so I see you've been lured in by the question posed in the title well I suppose there's no need for a longwinded intro today let's cut right to it this is the longest possible run in Lethal company Richard hit that intro the first question a lot of you might be wondering is wait is there a longest possible run in Lethal company the main gameplay Loop of this game is going into randomly generated levels Gathering as many items as you can and selling those items to try and beat a set quota if you meet the quota you're given another higher quota and three more days to meet it and this goes on forever there is no end credits there is no winning you just keep keep going to try and beat your high score but if the quota keeps increasing every time the question is will it ever grow to a point where it's so big that you could never meet it no matter how well you did in order to find out you're going to need two things a little bit of skill and a little bit of luck if you think you're going to reach this Mythic Max quota by messing around getting into Shenanigans and fleeing at the first sight of danger guess again you got to be on your A game you got to go into that factory like your Mr Clean and leave No Loot unlooted if you're skilled enough to get every single piece of Loot on a moon every single time you just might stand a chance the operative word of course being chance even if you play Perfect ly get all the items and never die there's a ton of variance in the number of items that can spawn how much those items are worth even what your next quota is so in order to find the longest possible run we also need to assume that you have perfect luck however unlikely that may be with that in mind the plan here is pretty simple we can easily calculate what each successive quota will be and we can calculate the maximum amount of money that you can make per day then all we need to do is figure out where those two curves intersect let's start with the quota because it's a lot easier every time you start a new run your first quota is 130 bucks after that your quota increases based on this formula where X is the cycle that you're currently on you'll notice that this formula is quadratic the little part with the x is raised to the second power this is how we can tell that there is a maximum possible quot the amount of money you're bringing in each day remains constant your intake increases linearly but the quota will increase faster and faster and faster the longer you go eventually growing to a point where you can't possibly reach it you'll also notice this uh this situation over here this whole thing going on that's too many letters for a math equation what the what the hell dude this is the part that contributes to the randomness of the quota to make the game a little less predictable every time the game gives you a new quota it generates a number from 0o to one converts that to a multiplier between negative. five and 0.5 using this normal distribution curve and then uses that as a random multiplier for your next quota sounds pretty confusing but remember in our case we're assuming that you have the best possible luck meaning you will always get a low roll on the quota increase and this chart winds up looking a little more like this so the final equation for your quota ends up looking like this with that in hand we can create a table to find each successive quota that you will need to beat and that that was the easy part our next task is to figure out how much money you could possibly make in a single 3-day cycle to do so we need to assume three things first we need to assume that each Moon spawns the maximum number of items every time every Moon has a range of the total number of items it can spawn and if you randomly get anything less than the the max you're basically screwed you got to start over second we need to assume that all of the items are the most valuable type all right I don't want to see any Metal Sheets up in here we need stacks on stacks on stacks of gold bars and nothing else or something else depending on the moon they all have different most valuable items and third even if you do find nothing but the rarest items those items also have themselves a range of how much they can be worth a gold bar can be worth as low as 102 bucks AKA literal garbage we're looking for that perfect 210 value so in summary to find the longest run we need to assume three things the max number of items spawn every day all of those items are the most valuable type and each of those individual items is at its maximum value and you actually have to get all of the items that's four things as an example experimentation can spawn anywhere from 8 to 12 items which can be anything from this list so if it happens to spawn 12 items every one of those items is a gold bar and each of those gold bars is worth $210 that that would be the absolute upper limit that is technically possible it's incredibly rare but it is possible if you do the same process for every single Moon factoring in the apparatus that you can find on all the factory moons worth an extra 80 bucks and the up to six beehives that you can find on select moons per day worth upwards of 150 each it turns out that the single moon with the highest