🎲 Probability Calculators

Run the numbers

How often will you open with your key card? What are the odds it's stuck in your Prizes? Find out instantly.

Opening hand odds

Chance to have a card in your opening 7.

Copies in deck Want at least Deck size Hand size

Mulligan odds

Chance your opening 7 has no Basic Pokémon.

Basic Pokémon in deck Deck size

Prized cards

Chance that copies of a card end up in your Prize cards.

Copies in deck Prize cards Deck size

Draw by turn

Chance to have seen at least one copy by a given turn (opening hand + draws + extra cards from draw effects).

Copies in deck By your turn # Extra cards seen Deck size

How these numbers work

These calculators use the hypergeometric distribution, the math of drawing cards without putting them back. Both players draw a card at the start of every turn, including the very first turn, so by your turn N you've seen 7 + N cards. Prize cards are set aside at random, so they don't change the odds for the cards you draw.

Real games include searching, shuffling and mulligans, so treat these as a solid baseline rather than exact predictions.