How to calculate hidden drop rate percentages in a video game? Say I am playing a game where killing a boss rewards a bag that has a chance to drop a certain item, the rarer the item, the lower the chance.
How would I go about calculating this by the process of running the dungeon over and over again, collecting the statistics of the drops I received within a decent accuracy range?
 A: Simply dividing the number of successful drops by the number of drops will give you a proportion. For example, 20 successful drops out of 100 drops is a 20% chance of getting the successful drop. This is the sample proportion.
You are correct that you will have to do it over and over, as any statistics you calculate are based on the sample, and you cannot have 100% confidence in them. You can, however, repeat it enough times to get a confidence level of 95%, 99%, etc. Also, if you know that the developers have a tendency to use nice numbers in their drops (1/32, 1/64, 1/2048, etc), you could use that to have more confidence in your answer.
This is assuming a few things, however:


*

*All drops are independent of each other. For example, in the game Overwatch, the odds of receiving the rarest tier of item increases every time you do not receive one. This would already be hard to calculate. Now imagine a system where each tier of item may add or remove the cumulative probability of the good drop. Calculating the percentage begins to border on impossible when you know less and less about the system.

*All drops are simply based on a drop percentage. For example, in the game Runescape, enemies may have a chance of dropping from the Rare Drop Table, as well as their own drop table. Some rare drops are shared by the enemy's drop table, as well as 'no drop' being shared by both, so without knowing the RDT's rate for that enemy it will be incredibly difficult to predict drop rates to a good confidence level. Other factors may include number of players attacking, items equipped (e.g Runescape's Ring of Wealth), or anything else the developer wants.


You should be able to perform a sample proportion confidence interval, that reads something like "I have 95% confidence that the drop rate lies between 0.79 and 0.81", where your sample proportion would have been 0.80 (in the middle). If this is a bit much effort, just use your sample proportion for a good estimate once you're happy that it's stable. At the end of the day, even if you eventually calculate that probability to be 0.5%, the drop rate doesn't guarantee a drop every 200 kills. Even with 2000 kills, the probability of receiving exactly 10 drops is 12.5%.
