"Though these numbers aren't actual, he characterizes the system like this: the first time you kill a monster, you have a
16% chance of getting the item. The second 32%,
third 48%, and this progresses to 100%. But he warns "it also got rid of all of the good streaks and we had to raise the base drop percentage higher."
-Christian Nutt gamasutra article.
Why in this day and age are there still
completely random drops to begin with?
By design this makes the player feel like he's not making any progress by grinding.
Let the op know after each kill with a bar or a number that his
chances of obtaining the said item is
approaching 100%
Another way to do it is just to give a lot higher
chances of drops but split the loot into parts like in monster hunter.