Deck Probability Calculator
Exact odds of drawing what you need from a deck of any size. Shows the full spread, how deep you must dig, and why multiplying percentages is wrong.
How many you will draw
How deep you have to dig
Cards you need to see for that chance of finding at least one copy — counting your opening hand, so seven means the opener alone.
Why not just multiply the percentages
- Drawing cards is not the same as flipping a weighted coin. Every card you draw changes what is left, so the right tool is the hypergeometric distribution and not the binomial one.
- The gap between the two is shown on the page. On a sixty-card deck it is small; on a forty-card deck or a large draw it is not, and the approximation always overstates the chance of missing.
- The average number of copies you will see is simply draws × copies ÷ deck. It is exact, and it is almost never the most likely outcome.
- A smaller deck concentrates everything. Three copies in forty is a better hit rate than four in sixty, which is why deck size is a decision and not a detail.
- These are the odds before any mulligan, scry or search. Anything that lets you look at more cards or throw a hand back changes the real figure and is not modelled here.
How to use
- Enter the deck size, how many copies you run, and how many cards you will see.
- Read the chance of at least one — or ask for at least two.
- Check the dig table for how far you need to get.
Frequently asked questions
Why not just multiply the percentages?
Because cards are drawn without replacement, so every card you draw changes the deck for the next one. Treating each draw as an independent coin flip is the binomial distribution, and it gives a visibly wrong answer on small decks — the page shows both figures and the gap between them.
What are the odds of a four-of in an opening hand?
Four copies in sixty cards, seven drawn: 39.95%. About two openers in five. Going to eight cards, which is what being on the draw means, takes it to roughly 45%.
Is a smaller deck really better?
For consistency, yes, and by more than people expect. Three copies in forty is a better hit rate than four in sixty, because the deck size divides into everything. It is the reason deck size is a decision rather than a detail.
What does the average number of copies mean?
It is exactly draws × copies ÷ deck, and it is genuinely exact rather than an estimate. It is also almost never the most likely outcome: an average of 0.47 copies does not mean you usually draw half a card, it means you usually draw none.
Does this account for mulligans?
No. These are the odds before any mulligan, scry, search or card draw. Anything that lets you see more cards or throw a hand back changes the real figure, and modelling that properly needs assumptions about how you would use it.
What deck sizes does it handle?
Any, up to 500 cards. The combinations are worked out multiplicatively rather than through factorials, so numbers that would overflow an ordinary calculation still come out exactly.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.