“Entropy” system for common loottables

[Orangbo]

I call it entropy because of my experience in Path of exile, and hear it out since, while the general idea might seem bad at first, I’ve done my best to maintain the same level of pain through the farming process.

The idea is to equalize your drops, so that you don’t end up like the unlucky guy I met who had to do 2000 spy mission runs to get his ivara, which has around the same odds of randomly picking a specific atom out of all atoms in the observable universe (I did the math). I’m also in a similar situation which inspired this post, having pulled 5 ivara blueprints and, you guessed it, 0 ivara neuroptics. I’m fine with unique loottables such as lua spy and the eris mission that drops some 60/60 electric mods not having it, as those are in fact meant to be target farmed, but when a loottable affects more than 2 nodes, I’d operate under the assumption that farming those isn’t meant to take so freakishly long that you go through 2 mastery ranks from levelling melee weapons before you get the item you’re after.

First of all, in order for this to take in effect, you must “chain” your runs. My technical definition would be to be in the same squad for the duration of the farming session and to not play another mission unless you’ve played the chained mission at least 5 times, with the counter resetting every time another mission is played.

And now the meaty math part: each time your drops are rolled, the new droprates are also recalculated based on the original droprate. If that sentence had you shaking your head, I’ll give an example below if you want to follow along. Once you recieve a reward, the original odds of that result not happening, ie the chance of not getting that reward, is multiplied with the current odds of getting the reward itself and removed before being redistributed among all other rewards based on original % odds distribution. In other words, it lowers the chance of getting multiple rewards in a row and maintains whatever “point” system is used to choose those rewards.

Example time. Lets take a loottable with a 70-20-9-1 % split between item drop rates. We are looking for the 9% item.

On our first run, we, predictably enough get the 70%. We remove the 30% odds of it not doing that, which turns out to be 21% and hand it to the other rewards based on their original probabilities.

Our new split is 49-34-15.3-1.7, and we again roll the super common item. We take a look at the original table, see that it’s should be a 30% chance of failure, and take out the, this time, 14.7% chance of success.

Our new split, rounded, is 34.3-43.8-19.8-2.1. We now play and-holy moly-we scored the legendary item! Look at all that plat! The odds of that not happening in the original distribution is 99%, so we take that out and redistribute it to all the other drops, and the new split, rounded, is 35.7-44.2-20-0.02.

Now, this is the main issue with this system: rare mods in the same pool as extremely common drops can be farmed more efficiently by quitting at this point. My counterpoint is that there are no mods in the previously mentioned “common” rotations that are worth all that much in practice, and there was still only a 2.1% chance of happening at the time. Additionally, I don’t know of any of those rotations that have these odds in the first place. However, if this still makes you nervous, we can apply less weight to the removal of percentage of more common items, say by dividing by one tenth of the original drop % chance, or by it’s square root, but I’d leave the specifics to someone other than me at 11:00 pm.

In any case, if we’ve gotten the hang of it, I’ll be using random.org and listing drops followed by the new splits as an example of how this will end. Since we’re going for the 9%, and it’s already at 20% chance to drop, we’ll say we decide to stick it and try to get the drop.

35.7-44.2-20-0.02

Got 70

25-46.3-21–0.12

Got 20

50-20.3-24.3-0.5

Got 9(yee)

65.5-24.7-2.2-0.7

And we’re done!

This process can be slowed simply by lowering the amount of % removed by some set fraction, i.e you remove a fifth of the amount, so if we get a 50% item we instead remove 0.5*0.5*0.2=5% of the chance. Looking at that simulation, I’d say it’s necessary, but I’ll leave the tweaking to those who have experience developing games.