User blog:Kevadu/Drop propability and the curse of long tails

Let's suppose a certain drop has a 3% chance. Fairly typical number, right? Of course if there are a million people playing a game even with a 3% drop chance that still means approximately 30,000 people will get that drop on their first try. But what about the opposite situation? How many drops does it take before there's a 3% chance of not getting it?

Well if the drop rate is x then then odds of not getting the drop after n runs is (1-x)^n. So if x is 0.03 and you want that formula to also equal 0.03 then n has to be about 115. Think about what that means for a second: On average for every person who gets the drop on their first try there's somebody else who won't get it after 115 tries. This sort of phenomenon is the result of what is known in statistics as a "long tail". The probability distribution may approach zero as n gets larger but at the high end it actually does so very slowly.

These long tails are why drops are such fucking bullshit. In any other situation if somebody took 1 try to do something and somebody else can't do it after 115 tries you might assume that the second person was incompetent. But this is pure dumb luck and these two situations are equally probable. If you're in the second category there is literally nothing you can except pray to RNGesus.