Game Theory: Super Mario Maker, BIGGER than the UNIVERSE!

So today we are talking about Mario Maker. But instead of starting with a joke or an embarrassing video of me pretending to be the Star Wars kid or whatever, I wanted to tell you about a fan-made

game

, "Mega Maker." It's a project like Mario Maker but obviously for Mega Man levels. It was released a couple of weeks ago and as I write this, Capcom hasn't ruled it out. I mean it makes sense, it's not like Capcom has cared about Megaman for years. Anyway, long story short, if you're watching this video because you like Mario or retro platformers, then go out and support this awesome, AWESOME free project.

And if you want to see some of the best early levels created by theorists like you, check out our live stream of the

game

on GTLive by clicking the (i) icon right there. But hey, don't do it until you've seen the

theory

, then you can click on the (i) icon. Go check out some levels and then create some levels so we can play. Alright? Cool! Introduction to the roll ♪ Hello Internet, welcome to Game Theory, the program that killed so many calculators that Texas Instruments accused us of war crimes. Today we'll answer a question I had while I was in the shower: (obviously the place where all the best theoretical 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 parallels in real life? How many possible levels can you create in Mario Maker? If only they made a waterproof laptop, I could use it to write the entire episode on there, that would be glorious. Just DON'T DROP THE SOAP! Anyway, I can hear you right now: "Dude, MatPat, Mario Maker was next-gen. We got a whole new console! Catch up, bro!" I know, I feel you brother. But as most of you already know, I love a good math problem to solve, and what starts out as a simple premise that you'll soon see turns into the biggest, most difficult counting task that Miss Allen, your math teacher, has ever done. , could ever come up with, without question, the largest numbers we have ever had to deal with here in Game Theory.

I don't think even Nintendo calculated this for their own game, so GET READY Miyamoto, when I tell you the final answer today, you'll want to change the box art to show off how powerful the game is. created really is. Put on your helmets, ladies and gentlemen, and let's go! Now, obviously the only way to calculate how many possible levels you can build 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. Oh damn, I forgot the two-block one. I have to go back and start again.

And then after the

universe

died, it collapsed, had a Big Bang again, expanded, died again, and I 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 won't be an efficient use of our time, but when you stop and think about it, most math is basically glorified counting. I mean, counting is what started mathematics to begin with. What was originally just a system for keeping track of sheep or the days of the week or how many oversized mammoth tusks you have to trade has evolved into a system complex enough to predict the orbits of planets. that 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 a matter of seconds; This is all just counting done very, very quickly and we are going to need to count very, very quickly because there are A LOT 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 is basically equivalent to creating a giant plane full of a bunch of Goombas in a line, so I could murder them all just by myself.

One. Shell kick. But for people who really know what they're doing, who really understand 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 are 50 different timer settings, and then there's scrolling. Do you want the level to scroll automatically? If so, do you want it to go fast, medium or slow? So those are four other options. and BOOM, before you blink we are already at 200 different level possibilities because when you count all the things that are possible, these numbers multiply. Now I have to be honest.

As much as I loved math and science during school, I always hated permutations, combinations, and probability. I HATE THEM! So let me quickly explain to everyone who ignored Miss Allen's embarrassing math jokes about how she will do algebra and statistics, but graphing is where she draws the line. Miss Allen, I appreciate what she's trying to do, really do a great job up there, but stop now. Anyway, here's an example. I want to make a level that lasts 50 seconds. Well, check it out. Now, for that 50 second level, there are four different options for scroll speed: fast, medium, slow, or no scroll.

Alright, that's a level multiplied by four. Options that give you four. I understand? Good. The next timer lasts 60 seconds. And then I have the same four options for scrolling through Esa; Rinse and repeat the same process for all 50 timer settings. You COULD if you wanted to count each one individually, but it's faster to just multiply 50 by four or 200 different combinations of levels. Next up is level style: Do you want your level like the classic Super Mario Bros., Super Mario Bros. 3, SNES Super Mario World, or New Super Mario Bros. U? Which, let's be honest, guys, that title is way too long.

What is this, a Kingdom Hearts title!? Kingdom Hearts HD II.8 Final Chapter Prologue 358 2+ Dream Drop Distances Coded Raindrop Memory Chain! Seriously: Prologue to the final chapter? Prolo of the final chapter: that is almost a logical paradox. Anyway, four different options for each of our 200 different levels, you know what to do: Multiply! 210*4 equals 800, then there is the song you want to play, it's the underground track, a normal weed level, blah blah blah, down the line until you have 6 different course tracks that take us where we want That is, 4800 different possibilities. And we're not ready to place a single block or place a single enemy yet, as there is still the question of how big the level will be.

