I know there's gaming stackexchange for gaming questions, but I believe this is purely maths related.
I'll try to avoid using game jargon and keep it simple. I'm collecting keys in game, each key taking a fair bit of time to obtain. They open a chest, which generates one random reward from a predeterimed table. On the loot table, there are five different armor pieces, each with a chance of 1/1000 to obtain. The catch is, because of game's inventory limitations, I can't open the chest every time I get a key and just get the five armor pieces that way - I have to do big openings of multiple keys at once. If I don't get a full set, but, for example, 4 out of 5 pieces, it would limit the speed of obtaining future keys.
Which is why I would like to count an optimal amount of keys to have to get the full set at once. Is there a set method or a formula for similar problems?
If the above explaination is too convoluted, I can try to further simplify it if needed.
from Hot Weekly Questions - Mathematics Stack Exchange
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