Photocard Collection Calculator (how many albums for the full set or one card)

How it works

Assumes every card in an album is drawn at random with equal chance and independently (the coupon-collector model). Full set: the chance of having all N cards after a albums is computed exactly step by step (each draw adds a new card with probability (N − cards held) ÷ N); the expected number of albums is Σ P(set not yet complete after a albums). With one card per album and none held this equals N × (1 + 1/2 + … + 1/N). One specific card: each album misses it with probability q = (1 − 1/N)^k, so the expected albums are 1 ÷ (1 − q). Real albums may have rarer cards or fixed ratios, which this model cannot know; trading duplicates with other fans lowers the real cost.

FAQ

Why is the full set so expensive?

The last few cards take the longest: with 8 cards, after you have 7 each album has only a 1-in-8 chance of the missing one. On average a full set of 8 needs about 21.7 albums.

Does buying more versions of the album help?

Only if each version has its own separate card set. Then treat each version as its own set and add the results.

Checked 11 Nov 2026. Coupon-collector problem: W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. (1968), ch. IX; exact distribution by a Markov chain over the number of distinct cards held.