BOOMSTICK CITYCard draw probability calculator
A free card draw calculator that gives your real odds of drawing a card, using the hypergeometric distribution (drawing without replacement, the way card games actually work). Set your deck size, copies, and how many cards you will see. The number and the curve update as you type. Works for any card game.
Odds of drawing at least your target as you see more cards. The dot marks your current draw count.
Card draw odds examples
Worked out for a 40-card deck, in case you want the numbers without touching the tool.
| A 3-of, chance you have seen at least one | Odds |
|---|---|
| By 7 cards seen | 44.8% |
| By 9 cards seen | 54.5% |
| By 11 cards seen | 63.0% |
| By 13 cards seen | 70.4% |
| By 16 cards seen | 79.5% |
| By 20 cards seen | 88.5% |
| In your opening 7 cards (40-card deck) | Odds |
|---|---|
| 1 copy in deck | 17.5% |
| 2 copies in deck | 32.3% |
| 3 copies in deck | 44.8% |
| 4 copies in deck | 55.2% |
How card draw probability works
The math is the hypergeometric distribution. Here is the whole idea in four steps.
1. Count your deck and your copies
Two numbers start it: the deck size and how many copies of the card you want are in it. A tighter deck and more copies both raise your odds.
2. Count the cards you will see
Add up the cards you will have drawn by the moment you care about: the opening hand plus one for each draw step or turn until then.
3. Use the hypergeometric formula
Because you draw without replacement, the odds shift with every card. The hypergeometric distribution handles that and gives the chance of seeing at least one copy in that many draws.
4. Read the curve, not one number
Consistency is the real question. The chart shows how your odds climb as the game goes on, so you can see how many copies you need to hit a card reliably by a given turn.
The formula, for the curious: the chance of exactly k copies in a draw of n cards from a deck of N with K copies is C(K, k) times C(N minus K, n minus k), divided by C(N, n), where C is the binomial coefficient. Sum from your target upward for the at-least odds. The calculator does all of it.
Common questions
How do I calculate the chance of drawing a card?
Use the hypergeometric distribution, which models drawing without replacement. Enter your deck size, how many copies of the card are in it, and how many cards you will see, and the calculator returns the chance of drawing at least one. The formula and worked examples are on this page.
What is the hypergeometric distribution?
It is the probability model for drawing without replacement, where each card you take changes what is left in the deck. Card games are exactly this, which is why it, and not a flat percentage, gives the correct draw odds.
What are my odds of drawing a specific card in my opening hand?
For a single copy in a 40-card deck, a 7-card opening hand gives about a 17.5% chance. Copies stack fast: three copies is roughly 44%. Use the calculator above for your exact deck size and numbers.
Does this work for MTG, Hearthstone, Yu-Gi-Oh, or Pokemon?
Yes. The math is the same for any card game. Set the deck size to match yours (Magic is often 60, Hearthstone is 30, and many others sit around 40) and the calculator does the rest.
How many copies of a card should I run?
It depends how badly you need it and when. More copies and a smaller deck both raise your odds. Use the curve above: raise the copies until the line crosses your comfort level by the turn you need the card.
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Know your odds. Then race to 15.
Boomstick City is a free card game where every draw counts and a match is over in about eight turns. In your browser, no install.
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