I'm trying to calculate the chance that an item will drop in the game I'm playing, or a similar event will happen. For a while I thought
100 – (chance it won't happen)^n * 100, was the corrent equation, where n is the number of times I've killed a monster. Then I realized, when you get, let's say up to 50%, then the chance would be 50%, then 75%, then 87.5, etc. meaning that I messed up.
My question is, what would the proper equation be. I've done some expermenting and found that 100 – (chance it won't happen)^(n^2) * 100 may be the correct equation. is this correrct?
BTW the game is called terraria, but that doesn't really matter with this.
EDIT: to be clear, the chance that the item will drop does not increase every time it's killed, it's always a certain chance that the item is dropped.
I used logic to realize that if you have a certain chance, let's call it a 50% chance that it'll drop, that means every time I kill it, it's 50% chance that it'll drop. However, I can use the idea that the chance of it NOT happening will "decrease" because the chance for it to not happen twice is, 0.5 time 0.5 or .25.
The problem I was noticing, that you would have to worry about the previous values in the graphed equation, so that chance # 100 doesn't just worry about the 1st chance, but also 2 through 99.
Best Answer
If at every time you kill a monster an item may appear let's assume it does appear independently of the previous number of monsters you killed then the probability is just fixed $p$
the probability that at least an item will appear after n mosters were killed is given by $$1 - (1-p)^n $$
If you assume $p = 50 \%$ then you can compute some numbers
$P(\text{ no item after 10 rounds}) = 1 - (0.5)^{10} = 0.9990234375$