Arcane Collector

Sealed packs of the collectible card game Arcane: The Congregation have a \(\dfrac{1}{8}\) chance to contain one of the 15 distinct mythic cards, chosen at random. If a pack contains a mythic card, each of the 15 mythic cards is equally likely.

If each pack of Arcane: The Congregation is independent of all other packs, what is the expected value of the number of packs needed to obtain at least one copy of each mythic card? Round your answer to the nearest integer.

Note: The coupon collector problem page contains an approximation that makes the solution easier to compute, and the approximation is sufficient to obtain the correct answer.

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