Gaming calculators

Card Draw Calculator

Updated Jul 18, 2026 By Jehan Wadia
Rate Formulas
Calculator Options
Off = Manual (press Calculate). On = auto‑recalculate.
Add an upper bound to each card row.
Show remove buttons on card rows.
Show remove buttons on hand columns.
Safety budget for heavy multivariate computations (1–30 s).
Deck Configuration
Total number of cards in your deck or library (2–250).
Cards seen — opening hand size and/or draws (1–40).
Assigned 0 / 60 — Other: 60
Import Decklist
Card Categories & Desired Hand
Calculating…

Overall Hand Probability

Probability of achieving your desired hand

Decimal fraction:  
Per‑Category Breakdown
Marginal probabilities based on each category's desired minimum (N) from the first hand scenario.
Cumulative Probability Table
Chance of drawing exactly k copies of each category (this table is the text alternative to the chart).
Probability Chart
Hypergeometric Formula (your numbers)
P = \dfrac{\dbinom{N}{n}}{\dbinom{N}{n}}
This shows one exact-outcome term of the multivariate hypergeometric distribution; the overall result sums every valid outcome.
Step-by-Step Solution

Introduction

This card draw probability calculator helps you figure out the odds of drawing the cards you need from your deck. Whether you play Magic: The Gathering, Yugioh, Pokémon, or any other trading card game, knowing your draw chances helps you build a better deck.

The tool uses a math formula called the hypergeometric distribution. It calculates the exact chance of pulling specific cards from your deck in your opening hand or after a set number of draws. You do not need to know the math yourself — just enter your deck size, the number of cards you draw, and how many copies of each card type are in your deck. For a more general look at the underlying math, you can also explore our hypergeometric calculator.

You can set up multiple card categories at once, like lands, removal spells, or creatures. You can also compare different hand scenarios side by side to see which deck build gives you the best results. The calculator shows your overall probability, a breakdown for each card type, a step-by-step solution, and a chart so you can see everything clearly.

How to Use Our Card Draw Calculator

Enter your deck details and the cards you want to draw. The calculator will show you the exact probability of getting your desired hand using hypergeometric math.

Deck Size — Type the total number of cards in your deck. For example, most Magic: The Gathering decks use 60 and most Yugioh decks use 40 to 60.

Cards Drawn — Type how many cards you will draw. This is usually your opening hand size. Set it to 5, 6, or 7 depending on your game.

Card Category Name — Give each group of cards a name, like "Lands" or "Lightning Bolt." Each row in the table is one group.

Copies — Type how many copies of that card or card type are in your deck. The total of all rows must not go over your deck size.

Min (Desired in Hand) — Type the smallest number of that card you want to draw in your opening hand. For example, enter 1 if you need at least one copy.

Add Card Type — Click this button to add a new card category row to the table. You can track as many card groups as you need.

Add Hand Scenario — Click this button to add another hand scenario column. This lets you compare different ideal hands at the same time. The calculator finds the chance of getting any one of them.

Jolly Toggle — Turn this on if a card can count as more than one category. Then pick which other categories it can fill from the dropdown list.

Set Hand Maximum — Turn this on in the Options panel to add a Max column. This lets you set an upper limit on how many of each card you want drawn, not just a minimum.

Live Mode — Turn this on in the Options panel to have results update automatically as you type. Turn it off if your deck is complex and you want to press the Calculate button yourself.

Import Decklist — Click Show/Hide to open the import box. Paste your deck list with one card per line, starting with the number of copies then the card name, like "4 Lightning Bolt." Press Import to load it into the table.

Calculate Probability — Press this button to run the math. The results section will show your overall hand probability as a percentage, a per-category breakdown, a cumulative table, a bar chart, the full hypergeometric formula with your numbers, and a step-by-step solution.

What Is a Card Draw Calculator?

