0

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%

joriki
  • 238,052
Keanu Concepcion
  • 11
  • 2
  • 1
    What do you mean by "exhaust" and how do weights change? – Abdullah Ali Sivas Jan 09 '20 at 21:10
  • I apologize for the wording. I mean how many rolls does it take until I get at least 1 of all items?

    As for weights, I first want to know what the distribution is if the weights don't change. And if the weights change to 0 after being picked up n times

     – Keanu Concepcion Jan 09 '20 at 21:15
  • See https://www.mathpages.com/home/kmath047.htm for fixed weight case. It answers your question a little bit more generally. – Abdullah Ali Sivas Jan 09 '20 at 21:53
  • Thank you, upon reading it fully it does seem to answer my question in a more general way however I get confused on the use of variables L and s(N,k). Could you help me understand it?

    I can't seem to understand the difference between L and kth partition and I don't understand what s(N,k) means

     – Keanu Concepcion Jan 09 '20 at 22:10

0 Answers0