A sharp correction of common probability myths that uses rigorous simulations to expose errors in community data. It’s a rare example of a creator using actual math to cut through the guesswork of game mechanics.
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Deep Dive
R.E.P.O Cosmetics Probabilities And Farming StrategiesAdded:
This entire video was recorded slightly after the update 4 dropped. So, the numbers are going to be different since they changed the odds of the crates. The logic and the mistakes that I found still stand though, and throughout the video I'll be showing updated data as I speak with the older numbers if I make sense. The only reason why I'm keeping the old footage is because I spent a lot of time on it. The video just couldn't be edited until now. So, I hope you guys understand that it won't be too confusing. Before you watch this video, I just want to inform you that this video is mainly for people that want to understand how game mechanics work behind the scenes and also for the people that enjoy math and probabilities. If you're only here to know how to farm cosmetics, you can skip to the end of the video. Today, I wanted to make a video about the chances of a crate spawning because in my overview, like I said, I was going to make a video about it since the math is actually very complicated. And also because the wiki actually has a lot of things wrong and I think poorly explained, but I assume that this will be fixed in the future.
I'll explain exactly how the crate spawn work as well as the math behind the probability and how it should work. And on top of that, I did simulations from level 1 to level 16 100 million times to have some accurate numbers because we love Monte Carlo simulations. This video will be very technical, so this is very for people that are interested in math.
And also, feel free to correct me if I'm wrong, but I spent a lot of hours doing this, so I'm pretty confident in my results. At the end of this video, I'll also be covering some strategies to get the crates you want, so stay till the end. The way crate spawn works is purely on level and quickly level 1 to 5, you have one crate. Level 6 to 10, you have two. And level 11 plus, you have three crates. There are things on Unity called animation curves. It's basically a graph where you give it a parameter and um depending on where that X is, it's going to give you the Y value. So, using the formula number of level completed modulo 5 divided by 5, it returns you the parameter. So, example here, we're at level 2. So, we have one level completed, meaning 1 modulo 5 equals 1 divided by 5 equals 0.2. So, my parameter is 0.2, meaning my value is 0.28 * 100, so 28% basically. They use this formula because after every five level, it resets, giving you a full crate that has a max odds in a new crate. Anyways, this 28% is basically the odds of spawning a crate. And if this 28% is hit, we go into a second algorithm with the same parameter 0.2 that we had earlier. Every crate variety also has an animation curve with these parameters. So, the 0.2 for example on the common crate is 0.46, uncommon 0.3, rare 0.13, and ultra rare 0.03. The game then takes the first one, which is a common, generates a random number from zero to the number that we just had multiplied by 100, which is 46, and then save that value. Let's say we rolled 11.
The next step is taking a second tier and rolling against it, meaning example uncommon was 0.30, meaning it's 0 to 30.
If I roll for example 10, it's smaller than 11, so the common still wins. Now, let's say the rare was 0.13. If we multiply by 100, it's 13, so the roll is 0 to 13, excluding the 13, so the max value would be 12 because Unity random range always include the first number and exclude the last one. But, anyways, we get 12, it's bigger than common, so now rare win, meaning the crate is now rare, but we still have the ultra rare to do. The only issue is that the ultra rare value is lower than the rare's current value, so it cannot be rolled at all. So, it is basically guaranteed to fail. Keep in mind that this cannot fail as if you even roll the lowest number, which is zero, it would guarantee a common crate. Now, let's add the second and third crate into the algorithm. As you remember, the parameter reset every five level, and there are methods that make it so basically after level five on level six, one crate will have the max parameter, which is um 0.6, as well as a second crate that has a chance to spawn with the minimum parameter, which is zero and 0.20 chance of spawning. So, then if you go down the line until level 10, it's the same thing that happens.
Level 11, two crates at 60% chance of spawning and a new one at 20% chance of spawning. You have to keep in mind that this stacks at three crates maximum.
Past level 15, there's nothing that changes. So, 16 and plus is basically always guaranteed three max crates.
Every time that you have a level that has no crates at all, it adds a penalty buff, which is a 25% chance that is added on the chances of having a crate spawning. So, for example, level one, 20%, you don't get a roll. Well, level two, instead of being 28% chance, it's going to be 53% chance. If you have multiple crates, this roll applies for every crate until it succeeds. This 25% penalty buff also stacks. So, if you have two level without crates, it becomes 50%. There are a lot of things that I don't understand on the wiki's math. But, for example, on level six, they show a total line and then below it two individual crate lines, right? One with 60% and one with 20%. The individual crate line shows rarity percentage like 38.87%, 37.03, 20.83, and 3.27. These are correct conditional probabilities. And here's where the confusion and problem start. Um, the individual crate lines are showing conditional odds, meaning given that the crate spawned, what are the chances of the each rarity, right? But, the total line is supposed to represent the overall odds across the whole level. And these two things are completely different scales and cannot mix in the same table without making it clear which is which. So, these two in the same table is very confusing. But, on top of that, there are things that I don't understand. If someone wants to explain to me, if you guys are geniuses in math, but um, I'm pretty sure this is wrong. I was very confused about the 2.22% for the ultra rare. And I think the correct way to calculate this is um, to actually account for each crate independently. Crate one has a 60% chance of spawning and a 3.27% chance of being an ultra rare chance if it spawns.
