Dungeon Loot problem

[Rongway]

the real problem is not the loot drop system, but they way loot is distributed. Boss 1 has this list of loot, boss 2 drops these items in particular, final boss has pants and chest piece. Accessories drop from random chests with a chance of getting some other junk.

See the problem? The gear drop is RNG, but the place where the loot drops is not. I am no math expert but having all loot drop randomly from any boss with no chance of getting repeats and having the final boss drop 2 pieces would be a better way to get things done.

I'll explain this with some simplified numbers so we don't end up with a mess of alphabet soup.

Say there are three bosses. Boss 1 drops 1 of 4 items. Boss 2 drops 1 of 4 items. Boss 3 drops 2 of 8 items. If you want a specific drop, the probability of seeing it on a given run is 1/4.

Now say we're in a different universe where they all share the same loot list and repeat drops are not allowed within the same run. If you want a specific drop, the probability of seeing it on a given run is 1/16 that you will see it in the first chest, 15/16 x 1/15 that you will see it in the second chest, 15/16 x 14/15 x (1/14 + 13/14 x 1/13) that you will see it in the final chest. This adds up to 4/16, or ... 1/4.

So overall, the probabilities are equal. But let's consider some conditional probabilities.

The specific piece you want drops from the first chest in the original universe. It has a 1/4 chance of dropping. You beat the first boss and don't get the item you want. The probability that it will drop from the other chests is 0%; you can leave now and start over.

In the second universe, when you start the run there is a 1/4 probability that you will see the item you want. If you beat the first boss and it doesn't drop, the probability that you will still see it on the current run is 1/15 + 14/15 (1/14 + 13/14 x 1/13), or 3/15 = 1/5. If it doesn't drop from the second chest, the probability of seeing it in the final chest is 1/14 + 13/14 x 1/13, or 2/14 = 1/7.

So while the two universes have the same overall probability of the piece you want dropping, the first universe has an advantage in that if the item you want is from the first chest, and you can restart after the first boss, you have a 1/4 chance of it dropping per boss battle. In the second universe, the probability that you will see it during a run, given that you have not seen it in the current run yet, drops with each boss. First 1/4, then 1/5, then 1/7.

If the item you want would drop from the final chest, you have to fight all three bosses every time for a 2/8 = 1/4 chance of getting what you want. In the second universe, you don't always have to fight all three bosses, but as before, whenever you beat a boss and don't see what you want, the probability that you'll still see it from one of the remaining bosses decreases.