As most of the grid is well aware, The Arcade Gacha Event is in full swing. We actually have some cute rings available there, but that is another post entirely. What I want to talk about is the disparity of rarity, in other words, why do I have a bunch of rare items but not the color/item I desire?
First off, for those unaware, Gacha (Gachapon to the Japanese) is basically a vending machine game. You pay to ‘play/spin’ and are given a prize at random. Random is always a relative term, for no computer algorithm is truly random, but I digress.
Basically, at the Arcade, each machine allows the vendor to set the percentage of distribution of rare items. Rare items are denoted by having the word ‘rare’ listed in their name. Since it is called in that fashion by the algorithm, only those items that are called rare are considered rare by the machine.
As you read this, you may be saying the following:
But why do I have five rare hamster accessory sets and no fawn hamster? (please substitute any item you have been trying to get, and their rare counterpart)
Ok, so I’m going to explain why, but I’m going to make an assumption. I’m going to assume that the gacha algorithm applies the rare percentage to each rare item. So if there are 2 rare items, they are each assigned that percentage chosen by the vendor.
If there is one rare item at 5%, that means you have a 95% chance of getting a non-rare item per spin. But you WANT a particular non-rare item, don’t you?
The nice thing about discrete probability is that all the individual probabilities have to add up to 1 (or 100%). This means the sum of all the individual probabilities must add up to 1. I will use the following formula:
aY + bX = 1
Where a is the number of rare items, Y is the percentage assigned to a rare item, b is the number of non-rare items and X is the percentage of getting each non-rare item. We will be solving for X.
So let’s look at an example.
From what I can tell, everyone and their mother is going wild over these hamsters. The thing is, everyone wants a panda or a fawn. So let’s see why that is so hard to do.
I checked this machine, the rare percentage is 5% and there are two rare items. So you should get an equation like this:
(2)(0.05) + 24X = 1
So X = 0.0375. That means, there is only a 3.75% chance at getting a panda hamster on a spin. Hence, in any particular spin, you are more likely to get an accessory item than a single particular hamster. Though you are more likely to get a hamster in general in comparison to an accessory set.
Let’s look at another example. Having a hard time filling up that last spice or your rack?
Again, we have two rare items at 5% each in a spin. Another way to look at this is you have a 10% chance of just getting a rack. So we have
(1)(0.1) + 18X = 1
So X = .05. Therefore, you have a five percent chance on any individual spin to get a particular spice, so you might see more racks than you see the absolutely last spice you need.
I actually saw someone state in group chat that Glam Affair is lying about their rare skin being rare. In fact, I can prove that it isn’t really rare at all, but non of the others are rare in comparison either.
This machine has one rare item at 10%. So:
(1 )(0.1) + 9 X = 1
X = 0.1. So this means, for each spin, there is equal probability to get any skin. Probably the most fair machine in the whole joint.
Anyway, here is a TP to The Arcade, hopefully probability will be on your side!