What does prized mean in the Pokémon TCG?

At the start of a Pokémon game each player sets aside 6 cards face-down as prizes, which they take one at a time by knocking out the opponent's Pokémon. A prized card is unavailable until you take that prize, so important singletons getting prized can disrupt your strategy.

How is the prize probability calculated?

The 6 prizes are a random sample drawn without replacement from your 60-card deck, so the number of copies of a card among them follows the hypergeometric distribution. The chance at least one is prized is one minus the chance none are prized.

How likely is a single copy to be prized?

With one copy in a 60-card deck and 6 prizes, the chance it is prized is exactly 6 divided by 60, or 10%. The calculator generalizes this to any number of copies, deck size, and prize count.

Why does running more copies reduce prize risk?

With more copies in the deck, the chance that every single copy lands in the prizes drops sharply. For instance, the odds that both copies of a two-of are prized is far lower than 10%, which is why important cards are often run as multiples.

What is the expected number prized?

The expected number of copies in your prizes is simply copies times prizes divided by deck size. For a two-of in a 60-card deck that is 2 times 6 over 60, or 0.2 cards on average prized per game.

Pokémon Prize Card Probability

In the Pokémon TCG, six of your cards start the game face-down as prizes — and if a one-of you need is among them, your whole plan can stall. This calculator uses the hypergeometric distribution to tell you exactly how likely it is that one or more copies of a card get prized, so you can judge how many copies a critical card really needs.

How it works

The six prizes are a random sample drawn without replacement from your deck, so the number of copies of a card that land in the prizes follows the hypergeometric distribution. With deck size N, prize count P, and K copies of the card, the probability that exactly k are prized is:

P(X = k) = C(K, k) * C(N - K, P - k) / C(N, P)

From this the tool reports:

At least one prized — one minus the probability that zero copies are prized.
None prized — the k = 0 term, the happy case where every copy is in your deck.
All copies prized — the worst case, where the card is unavailable all game until you take those prizes.
Expected number prized — the mean of the distribution, equal to K * P / N.

Example and notes

A single copy of a card in a 60-card deck with 6 prizes has exactly a 10% chance of being prized (6/60). Run two copies and the chance that both are prized falls to under 1%, while the chance that at least one is prized rises to about 19%. The expected number prized for that two-of is 0.2 cards.

Worth keeping in mind:

Higher prize risk on a must-have card is a strong argument for running more copies or adding search effects that can dig past prizes.
Some cards let you look at or recover prizes; this calculator measures the starting risk before any such effect.
Pair this with the Pokémon Draw Probability calculator to balance how easily you draw a card against how often it gets prized.