A card draw calculator tells you the chance of pulling specific cards from your deck. When you shuffle a deck and draw a hand, some cards show up and others stay hidden. This tool uses math to figure out how likely you are to get the cards you need. If you are interested in general probability calculations beyond card games, we have a dedicated tool for that as well.

How Card Draw Probability Works

Every card game that uses a deck involves luck. Whether you play Magic: The Gathering, Pokémon, Yu-Gi-Oh!, or any other trading card game, your opening hand is random. But random does not mean unpredictable. If you know how many cards are in your deck, how many copies of a card you run, and how many cards you draw, you can calculate the exact odds of seeing that card in your hand. Yu-Gi-Oh! players looking for a tool tailored to their game can also try our Yugioh probability calculator.

This type of math is called hypergeometric probability. It counts the number of ways you can draw a certain group of cards out of all the possible hands you could get. The formula relies heavily on combinations — the number of ways to choose k items from n items regardless of order — which are also called binomial coefficients. It works because card draws happen without replacement — once you draw a card, it leaves the deck and cannot be drawn again. This is different from a binomial distribution, which assumes each trial is independent with replacement.

Why This Matters for Deck Building

Good deck builders do not guess. They use probability to make smart choices. For example, if you want to see at least one copy of a key card in your opening hand, this calculator shows you whether running three or four copies makes a real difference. It also lets you check multiple card types at once, so you can see the odds of drawing a strong mix of cards — like having both a creature and a removal spell on turn one. Pairing draw probabilities with an expected value calculator can help you evaluate the average payoff of different deck configurations over many games.

This same style of probability thinking applies to other card games too. If you play poker, tools like our poker odds calculator and blackjack calculator use similar math to figure out the chances of hitting specific hands. Even video-game card games like Balatro benefit from this approach — check out our Balatro calculator for that. And if your game involves dice alongside cards, our dice probability calculator can handle those rolls.

Key Terms to Know

  • Deck Size — The total number of cards in your deck.
  • Cards Drawn — How many cards you draw, such as your opening hand size.
  • Copies in Deck — How many of a certain card or card type you put in your deck.
  • Desired Minimum — The fewest copies of that card you want to see in your hand.
  • Hand Scenario — A specific combination of cards you hope to draw together.
  • Jolly (Wild) Card — A card that counts toward more than one category, like a dual-purpose spell.

By adjusting these numbers, you can test different deck builds quickly and find the setup that gives you the best odds of drawing strong hands. The underlying formula uses factorials to count every possible arrangement, but the calculator handles all of that heavy math for you.


Formulas used

Binomial Coefficient
\binom{n}{k} = \frac{n!}{k!\,(n-k)!}
Hypergeometric PMF (single category, exactly k copies drawn)
P(X = k) = \frac{\dbinom{K}{k}\dbinom{N-K}{n-k}}{\dbinom{N}{n}}
Cumulative probability of drawing at least d copies
P(X \ge d) = \sum_{k=d}^{\min(K,\,n)} \frac{\dbinom{K}{k}\dbinom{N-K}{n-k}}{\dbinom{N}{n}}
Cumulative probability of drawing at most d copies
P(X \le d) = \sum_{k=0}^{d} \frac{\dbinom{K}{k}\dbinom{N-K}{n-k}}{\dbinom{N}{n}}
Multivariate Hypergeometric (overall hand probability across all categories)
P(\text{hand}) = \sum_{\substack{(k_1,\dots,k_m) \\ \text{satisfying constraints}}} \frac{\displaystyle\prod_{i=1}^{m}\dbinom{K_i}{k_i}\;\dbinom{N - \sum K_i}{\;n - \sum k_i\;}}{\dbinom{N}{n}}

Frequently asked questions

What card games does this calculator work for?

This calculator works for any card game that uses a deck. It supports Magic: The Gathering, Yu-Gi-Oh!, Pokémon TCG, Flesh and Blood, Lorcana, Marvel Snap, Hearthstone, and more. Just set your deck size and cards drawn to match your game.

What deck size should I use for my game?

