Consistency wins Pokémon TCG games, and consistency is just probability in disguise. This calculator uses the hypergeometric distribution to tell you how often a specific card — a key Pokémon, a Trainer, or an Energy — shows up in your opening hand or by a given turn in a 60-card deck.
How it works
With a deck of N cards holding K copies of your card, the probability that a draw of h cards
contains at least need copies is:
P(X >= need) = 1 - sum over i from 0 to need-1 of [ C(K, i) * C(N - K, h - i) / C(N, h) ]The opening hand is always 7 cards. To compute the by-turn figure the tool adds your draw steps:
the player going first skips the turn-1 draw, so by turn T they have seen 7 + (T - 1) cards,
while the player going second has seen 7 + T cards. The probability is then recomputed over that
larger sample.
This is drawing without replacement, which is exactly what shuffling and drawing from a deck is — so the result is exact, not an approximation, for raw draws.
Example and notes
In a 60-card deck running 4 copies of a card, the chance of opening with at least one is about 39.9%. By turn 3 going second (10 cards seen), that climbs to roughly 52%. Seeing those numbers side by side helps you decide whether four copies is enough or whether you need search cards to bridge the gap.
Things to remember:
- The math covers raw draws only. Search and draw Trainers raise your real odds well above these figures — use the calculator as a baseline.
- The opening-hand reshuffle for a no-Basic hand is not modelled; it slightly changes the cards you ultimately see but not the underlying draw odds for a single shuffle.
- For questions about cards being stuck in your prizes, use the companion Pokémon Prize Card Probability calculator.