possible daily earnings is Titan the items inside aren't crazy valuable the most expensive thing is a fancy lamp with 128 doesn't look that fancy to me and it doesn't have any hives but it can spawn a total of 38 items per day which is way more than any other Moon so it ends up working out as the best so in order to get the perfect run you need to go to Titan every single day rain or shine and find 38 fancy lamps and the apparatus every single day there's no other combination that's going to get you more than that but there's one problem you need to pay a $700 fee to go to Titan and when you first start you're dirt poor so you can't get to Titan right away of the moons you actually can go to March is the best with its 17 possible gold bars one apparatus and six beehives a day so in order to achieve this perfect run you need to start on March for your first 3-day cycle loot at least $700 but realistically loot as much money as you possibly can every single day and then every cycle after that go to Titan because of this strategy we actually need to adjust our qua formula a bit because we want to go to Titan as often as possible we need to sell at least $700 worth of loot every cycle so if the quota was ever less than 700 we should set it to be equal to 700 now we know the amount that you have to spend every cycle we can use the max value of each item acquired to figure out how much you make every single cycle but there's still one problem in this game it's basically impossible to be perfectly efficient with your spending the company won't accept half a lamp so you'll probably have to overspend a bit each time so we need to keep careful track of how many of each item we have at any given time and how we can best optimize spending them to hit the quota while still saving as much much money as possible for the next time as you can probably tell this is a lot to keep track of so I did what I do best I made a spreadsheet there's a lot here but starting from the left we have the cycle number that you're on the minimum quota based on the formula we talked about at the beginning and the amount that you'll actually have to spend to account for the Titan entrance fees for the first few Cycles then for the next section we have the total amount of loot you can acquire this is all your intakes on the first cycle over 3 days you should have 51 gold bars 18 beehives three apparatuses and zero lamps going forward after that you won't find any more gold bars or hives they don't spawn on Titan but you will gain an extra three apparatuses and 114 lamps every cycle if you're lucky then we need to find out how many of these items you actually need to sell to hit the quota for the first day you can cash in three gold bars and one apparatus to get to 710 just barely enough to get to Titan after that we're going to want to cash in lamps first since they're the most common resource and throw in some apparatuses to cover the extra cost to be the most efficient to find out how many lamps we need to spend we can divide the current amount owed by 128 the value of 1 one lamp and round any decimals down to find out how many lamps we need to spend to get as close to the quota as possible without going over then we'll use either an apparatus or a hive to cover the remainder we'll try to save as many gold bars and hives as we can till the very end to try and get a big burst to possibly put us over the final hurdle since they're not renewable then we need to add in one last section to keep track of how many of each item we have left after selling to meet the quota multiply each of those by their max value to find the total value of loot you've got on the ship after selling and whenever that number dips below zero that is the legendary quota that you cannot possibly surpass and now after all of that it's time to reveal the answer the maximum number of quotas that you can possibly complete in Lethal company is 37 after that even if you get as lucky as possible and do as well as possible the next quota will be $56,950 even if you sell all the gold bars and hives and apparatuses that you've been hoarding you'll still be1 19,000 780 short not even close this is why I didn't talk about things like overtime bonuses or better selling optimization sure you could probably save a couple hundred in the long run but you're going to need a lot more than a couple hundred if we plot the total amount of Loot on board versus the cycle number that you're on you'll see that for the first 2/3 of the Run you're sick didn't pretty increasing steadily until you have an alltime eye of $248,400 worth of lamps and gold on board your ship I mean this place is truly overflowing with lamps it is an excessive amount of lamps I dare I say too many lamps but after that you start having to sell at least 115 lamps per cycle more than the max 114 that you can bring in and at this point your bottom line gets real low real fast so there you have it the longest possible run in a lethal company would be clearing 37 quotas the highest of which would be around 52,5 74 anything higher than that is mathematically impossible if you play flawlessly and have perfect luck you can effectively beat lethal company in 37 Cycles now I could end the video here but I