60% to 80% by the turn you need them is solid.
  • Combo pieces: even 30% can work if the payoff wins the game.

If a number looks too low, add copies, add tutors, or add card draw.

How many lands do I need to hit three land drops by turn 3?

With 24 lands in 60 cards, you see 9 cards by turn 3 on the play and hit 3 or more lands about 79% of the time. Cutting to 22 lands drops that number, and 26 lands raises it but floods more. Try both in the Single Card tab and compare.

Should I type 99 or 100 for a Commander deck?

Type 99. Your commander starts in the command zone, not the library, so it is never part of your draws. Use 100 only for formats where all 100 cards get shuffled together.

Does the tool count draw spells, scry, or tutors?

Not on its own. It counts raw cards seen. The easy fix is to raise Cards Drawn by the extra cards a spell gives you. A cantrip that draws one card is worth one more card seen. Scry and tutors bend the odds in your favor even more, so treat the tool's number as a floor.

Can the same card go in two groups on the Combo Draw tab?

No. Keep every group separate so no card is counted twice. A land that also taps for a combo should live in one group only. You can add up to six groups, and the tool warns you if your group totals go past your deck size.

What does the Odds box mean when it says 1 in 3.5?

It means that over many shuffles you hit your target about once every 3.5 draws. It is an average, not a promise. You can whiff five times in a row and still hit twice back to back. Lower numbers are better.

What is the Expected Copies Drawn column?

It is the average number of that group you draw, found by cards drawn × copies ÷ deck size. With 24 lands in 60 cards and a 7-card hand, you average 2.8 lands. It is a quick gut check, not a chance, since you can never draw 2.8 cards in one hand.

Why does Niv-Mizzet Reborn almost never draw 10 cards?

You would need all ten guilds in the same ten-card reveal, one of each and no repeats. That is very rare. Most builds land in the 3 to 5 card range. Spreading your gold cards evenly across all ten guilds pushes your average up.

My guild counts do not add up to my whole deck. Is that a problem?

No, that is normal. Lands, mono-color cards, three-color cards, and colorless cards do not match a guild, so they stay out of the boxes. The tool treats every leftover card as a blank for the reveal, which is exactly how the card works.

Can I enter more than 4 copies of a card?

Yes. The four-copy limit is a deck rule, not a math rule. Higher numbers are useful when you group cards, like 8 removal spells or 12 one-mana creatures. Any whole number up to your deck size works.

Does the calculator assume a fair shuffle?

Yes. It assumes your library is fully random and that you never put a drawn card back. That is the same math judges and deck builders use. Sloppy shuffling, stacked piles, or cards left in known spots will make real games drift from these numbers.