Free trading card game drop-rate calculator. Define set size, pack composition, and rarity tier ratios; outputs probability of pulling a specific rare per pack and the number of packs for 50% / 95% certainty.
Built and maintained by Paul Clark, Redmoon Software
Use when designing pack composition for your indie TCG. Players will reverse-engineer the math; better to know your own odds first.
Math is the same as Magic's "to pull a mythic" calculators. This tool generalizes to any rarity structure.
A player needs to open 89 packs to have a 95% chance of pulling a specific rare card.
Each pack independently rolls a rare; P(specific rare) = rares per pack ÷ total rares in the set.
Number of packs needed for a given confidence: n = log(1 − P) ÷ log(1 − p). For 95% confidence, n = log(0.05) ÷ log(1 − p).
The math assumes packs are independent (Wonka golden-ticket model). Sets with anti-duplicate rules behave slightly differently.
Yes. It uses the geometric distribution. If your set uses guaranteed rare slots (no duplicates within a pack), the real odds are slightly different.
95% is a common design target — most players will hit the pull within that range. 50% is the "median" experience.
Pull rates are probabilities, not guarantees, so a 1-in-10 rare averages ten packs but individual luck varies widely. Reaching 95% certainty for a specific card can take roughly three times the average because random misses stack up.
No. Each sealed pack is randomized independently, so past pulls do not change future odds. The gambler's belief that you are due for a hit after a dry streak does not hold for booster packs.
Input
30 rares in set, 1 rare per pack, target 1 specific copy.
Output
~88 packs for 95% confidence.
P(specific) = 1/30 ≈ 3.33%. n = log(0.05) / log(0.9667) ≈ 88.
The calculation is a probability of missing: if a rare slot draws uniformly from a pool, the chance of not getting a specific card in one pack is (n−1)/n, and across k packs that compounds. The expected number of packs for a given confidence follows from that.
The result is usually higher than intuition suggests. Wanting a specific card from a 30-card rare pool at high confidence takes considerably more than 30 packs, because random draws repeat — the coupon-collector effect.
The model assumes a uniform pool and independent packs, and real products break both. Rarity tiers within the rare slot mean cards are not equally likely; print-run structure means packs from one box are frequently not independent; and many sets have collation rules that deliberately spread duplicates across a box.
Treat the figure as a floor for how many packs a card will cost, and compare it against the singles market. For a specific card, buying the single is almost always cheaper than opening to it — the arithmetic here is the clearest argument for that.
Games publish pull rates in half a dozen incompatible formats — guaranteed slots, upgrade rates, per-card percentages. How to convert each one into the calculator's two inputs, and when the independent-pack model stops applying.
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