So, its contribution is 60% * 3.27, which equals to 1.962%.
Crate two has a 20% chance of spawning with 0% chance of ultra rare, so when contributes nothing. Combined that gives about 1.96%. But the wiki shows 2.22%, so I assume they got there, um, by taking the chance from the crate one, multiplying it by 68%, which is a total spawn rarity across both crates added together. So, 3.27% * 68% = 2.2236.
That's probably where the 2.22 comes from. And if it's the case, it wouldn't be how probabilities work. You cannot add independent probabilities like that in the same combined chances. And also, for level seven, for example, the wiki gets 2.34 for ultra rare. Working backwards, this appears to be calculated as stake crate one's conditional ultra rare, 3.27, and crate two conditional ultra rare, 0.02, and multiplying the whole thing by the combined spawn rate of 71.2. That gives roughly 2.34. Um, this compounds both errors. They're adding conditional probabilities from different crates as if they're the same unit, then multiplying by a number that isn't a valid probability. The way I did it, and also the way that the math added up as well when I did my simulations, is basically for each crate, multiply its spawn chance by its conditional rarity chance. That gives you the absolute probability per crate. Then to combine them correctly, you use the complement rule, one minus the product of each crate's chance of not giving you that rarity. And written out, it looks like this. So, one minus one minus spawn chance times rarity chance, and then you do this for how many rolls there are.
This correctly handles the fact that on some runs, multiple crates could both spawn and both give you the same rarity, which the simple additive method would double count, if I make sense. For level 16, which has three crates, all at 60% chance, ultra rare works out to about 5.81% using this formula. Simply add three times 1.962% gives 5.886%, which is exactly what I got in my simulated runs, compared to the wiki at 8.87%. All I want to say, basically, is that summing the chances isn't valid if the goal is to determine the chances of one or more of the rarities spawning.
It's also not valid if the goal is to determine the chance per crate of that specific rarity spawning. I meant to explain in detail because I want to be corrected if I'm wrong, of course. But now let's get back to my simulations that are exactly what my math actually gives me. For the ones that are curious, I basically rewrote the code of the class that has all this logic into a unit explorer script and I ran this 100 million times for every level from 1 to 16 using the same logic. Accumulated the data and put it in Excel sheet. So the first is out of all runs. If you play this level 100 times for example, how many times would you expect to see each rarity including all the runs where the crates never showed up at all. This is the true real-world odds basically. When crate spawned, assuming a crate is already sitting in front of you, what are the odds of each rarity? This is what the crates screen itself reflects basically. It ignored the fact that the crate might never have appeared in the first place. So I guess the true odds and distribution between the crates when it actually is guaranteed to spawn. And the total all runs, the overall odds of seeing each rarity at least once during the level. Combining all these crates together, this is the headline number basically, the one you'd use to compare levels against each other. And yes, it is normal that it exceeds 100%. The green category is basically what are your chances of seeing at least one crate of that specific rarity in your level. So probably the most important number, the one that makes the most sense. Down in the description of the video there will be my sheet with all the versions and all the chances on each version. So just take a look at it if you want to see the updated values.
There are three main ways to farm crates. The first one being obviously just play with friends, play with people. The more players you are the easier it is to get through levels and also finding all the crates. Just make sure to check in the saves or the vent system. The green crates can be pretty sneaky sometimes. If you don't have anyone to play with and you want to grind, you can also find a lot of lobbies in the public lobby section or also people in the official Discord.
Link will be below in the description.
The second and the third method are kind of more scummy I would say. It is really for people that just want to grind the cosmetics legitimately by abusing game mechanics. If you want the rarer crates, all you need is a save file that is at least level 16 for the best odds.
Basically, all you want to do is reset the level every time you don't have the crates that you're satisfied with. As going back to main menu and resetting the level just generate a completely new level. This way, if you find a yellow or pink crate, you can simply just collect them, finish a level, and if you have nothing, you can just do it again. This is a very effective way of getting all the rarer crates, especially ultra rare with the buff now, and also because there are only 31 total. The last method is more for the green and the blue crates. The best way to get them easily without playing too much is basically just resetting level one and two. You can simply start a new save at level one since the level is very linear, and you already have a 25% chance of finding a crate. If you don't find any crate, you can just do the only extract on the map.
And on level two, you'll have the level two base chance plus the 25% chance that is extra since you didn't get a crate level one. If you don't find anything level two, just die or reset to level one. And if you find one, just extract it, finish the level, and also reset to level one. There's not really any secret. These are just the most efficient ways of getting all the crates. So, yeah, I hope you guys enjoyed this video. If you did, please make sure to like and subscribe. I have a lot of more content that is planned, especially challenge runs, and also some special videos that you guys might enjoy a lot. So, yeah, until next time.
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