Given a table of items with weighted probability, calculate the distribution of how many rolls it would take to go through all items.

Question

Here's my full question

Given a table of items with weighted probability, calculate the distribution of how many rolls it would take to go through all items if each item decreases in weight n times.

I'm currently trying to make a video game with a random chance mechanic and want to see how, on average, many rolls it takes to exhaust my item list if each item has less chance of appearing (or is taken out completely of the pool) after n times.

Below I have more detail concerning my item table.

Here's some more detail:

Image of Table

Item weight probability

doll_Common_05 250 14.07%

doll_Common_06 250 14.07%

doll_Common_07 750 42.21%

doll_Common_08 200 11.25%

doll_Rare_01 100 5.63%

doll_Rare_02 100 5.63%

doll_Rare_03 100 5.63%

doll_Rare_04 20 1.13%

doll_Epic_01 5 0.28%

doll_Epic_02 2 0.11%