I am trying to prove to a friend that a video game's drop rates are not what they say they are. However, it's been a while since I've taken a statistics class and have been unable to figure this one out.
How does one calculate an increasing success chance of 3% per drop chance? For example, my friend has 'rolled' 20 times and is now at a drop chance of '60%'. What is the chance that this item should have dropped by now?
These horrendous drop rates just recently started appearing for us.
I did the calculation below (formula is in column C). But, I am afraid it is not correct.
If the initial drop rate was 3% and the drop rate goes up 3% at each failure, then the probability of at least $n$ failures is $\prod_{i=1}^n (1-0.03i)$. This $\prod$ symbol means you multiply each of the numbers in the range, so for $n=3$ it is $0.97 \cdot 0.94 \cdot 0.91$. Consequently the probability of less than $n$ failures is $1-\prod_{i=1}^n (1-0.03i)$. For $n=20$ the product is about $2.6 \cdot 10^{-4}$, so your friend had about a 0.026% chance to have this string of bad luck.