Deck Draw Probability Calculator
Calculate the odds of drawing a specific card from your deck.
Get the opening-hand probability, the cumulative probability for each turn, and the expected turn on which you draw it.
Need the odds of assembling a multi-card combo? Try the Combo Probability Calculator
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This tool has been used … times.
📊 Basic settings
🎯 Presets
📈 Results
Chance of drawing at least 1 copy in the opening hand
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Expected turn to draw at least 1 copy (rounded up)
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The average turn on which you draw the card. Individual games vary with luck.
📊 Turn-by-turn probability
(chance the card has shown up by the end of that turn)
| Turn | Cards seen | Cumulative probability |
|---|
How to use
This tool calculates how likely you are to draw a specific card in your opening hand, and on which turn you can expect to see it.
- Basic settings: enter your deck size, how many copies of the card are in the deck, and your opening hand size.
- Advanced settings: set how many cards you draw per turn, and how many copies you want to draw (k or more).
- Presets: apply the standard setup for MTG, the Pokemon TCG, or Yu-Gi-Oh! with a single tap.
- Results: the opening-hand probability, the expected turn, and the cumulative probability for each turn.
Calculations use the hypergeometric distribution.
FAQ
How is the opening-hand probability calculated?
With the hypergeometric distribution. From the deck size, the number of copies in the deck, and the opening hand size, the tool returns the chance of drawing at least 1 copy (or at least the number of copies you specify). No manual math required — just type in the numbers.
Does it work for MTG, the Pokemon TCG and Yu-Gi-Oh!?
Yes. The preset buttons apply the standard setup for MTG (60 cards, 7-card hand), the Pokemon TCG (60 cards, 7-card hand) and Yu-Gi-Oh! (40 cards, 5-card hand). Change the numbers and it works for any other card game or TCG.
Can I get the odds of drawing more than one copy?
Yes. Open “Advanced settings” and set “Copies you want to draw”, and the tool returns the chance of drawing at least that many. Useful when a combo needs two or more copies of the same card.
How much does running 1 copy versus 3 copies change my odds?
Switch “Copies of the card in the deck” between 1 and 3 and compare the results directly. In a 40-card deck with a 5-card opening hand, 1 copy gives about 12.5% while 3 copies give about 34% — every extra copy raises the opening-hand rate substantially.
How do a 40-card deck and a 60-card deck compare?
With the same number of copies, a thinner deck means each copy makes up a larger share of the library, so your odds of drawing it go up. Swap “Deck size” between 40 and 60 to see the difference the deck size makes.
What is the expected turn?
The average number of turns it takes before you draw the card. Real games swing either way, but combined with the turn-by-turn cumulative probability it gives you a reliable planning number.