I'm trying to create a equation simulating the gacha probability of a game. Here are the rules:
- From attempts 1-50, the probability of getting a unit is 2%
- From attempts 51+, this probability increases by 2% every attempt, so it's 4% at 51, 6% at 52 and so on.
I want to create an equation that represents my accumulated probability of obtaining one or more copies of this unit given x attempts. So far, my equation looks like this:
There is an issue with this equation, which is that after 50 attempts, I assumed that the accumulated probability is (98%-2%×n)^x where n is the no. of attempts after 50, when the correct equation should be (98%)×(98%)×...×(98%-2%×n). I don't really know enough about equations to solve such a relationship between the x and y values, so can anyone help me out?