So today, we're talking Mario Maker. But instead of opening with a joke or cringy video of me pretending to be the Star Wars kid or whatever, I wanted to let you know about a fan made game "Mega Maker." It's a project just like Mario maker but obviously for Mega Man levels It was released a couple weeks ago and as I write this, Capcom hasn't struck it down. I mean it kind of makes sense, it's not like Capcom's cared about Megaman for years now. Anyway, long story short if you're watching this video 'cause you like Mario or retro platformers then go out and support this awesome, AWESOME free project. And if you want to check out some of the best early levels created by Theorists like yourself, check out our livestream of the game over on GTLive by clicking the (i) icon right there. But hey, don't do it until you watched the theory, then you can click the (i) icon. Go check out some levels, and then go create some levels for us to play. All right? Cool! Roll intro ♪ Hello internet, welcome to Game Theory, the show that's killed so many calculators, That we've been charged with War Crimes by Texas Instruments. Today, we're answering a question that I had while in the shower: (obviously the place where all the best theory ideas come from.) Why is Link going through the stages of grief? Would Minecraft's block-world be flat? Or would it be round? Does Bendy and the Ink Machine have any real-life parallels? How many possible levels can you actually make in Mario Maker? If only they made a water-resistant laptop, I could use to write the whole episode in there it'd be glorious Just DON'T DROP THE SOAP! Anyway, I can hear you right now, "Dude, MatPat, Mario Maker was like so last gen. We have a whole new console! Get with the times, bro!" I know, I feel ya bro. But as most of you already know, I love me a good math problem to solve, and what starts as just a simple premise you'll soon see spirals out into the largest, hardest counting task Miss Allen your math teacher could ever devise and without question, The largest numbers we have ever had to deal with here on Game Theory. I don't think even Nintendo has Calculated this for their own game, so GET READY, Miyamoto, when I tell you the final answer today, You're going to want to change that box art to brag about just how powerful the game you created actually is. Put on your Hard Hats ladies and gentlemen and lets-a-go! Now, obviously the only way to figure out how many possible levels can be built in Super Mario maker is to count them. So that's what I did. Level 1, no blocks, Level 2, one block, Level 3, three blocks. Ah, dammit, I forgot the one with two blocks I gotta go back and start again And then, after the universe died, collapsed, Big Banged again, expanded, died again and repeated the process billions of times I finally invented the time machine to travel back to 2017, wrote this script, and BOOYASHAKA; here we are. Clearly manual counting like this is not going to be an efficient use of our time, but when you stop to think about it, most math is basically just glorified counting. I mean counting is what started math to begin with. What was originally just a system to keep track of sheep or days of the week or how many oversized Mammoth Tusks you have to barter with, has evolved into a system intricate enough to predict the orbits of planets we can barely see. Make computers house the entire history of human information, and calculate the most efficient path from my house to the nearest Wendy's in mere seconds; all of this is just counting done really really quickly and we're going to need to count really really quickly because there are a TON of different things to take into account when it comes to building Super Mario Maker levels. I mean if you're like me, your level basically amounts to creating one giant flat plane filled with a bunch of Goombas in a line, so I could murder death them all with just. One. Shell kick. But for people who truly know what they're doing, who truly get this, there are literally 4,800 different options or different combinations to choose from before you even leave the first screen. Right off the bat there's 50 different timer settings, and then there's scrolling Do you want the level to Autoscroll? If so, do you want it to go fast, medium or slow? So that's another four options. and BOOM, before you blink we're already at 200 different level possibilities because when you're counting all things that are possible, these numbers multiply. Now, I got to be honest. For as much as I loved Math and Science throughout school, I always hated permutations, combinations and probability. HATED THEM! So let me quickly explain for everyone who ignored Miss Allen's cringy math jokes about how she'll do Algebra and statistics, but graphing is where she draws the line. Miss Allen, I appreciate what you're trying to do really do doing great work up there, but please stop now. Anyway, Here's an example. I want to make a level that's 50 seconds long. Okay, check. Now for that 50 second level, There's four different options for scrolling speed: fast, medium, slow or no scroll. All right, So that's one level times four Options giving you four. Got it? Good. The next timer is 60 seconds long. And then I have the same four options for scrolling on That one; rinse and repeat the same process for all 50 timer settings. You COULD if you wanted count each individual one out, but it's faster just to multiply 50 times four or 200 different combinations of level. Next up is level style: Do you want your level as classic Super Mario bros., Super Mario Bros. 3, Super Mario World from the SNES, or the New Super Mario Bros. U? Which let's be honest here guys, that title is just way too frickin' long What is this, a Kingdom Hearts title!? Kingdom Hearts HD II.8 Final Chapter Prologue 358 Over 2 Dream Drop Distance Recoded Raindrop Chain of Memories! Seriously: Final Chapter Prologue? Final Chapter Prolo- that's like, almost a logical paradox. Anyway, four different options for each of our 200 different levels, y'all know what to do: Multiply! 