Use the standard deck size for your game. For Magic: The Gathering, use 60 (or 99 for Commander). For Yu-Gi-Oh!, use 40 to 60. For Pokémon TCG, use 60. You can enter any number from 2 to 250.

What does the Other Cards row mean?

The Other Cards row shows how many cards in your deck are not assigned to any category. The calculator figures this out by subtracting your category totals from the deck size. These leftover cards are included in the math automatically.

Do I need to add every card in my deck as a category?

No. Only add the cards you care about drawing. Any cards you do not list go into the Other Cards group automatically. For example, if you only want to know your odds of drawing a specific combo piece, just add that one card.

What is a Jolly card?

A Jolly card is a card that counts toward more than one category. For example, a card that works as both a creature and a removal spell. Turn on the Jolly toggle for that row, then pick which other categories it also counts as.

What is the difference between Min and Max?

Min is the fewest copies you want to draw. Max is the most copies you want to draw. By default only Min is shown, meaning "at least this many." Turn on Set Hand Maximum in the Options to add a Max column so you can say "between 2 and 4 copies."

What does Add Hand Scenario do?

It adds another column of Min (and Max) values so you can describe a different ideal hand. The calculator then finds the chance of getting any one of those hands. This helps you compare different opening hand goals side by side.

What is Live Mode?

When Live Mode is on, the results update automatically as you type. When it is off, you must press the Calculate Probability button yourself. Turn it off if your deck has many categories and the calculator feels slow.

Why did I get a timed out warning?

The calculator has a time limit to stop very heavy calculations from freezing your browser. If you see this warning, try reducing the number of card categories or hand scenarios. You can also raise the timeout in the Options panel up to 30 seconds.

How do I import my decklist?

Click Show / Hide under Import Decklist. Paste your list with one card per line, starting with the number of copies, then the card name. For example: 4 Lightning Bolt. Then click Import. This replaces any existing card rows.

Why does my overall probability show 0%?

A 0% result means it is impossible to draw that hand. Common causes: your desired minimum for a card is higher than the copies in your deck, or the total minimum cards you want exceeds the number of cards drawn. Check your inputs and lower your minimums.

Can I calculate the odds of drawing a specific card by a certain turn?

Yes. Set Cards Drawn to your opening hand size plus the number of extra draw steps. For example, in Magic: The Gathering, to check your odds by turn 3 on the play, set cards drawn to 9 (7 hand + 2 draw steps).

What does the per-category breakdown show?

It shows the marginal probability for each card category on its own. You see the chance of drawing exactly your desired number, at least that many, and at most that many. These numbers treat each category independently from the others.

What is the cumulative probability table?

The cumulative table shows the exact chance of drawing k copies of each card category, from 0 up to the maximum possible. It gives you a full picture of every possible outcome for each card type.

Is this calculator accurate?

Yes. It uses the multivariate hypergeometric distribution, which is the exact mathematical formula for drawing cards without replacement. There is no estimation or simulation involved. The results are precise to six decimal places.

Does the calculator account for drawing without replacement?

Yes. The hypergeometric distribution is built for sampling without replacement. Once a card is drawn, it leaves the deck. This is different from coin-flip or dice-roll math where each event is independent.

How many card categories can I add?

There is no hard limit, but more categories make the calculation heavier. If you add too many and the calculator times out, reduce the number of categories or increase the timeout in the Options panel.

Can I use this for Commander or EDH decks?

Yes. Set the deck size to 99 (or 98 if you exclude your commander). Since most Commander cards are one-ofs, set copies to 1 for each card you want to track. The math works the same way regardless of deck size.

What does the formula section show?

It shows the hypergeometric formula filled in with your actual numbers. You can use the slider to control how many category terms are visible. This is helpful if you want to understand the math behind your result or share it with others.

How do I reset the calculator to its default values?

Click the Reset button next to the Calculate button. This restores the deck size to 60, cards drawn to 7, and loads the default three card categories. All options and settings go back to their starting values.