TCG Card Draw Probability Calculator
Calculate the chance to draw your target card using the hypergeometric distribution. Works for MTG, Hearthstone, Yu-Gi-Oh, Pokemon TCG, and more.
Enter deck size, copies, and cards drawn.
TCG Card Draw Probability Calculator: Opening Hand Odds
Knowing the odds of drawing the right card is the foundation of deck building in any trading card game. This calculator uses the hypergeometric distribution to find the exact chance of drawing your target card in your opening hand or after any number of draws. It works for Magic: The Gathering, Hearthstone, Yu-Gi-Oh, Pokemon TCG, Marvel Snap, and any game where you draw from a shuffled deck. Because the math is universal, the same formula applies to every format and region.
N = deck size, K = copies in deck
n = cards drawn, k = copies you draw
C(a,b) = combinations of b from a
Example: 40-card deck, 4 copies, draw 7
At least 1 copy = about 55 percent
What Is the Hypergeometric Distribution?
The hypergeometric distribution describes drawing items from a finite group without replacement. A deck of cards is the perfect example: every card you draw is removed from the deck, so each draw changes the remaining odds. This is why you cannot use a simple coin-flip or dice formula for card games. Those treat each event as independent, but card draws are dependent. This calculation is based on the hypergeometric distribution from statistics.
Why It Matters for Deck Building
Consistency wins games. If your deck relies on finding a key card early, you need to know how many copies to include to hit it reliably. Running four copies of a card in a 60-card deck gives roughly a 40 percent chance to open with at least one. Drop to a 40-card deck and that climbs to about 55 percent. The calculator lets you test copy counts and deck sizes side by side so you can tune your list for the consistency your strategy needs.
Games It Supports
Any game with a shuffled deck and no replacement works. Magic: The Gathering players use it for opening hands and topdecks, Yu-Gi-Oh players for combo starters in a 40-card deck, Hearthstone players for mulligan decisions across a 30-card deck, Pokemon TCG players for finding a Basic or a key Trainer, and Marvel Snap players for the chance to draw a specific card across the early turns. The presets cover the most common opening-hand sizes to get you started fast.
Tips & Recommendations
Change the copies field and watch the at-least-one chance move. Three to four copies is the usual sweet spot for opening-hand consistency.
A 40-card deck finds a 4-of far more often than a 60-card deck. If a card is core to your plan, run the minimum legal deck size.
Compare odds at your current hand size versus after a mulligan. Low chance of your key piece is a strong reason to ship the hand.
The table shows the chance of drawing zero, one, two, or more copies. Use it to judge flooding risk, not just the at-least-one number.
Frequently Asked Questions
Which card games does this calculator work with?
It works with any game that draws cards from a shuffled deck without replacement, which covers nearly every trading card game. That includes Magic: The Gathering, Hearthstone, Yu-Gi-Oh, Pokemon TCG, Marvel Snap, Flesh and Blood, Lorcana, and more. Enter your deck size, how many copies of the card you run, and how many cards you draw.
What is the opening hand probability?
It is the chance of drawing one or more of a specific card in your starting hand. For example, in a 40-card deck with 4 copies of a combo piece, drawing a 7-card opening hand gives roughly a 55 percent chance of seeing at least one copy. This calculator shows that number plus the full distribution for zero, one, two, or more copies.
How many copies should I run in my deck?
It depends on how reliably you need the card. If you want to see a card in your opening hand most games, running 3 to 4 copies in a 40-card deck gives a 50 to 65 percent chance. Use this calculator to test different copy counts: increase the copies and watch how the at-least-one probability climbs toward your target consistency.
What does hypergeometric mean?
The hypergeometric distribution models drawing items from a finite group without putting them back. A deck is exactly this situation: once you draw a card it is no longer available, so each draw changes the odds. This is different from rolling dice or flipping coins, where the odds reset every time. Card draws are dependent events, which is why the hypergeometric formula is the correct tool.
Does the draw order matter for the probability?
No. The probability of having at least one copy in your opening hand is the same whether you imagine drawing the cards one by one or all at once, because every possible hand is equally likely in a shuffled deck. The calculator computes the chance across all equally likely hands, so the order you physically draw does not change the result.
Can I use this for mulligan decisions?
Yes. Compare the chance of finding your key card in your current hand size versus after a mulligan. If your opening hand misses a crucial piece and the probability of finding it is low, the numbers can support a decision to mulligan for a fresh hand. The distribution table helps you weigh the trade-offs.
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