210*4 equals 800, then there's the song you want to play is it the underground theme a normal grassy level blah blah blah down the line until You have 6 different course themes which gets us where we want it to be, 4800 different possibilities. And we are still not ready to lay a single block, or place a single enemy since there's still the question of how big the level is gonna be. Super Mario maker levels can be as short as 1 screen width of 24 blocks and as long as 10 screens of 240 blocks. With every width possibility in between, that's 240-24 giving us 216 different length options multiplying our original 4800*216 means that STILL before you have placed a single Goomba there are over 1 million Different options. And while that's a horrifying figure to consider it still hasn't topped the number of levels that have actually been built In 2016 Nintendo counted how many levels have been made by players of game and the current publicly known total is over 7.2 million 7.2 million levels in this one $60 Mario maker game. It's crazy! But hold on to your butts because that 7.2 million is about to get left in the dust, because it is possible to create sub-areas in various levels. Y'know, those bonus areas with coins and different challenges and stuff. Well those can also be ten screens wide or maybe they won't exist at all. That means that we have a whole nother 217 options available for our course 216 Length options and the option of it not existing at All bumping our previous 1 million 36,800 total to over 200 million that means that if everyone who started out passionate about Super Mario maker for that first year stayed Passionate for the rest of their lives and devoted that time to making every single combination of level set up before even placing a single Block on screen and managed to maintain the rate of 7.2 million levels per year, it would take over 30 Years just to make every available option. And remember, we are still just talking about 200 million blank levels: different times, lengths, themes and scrolls for $60 or whatever Mario Maker costs these days you are literally getting a game that has the possibility of over two hundred Twenty four million levels in it. That is point zero zero zero zero zero Zero two cents per level. Talk about a steal! I mean granted all those levels just involve pressing right to win But still; quantity over quality. That said, we maybe want just a bit more Quality. A level with a bit more substance to it or at least a bit more something to it, and that means it is Finally time to talk level Decorations. Ladies and gentlemen, we are about to place a block, and here's where the numbers go from merely big to Reality breaking. No exaggeration, reality. breaking. numbers. A square on the grid of a Mario Maker level can have one of 96 different items on it: a block, a coin a bill blaster a bowser, etc. etc. etc. That's already a lot, but there's actually more: there's half a dozen different modifiers out there. Let's take a simple note block for example. This note block can be just that: a plain note block. It can also be pitched, it can also be winged. It can also be pitched AND winged. That's four different combinations for one note block. It can also be filled with one of one of the 125 different enemies between the different enemy varieties: Regular Koopas, flying Koopas, Giant Koopas, Giant flying Koopas on, and on, and on, and you get the drill. That's 4*125 giving us 500 different possibilities. 500 different possibilities for just one block. Let me say that again: you can do 500 different things with just this one thing! There are way too many differences and options and qualities that I could list here But I did go ahead and count them all. It was a very, very long night. So for any one grid in Super Mario Maker when all is said and done there are exactly 18,147 different things that you can do with it. Including doing nothing at all. Now it's time to make that fateful decision of what to put into that first grid. ♪ *Decision making intensifies* ♪ *POP* And with that I have made the first of over 4 Trillion possible levels: 225 million time 18,147 to change. Think back to that army of folks making levels at a rate of 7.2 million per year. It would take them over five hundred and sixty-seven thousand years to make every Possibility of level where they fill in just one grid space. Time move on to the next one. ♪ With that choice of another 18,14 possibilities, we're starting to get close to numbers that have no name. My calculator returns 7.409X10^16 Which is 7 followed by 16 zeros otherwise known as 70 quadrillion So instead of doing this like a billion times, we're going to do a bunch of multiplying and exponentiating and going through all the different possible iterations of blocks for each grid on the square, We arrive at a nice and crisp 9.1*10^6217. For as huge as that is, and believe me it is freaking ridiculous. That's not even the whole story. There's just so many different ways the things can be laid out. We still got to multiply it by the various level iterations. There are and then multiply that number by 217 because again, there are the possibility of sub-areas and all of those grid blocks can be filled with their own items and then finally multiply that number yet again by our 9.1X10^6217 giving us the absolute ultimate grand total of 1.8*10^12444. That number is HUGE! Huge, I'm telling ya. That's a really bad Donald Trump impression if you're wondering what that was supposed to be. But Matpat, I hear you saying to me This is all well and good, but that's just how many random levels can exist that doesn't actually make them playable. and you're absolutely right. Among those 1.8*10^12444th levels, There's a bunch that are just Mario surrounded by bricks, unable to do anything as the timer runs out, or levels where he just gets crushed by the autoscroll and Nintendo requires that all levels made in Mario maker must be completeable. That number unfortunately Is impossible to know but using another fun mathematical principle? We can get pretty close to estimating the number of levels that we have to eliminate because they're just invalid levels. I