Calculator Inputs
Example Data Table
| Scenario | Deck | Copies | Cards Seen | Target | Question |
|---|---|---|---|---|---|
| Opening hand | 60 | 4 | 7 | At least 1 | Chance to open with a key card |
| Turn three draw | 60 | 8 | 10 | At least 2 | Chance to find enough lands |
| Sideboard answer | 60 | 3 | 11 | At least 1 | Chance to find one answer |
Formula Used
The calculator uses the hypergeometric distribution. It is ideal for card draw probability because cards are drawn without replacement.
P(X = k) = [C(K, k) × C(N - K, n - k)] / C(N, n)
N is the effective deck size. K is the number of target cards. n is the number of cards seen. k is the wanted target count. At least and range probabilities are found by summing exact probabilities.
Mulligan estimate = 1 - (1 - p)attempts. This treats each attempt as an independent chance to meet the minimum target.
How to Use This Calculator
Enter your deck size and the number of cards that count as success cards. Set the opening hand size and target turn. Choose whether you are on the play or on the draw. Add extra cards if effects draw or see more cards. Then set exact, minimum, and maximum success values.
Use known removed cards when some cards are already unavailable. Press the calculate button. The result appears below the header and above the form. Use CSV or PDF export to save the result.
Probability Planning for Magic Decks
Why Draw Odds Matter
A Magic deck is a small probability engine. Each draw changes the chance of finding lands, removal, combo pieces, or sideboard answers. This calculator helps you model those moments with clear inputs. It uses the hypergeometric distribution, which fits card games because the deck is drawn without replacement.
Opening Hands and Turns
You can study an opening hand, a later turn, or a mulligan plan. Enter the deck size, the number of wanted cards, and the number of cards seen. The tool also lets you remove known cards from the deck. That helps when a card is already in exile, in hand, or otherwise unavailable.
Exact, At Least, and Range Odds
The result panel shows exact, at least, and range chances. These views answer different play questions. Exact odds help when you need one copy only. At least odds help when any number of copies is useful. Range odds help when too many copies can be bad, such as drawing several high cost spells early.
Mulligan Planning
Mulligan output is shown as an independent attempt estimate. It answers a practical question. What is the chance that at least one of your tries meets the minimum target? Real game choices can be more complex, because the final kept hand is affected by card selection and bottoming rules. Still, the number is useful for comparing deck plans.
Deck Building Use
For deck building, test several copy counts. Compare four copies with three copies. Then adjust the target turn. A combo card needed by turn two requires a higher density than a late game answer. Lands can be tested the same way by treating each land as a successful card.
Practical Notes
The calculator is not a judge call. It is a planning aid. Use it before events, sideboarding, or testing sessions. It can show why small card count changes matter. It also helps explain risk to teammates. Good probability work does not guarantee a win. It does make choices clearer before the shuffle.
Saving Results
Try saving several results. The CSV export is useful for notes and spreadsheets. The PDF export is useful for sharing a quick estimate. Keep assumptions visible when you compare builds. A probability based on seven cards is not the same as a chance by turn four. Cards seen must match the play situation before focused testing.
FAQs
What does a target card mean?
A target card is any card counted as a success. It can be one named card, any land, any removal spell, or a group of functionally similar cards.
Does this work for Commander decks?
Yes. Set deck size to 99 or 100 as needed. Then enter the number of cards that count as successes for your question.
What does cards seen mean?
Cards seen means the opening hand plus normal draws and extra draws. The calculator limits this value to the effective deck size.
Why use hypergeometric probability?
Card draws happen without replacement. Hypergeometric probability is designed for that situation, so it fits deck draw questions well.
How should I handle cantrips?
Add the extra cards seen through cantrips in the extra draws field. For complex selection effects, treat the result as an estimate.
What is the mulligan estimate?
It estimates the chance that at least one attempt meets the minimum target. Real mulligan choices can differ because players bottom cards strategically.
Can I calculate land probability?
Yes. Enter your land count as target copies. Then choose the minimum, maximum, or exact number of lands you want to see.
Can I export the result?
Yes. After calculation, use the CSV or PDF buttons. The exported files include the main probability results and key assumptions.