Pokémon TCG Draw Odds Calculator
Pokémon TCG draw odds calculator: exact chances to open with a card or draw it by any turn, with mulligans and Prize card odds.
How to use the draw odds calculator
- Set up your deck. A standard Pokémon TCG deck has exactly 60 cards. You draw a 7-card opening hand and set aside 6 Prize cards. Enter how many Basic Pokémon your deck runs.
- Add the cards you want. Enter how many copies of each card are in your deck and how many you need, and tick Basic Pokémon if it is one. You can add up to four cards, and the main result is the chance to have all of them.
- Pick a turn. You get your odds in the opening hand and by the turn you chose, plus a table for every turn up to turn 10.
Each card also gets its own breakdown, including its Prize card odds.
How the odds are calculated
Drawing from a shuffled deck is drawing without replacement, which follows the hypergeometric distribution. The chance of exactly k copies of a card with K copies in an N-card deck, when you've seen n cards, is:
P(k) = C(K, k) × C(N − K, n − k) ÷ C(N, n)
C(a, b) is the number of ways to choose b cards out of a. The chance of at least one copy is 1 minus the chance of none. For a 4-of in a 60-card deck, that's 1 − C(56, 7) ÷ C(60, 7), or 39.9% in your opening hand.
The calculator also follows three game rules:
- Mulligans. A hand with no Basic Pokémon is revealed, shuffled back and redrawn, so the calculator only counts hands with a Basic. Untick the box for the plain numbers.
- Turn draws. You start each turn by drawing a card, so by turn 3 you've seen 10 cards: your 7-card hand plus 3 draws.
- Prize cards. Your 6 Prize cards come off the top of the deck after you draw your hand. You don't know what they are, so they don't change your chance of drawing a card by a given turn. They only decide how often a card gets stuck there.
The math is exact, not simulated.
Quick reference for a 60-card deck
Chances of seeing at least one copy of a card, without mulligans:
| Copies | Opening hand | By turn 1 | By turn 3 | At least one prized | All copies prized |
|---|---|---|---|---|---|
| 1 | 11.7% | 13.3% | 16.7% | 10.0% | 10.0% |
| 2 | 22.1% | 25.1% | 30.8% | 19.2% | 0.85% |
| 3 | 31.5% | 35.4% | 42.7% | 27.5% | 0.058% |
| 4 | 39.9% | 44.5% | 52.8% | 35.1% | 0.003% |
Basic Pokémon count and mulligans
The more Basic Pokémon you run, the less often you mulligan. Here's the chance that a 7-card hand from a 60-card deck has none:
| Basic Pokémon in deck | Chance of a mulligan |
|---|---|
| 8 | 34.6% |
| 10 | 25.9% |
| 12 | 19.1% |
| 16 | 9.9% |
| 20 | 4.8% |
Each mulligan also lets your opponent draw an extra card, so a low Basic count has a real cost.
Tips
- Combine your outs. If any of several cards does the job, add their copies together in one row. A card with 8 total copies shows up in 65.4% of opening hands, against 39.9% for a single 4-of.
- Mind your 1-of cards. A single copy is prized 10% of the time, so a plan that needs it fails about 1 game in 10.
- Check what you need 2 of. Opening with 2 copies of a 4-of happens only 6.3% of the time, and 12.6% by turn 3.
Frequently asked questions
What are the odds of drawing a card in your opening hand?
With 4 copies in a 60-card deck, you have a 39.9% chance of at least one in your 7-card opening hand. With 3 copies it's 31.5%, with 2 copies 22.1% and with 1 copy 11.7%.
What are the odds of a card being prized?
A single copy ends up in your Prize cards 10% of the time, because 6 of your 60 cards are prized. With 4 copies there's a 35.1% chance at least one is prized, but only about a 1 in 32,500 chance all four are.
Does going first or second change my draw odds?
No. You draw a card at the start of every turn either way, so by your turn 2 you've seen 9 cards. Going first matters for other reasons: that player can't attack or play a Supporter on their first turn.
Do Prize cards change my chances of drawing a card?
Not unless you know which cards are prized. They're random cards from your deck, so your chance of drawing a card by a given turn depends only on how many cards you've seen.
How does the calculator handle mulligans?
It only counts hands that contain at least one Basic Pokémon, because you'd shuffle any other hand back and draw again. This slightly lowers the odds for cards that aren't Basic Pokémon and raises them for cards that are.
Can I calculate the odds of drawing two different cards?
Yes. Add each card as its own row, and the main result becomes the chance to have all of them. The chance to open with at least one copy of each of two 4-of cards is 14.5%.
Sources
- Setup, mulligan and turn rules: the official Pokémon TCG rulebook and Wikipedia's Pokémon Trading Card Game article.
- First-turn Supporter rule: PokéGuardian.
- Deck size and copy limits: JustInBasil's deck building guide.
New to the game? Read how to play the Pokémon TCG or try the pack opening simulator.