I am playing a game in which I need to earn 171 unique items to earn a trophy. There is a guaranteed drop of one item after every match, and I can get duplicates. Each item has an equal chance of dropping after every match, implying a 1/171 drop rate for each item. How many matches will I have to play, on average, before I collect each unique item given that I earn one every match?
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There is an entire tag devoted to this question as well as a Wikipedia entry https://en.wikipedia.org/wiki/Coupon_collector%27s_problem about it. – heropup Sep 27 '21 at 06:24
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Right around 382. See https://en.m.wikipedia.org/wiki/Coupon_collector%27s_problem – QC_QAOA Sep 27 '21 at 06:24