Disney Lorcana rewards a smooth, consistent draw, and consistency is just probability you can measure. This calculator uses the hypergeometric distribution to tell you how often a key card appears in your opening 7 or by a given turn, with play order factored in.
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 7 cards. To find the by-turn figure the tool adds your draw steps: because the
player going first skips their first draw, by turn T they have seen 7 + (T - 1) cards, while the
player going second has seen 7 + T cards. The probability is recomputed over that larger sample.
This is exactly drawing without replacement from a shuffled deck, so the result is exact 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) it rises to roughly 52%. Comparing a 3-of against a 4-of with this tool is the fastest way to see how much consistency each extra copy buys you.
A few notes:
- The figures cover raw draws only. Lorcana’s alter-hand mulligan and any draw or ink-search effects raise your real odds above these numbers.
- Lorcana decks are a 60-card minimum with a 4-copy cap, but the calculator accepts any deck size so you can model larger lists.
- For prize-style or set-aside mechanics in other games, use the companion Pokémon and MTG calculators linked above.
Deck-building decisions the math can answer
How many copies of a key card do you need?
The most common deckbuilding question is whether a card warrants 3 or 4 copies. In a 60-card deck:
| Copies | Chance in opening 7 | Chance by turn 3 (going second) |
|---|---|---|
| 2 | ~22% | ~30% |
| 3 | ~30% | ~41% |
| 4 | ~40% | ~52% |
If the card is your win condition or a critical 1-drop, the jump from 3 to 4 copies meaningfully raises consistency. For a situational answer card, 2 copies often suffices.
Evaluating combo pieces
When two cards must appear together, the joint probability is lower than either alone. If each card has a 40% chance of appearing in your opening hand independently, the probability of seeing both is well under 40% — considerably less when the sample is small. Use the calculator for each piece, then understand that the real “both in hand” probability is the product of roughly the individual draws minus overlap. Typically, combos requiring three specific pieces in the first few turns are inconsistent enough to build around alternate win conditions.
The alter-hand adjustment
Lorcana’s alter-hand mechanic (shuffle back any number and redraw those cards, no penalty) is arguably the most powerful mulligan in any major card game. It means your effective opening-hand consistency is noticeably higher than the raw hypergeometric figure. As a rough rule of thumb:
- If the raw probability of seeing at least one copy by turn 1 is 40%, post-alter it may be closer to 55–65% depending on what you return.
- Cards you would keep on their own (high-value 1- and 2-cost cards) cannot be traded back without losing them, which limits how much you can dig for a single specific card.
Use the raw figure here as a conservative floor and expect real-game consistency to be higher.
When to run more than 4 copies (via similar effects)
You cannot run more than 4 copies of a named card in Lorcana, but you can supplement consistency with cards that share a function. If you rely on early ink production and your key inkable card has only 4 copies, add inkable characters with similar cost curves. The calculator helps you see how thin 4 copies across a 60-card deck really is by turn 2 and whether supplementing with lookalike effects is worthwhile.