do have one lingering question this whole scenario relies on you being lucky but just how lucky would you need to be figuring this out is is not as easy as I thought but as you can see there's a lot of stuff that we didn't actually need for starters we assume that the quota needed to be as low as possible every time but we have a ton of stuff left over so clearly we didn't actually need it to be that lucky in those instances because the randomness of the quota is a multiplier getting unlucky at the beginning of the Run isn't that bad and for the first five runs you could can afford to get a little unlucky after that though you're definitely going to need that low5 multiplier based on my understanding of how this game generates that number you have a 5% chance of getting that low roll but you only need it on the last 30 Cycles the others you have a 50/50 chance of getting a multiplier low enough to not screw you over we also assumed that you needed a bunch of gold bars and beehives on the first cycle but we never ended up using most of them in reality you only need to get at least three gold bars and 10 hives or some other loot of equivalent value that's probably a lot easier to find now finding the odds of getting at least three gold bars Each of which only has a0 52% chance to spawn over the course of 3 days where you could have anywhere from 13 to 17 items per day is not easy to figure out look I like math more than your average fellow but this is a bit much so I tried to ask chat GPT to calculate it for me and it got super confused and started talking in circles for like 5 minutes until it randomly spit out the value of 3.51% I have no idea if this is right or where it got this from but as you'll see in a second this is probably the most likely part of the run and it doesn't really matter that much the real rare thing here is the lamps because as opposed to the gold and the hives we did end up spending every single lamp that we picked up to hit that last quota we literally had exactly enough kind of a crazy coincidence this means that we actually do need Titan to spawn 38 items 108 days in a row all of those items need to be lamp LS and those lamps need to be of max value that's a 1 in6 chance of getting Max items raise to the 108th power for how many days in a row we need this to happen times a 2.84% spawn rate for lamps raised to the 4,14 lamps that we need times a 1 in 164 chance for each lamp being max value raised to the 4,14 lamps factor in the 1/2 to the 5th time 12th to the 30th for the quota rolls and the 3.5% chance of getting those gold bars at the start and you'll find that the odds of all these pieces aligning just right to allow you to actually achieve this perfect run is 1 in 10 to the 13, 932 if that number is too big for you to comprehend good normally whenever I come up with a massive number like this in a video I like to find out the insane technical name for it and put one in 23 unilin skillion in the title but this number is too big for names you ever heard of the Google that massive number that you use to win arguments on the playground that's 10 to the 100th power insanely big this is 10 to the 13.9 th000 power the calculator that I use to figure this out Wolfram Alpha One of the most powerful calculators on the web that I know of whose whole thing is dealing with insanely large numbers looked at it and was like Hey Hey that that number you got right there uh yeah that's basically Infinity here's a little thought experiment for you say I have a Bowl the size of the whole entire universe and I fill that bowl with marbles the size of a single proton that is 10 to the 125 marbles over a Google marbles if you had the choice of trying to pick one lucky marble out of that bowl or completing this longest run in Lethal company which one should you pick if you picked a lethal company then you're a damn fool I mean clearly I chose this example for a reason because you have a better chance of picking that one lucky proton siiz marble 111 times in a row than getting this Lucky in Lethal company in fairness there probably are ways to lower this probability there's undoubtedly loads of combinations and permutations to get you to that 37 quotas that I haven't accounted for heck I had to redo these calculations for these odds like five times I wrote this part of the script at 1:30 in the morning on a Tuesday so I'm not entirely sure that even I have it correct I'm an engineer not a mathematician but if there are any math experts out there who want to take up the challenge of finding the true odds of getting a run any run that can pass 37 quotas I would be super interested to hear it I bet the actual odds are a lot better than one in 10 to the 13,930 though low enough to where a human could conceivably do it you know I somehow doubt it and there you have it the longest run in a lethal company that is technically possible is 30 seven quotas completed and if anyone ever claims to have done this then you can say with more certainty than anything else in the universe that they cheated Happy Hunting folks a huge thanks to all my patrons including Alakazam Ethan Fano Sheri and Mark star Joy big dog tie for to win the boss killer 94 alberon Freud andate and Sir [Music] Hammy
