So this is a probability/statistics problem that I got from playing a video game called World of Warcraft. I only have a basic knowledge of probability and statistics so I was wondering if anyone could help me to a solution.
Basically in the video game there are "legendaries" that you can acquire based on a hidden probability. Every time you partake in an activity, you get a chance of getting a "legendary". There is a set number of legendaries but having more or less does not affect the chances. On top of that you can only acquire one legendary at a time.
The makers of World of Warcraft implemented a system called "Bad Luck Protection" that basically "protects" people from having extremely bad luck and long periods between getting legendaries. Every activity you do without getting a legendary increases your chances until you finally get one and the probability resets back to the original value.
Now there are multiple activities you can do to get a chance at these legendaries but each one gives a different amount of bad luck protection.
My primary goal is to find out how one can calculate how much each activity gives in terms of bad luck protection. I would be given a lot of data that lists how many of each activity a player took part in before they got a legendary.
Again I'd like to reiterate that I am not great at probability and I'm not even sure there exists an algorithm to solve this problem but really wanted to ask somebody. Thank you!