would say Within a million. Saying that made me feel like one of those amusement park casters. Hey kid I can guess your birth month, age, weight or the number of possible levels in Mario maker. If I'm within a million, you don't get that cheaply made giant Spongebob plushie. Now missing by a million seems like it would be a huge number But when you're considering how big of a number We're dealing with a million is actually a drop in the bucket put it as a fraction in the calculator And it just rounds it self to zero. We're literally guessing a number which when you put it in the calculator says Infinity to a range of about a million so honestly that's a pretty small margin for error. So, how are we going to figure this out with little to no information to go off of? By using something called? Fermi Estimation Enrico Fermi was an Italian physicist who's famous for a whole bunch of stuff. Not the least of which being the creation of the very first Nuclear reactor That's a pretty impressive feather in your cap. Fermi was a really smart guy, so get this: during the testing of the first atomic Bomb, he drops some sheets of paper in the blast zone. Sheets of paper, literal sheets of paper. He then measured how far though sheets traveled due to the blast, and estimated that the first bombs were about ten kilotons They were in fact 20 kilotons. This is pretty darn close considering all he was using was dropped pieces of paper on the ground Fermi Estimation relies on getting rough estimates that are within an order of magnitude of the correct answer. It can be useful for guessing jelly beans in a jar or how many piano tuners are in Chicago or how many flights are in the air at any given point in time. Basically it's a skill that you want to get good at if you're ever interviewing for a job at Google because they love to ask questions like that at the end of their interviews. If you were to create a stack of quarters to the height of the Empire State building would you then be able to fit all of those quarters into a Normal-sized room? No joke, that was a question that I was asked at the end of one of my Google interviews; the answer is Yes, Easily. Fermi Estimation, it relies on the principle that the over estimates that you're going to make in the process Balances out the under estimates getting you pretty close to the right answer. So using Fermi Estimation we can guess that out of randomly created levels, point zero zero zero zero One percent of them will be completeable. And of those that are actually completeable let's say that only point zero zero zero Zero zero zero zero one percent will be any fun that's basically us saying that point zero zero zero zero zero zero zero zero zero zero zero zero one percent of Possible levels in Mario Maker are actually fun and completable. That is in case you missed it, a really really small percentage. That's like one grain of sand in a beach percent. Running all those numbers through our high precision calculator We end up with a final number of 1.8*10^12431 Ha! It barely made a dent. And that is why Fermi estimation works. We are taking such small percentages to say, "Wow, what if there's this incredibly slim chance that all of these things work together?" But you see that the number is still huge. The over estimates balance out against the under estimates. When you plug that number into a calculator it basically gives you back infinity. I mean I did it on Google scientific calculator, and it literally spits back infinity. So think about it this way: this means that there are more possibly fun Mario levels that could be made in the universe than you will ever play. In Super Mario maker a $60 game with infinite levels of fun-possibility. That's crazy! The only problem is we never (A) have the time to grade them all or (B) Have enough space to store them. And I mean that seriously; according to Universe Today it's estimated that there are between 10^78 and 10^82 atoms in the observable universe. There are more level possibilities in this one little $60 game for the crappy Wii U than particles in the entirety of the observable universe Wrap your head around that one. And there you have it loyal theorists, the answer to a question Nobody asked or wanted to know the answer to: How many playable and fun Super Mario maker levels can be made? It is actually a finite number: roughly 10^12431 A number so huge it actually doesn't have a name the only number bigger is a googolplex which is one with a googol of zeroes behind it and google is a one with a hundred zeros behind it so it's Really big number or at least it didn't have a name until today. This is our opportunity right? Nobody else has claimed this number So by the power vested in me by no-one, the number 10^12431 A number unreachable in this universe and almost as many universes as can be imagined I dub this huge and oddly specific number as a MarioPlex™. Thus it shall be written in the annals of history for our Children and our children's children to remember. Feel free to cite me in all future uses of this very specific number. And remember that it all Started here with a theory. A game theory. Thanks for watching. *music* *Mario sounds*
MatPat apparently already took the number of possible level in grand total and subtracted the number of unplayable levels. How he did this, I don't know, but he did TRY to take in into account. A MarioPlex still stands in my book.
After doing a Latin prefix translation, I've deduced that a Marioplex is mathematically known as a quattormillinillitresquadragintacentillion, or some ever-so-slight variation upon it. As far as the calculations go, he got them pretty much all right, though he did indeed forget things like pipe extensions. To calculate all that would probably make this number exponentially larger, though I'd say that it would definitely stay somewhere under 10100000
The real followup question: How long will it take you to get a Marioplex dollars in Adventure Capitalist (or whatever other unit in some other comparable cookie-clicker-style game)?
I just realised the video itself could be posted here, without being a request