Super Mario Maker levels can be as short as 1 screen of 24 blocks wide and up to 10 screens of 240 blocks wide. With all the width possibilities in between, that's 240-24, giving us 216 different length options. Multiplying our original 4800*216 means that STILL before we've placed a single Goomba there are over 1 million different options. And while that's a horrible number to consider, it still hasn't surpassed the number of levels that have actually been built. In 2016, Nintendo counted how many levels players of the game have created and the current publicly known total is over 7.2 million 7.2 million levels. in this $60 Mario Maker game.

It's crazy! But hold on, because those 7.2 million are about to be left in the dust, because it is possible to create sub-areas at various levels. You know, those bonus areas with coins and different challenges and stuff. Well, those could also be ten screens wide or maybe they don't exist at all. That means we have another 217 options available for our course, 216 length options and the option for it not to exist at all, bringing our previous total from 1 million 36,800 to over 200 million, that means that if everyone who started out passionate about Super Mario Maker during that first year they remained Passionate for the rest of their lives and spent that time making every combination of levels set up before even placing a single Block on the screen and managed to keep up with 7.2 million levels per year. , would take control. 30 years just to take advantage of all the options available.

And remember, we're still talking about 200 million blank levels: different times, lengths, themes and scrolls. For $60 or whatever Mario Maker costs today, you're literally getting a game that has the potential for over two hundred and twenty-four million levels in it. That is, point zero zero zero zero zero two cents per level. Talk about a robbery! I mean, all those levels just involve pressing right to win. But still; quantity over quality. That said, maybe we want a little more quality. A level with a little more substance or at least a little more of something, and that means it's finally time to talk level decorations.

Ladies and gentlemen, we are about to lay a block, and this is where the numbers go from simply being large to breaking reality. Without exaggeration, reality. rip. numbers. A square on the grid of a Mario Maker level can have one of 96 different elements: a block, a coin, a bill blaster, a bowser, etc., etc., etc. That's already a lot, but there's actually more: there are half a dozen different modifiers. Take, for example, a simple note block. This note block can be just that: a simple note block. It can also be thrown, it can also be winged. It can also be inclined AND winged.

That's four different combinations for a block of notes. It can also be filled with one of 125 different enemies among the different enemy varieties: Regular Koopas, Flying Koopas, Giant Koopas, Giant Flying Koopas and so on, and you're done. That's 4*125 giving us 500 different possibilities. 500 different possibilities in a single block. Let me say it again: you can do 500 different things with just this! There are too many differences, options and qualities that I could list here, but I went ahead and counted them all. It was a very, very long night. So for any given grid in Super Mario Maker, when all is said and done, there are exactly 18,147 different things you can do with it.

Including doing nothing at all. Now it's time to make the fateful decision of what to put on that first grid. ♪ *Decision making intensifies* ♪ *POP* And with that I have made the first of over 4 billion possible levels: 225 million times 18,147 to change. Think about that army of people leveling up at a rate of 7.2 million per year. It would take them more than five hundred and sixty-seven thousand years to achieve every possible level where they fill a single grid space. Time passes to the next. ♪ With that choice of 18,14 other possibilities, we begin to approach numbers that have no name.

My calculator returns 7.409X10^16, which is 7 followed by 16 zeros, also known as 70 quadrillion. So instead of doing this a billion times, let's multiply and exponentiate a bunch and go through all the different possible block iterations for each grid in the square. We arrive at a nice, crisp 9.1*10^6217. No matter how big it is, and believe me, it is tremendously ridiculous. That's not even the whole story. There are so many different ways things can be laid out. We still have to multiply it by the different iterations of levels. There is and then multiply that number by 217 because again, there is the possibility of subareas and all of those grid blocks can be filled with their own elements and then finally multiply that number once again by our 9.1X10^6217, which gives us the absolute final total of 1.8*10^12444.

That number is HUGE! Huge, I tell you. That's a very bad impression of Donald Trump if you're wondering what he was supposed to be. But Matpat, I hear you tell me that this is all well and good, but that's how many random levels can exist that don't actually make them playable. And you're absolutely right. Among those 1.8*10^12444 levels, there is a group that is simply Mario surrounded by bricks, unable to do anything when time runs out, or levels where he is simply crushed by auto-scrolling and Nintendo requires all levels to be They believe in Mario Maker. It must be complete.

Unfortunately, that number is impossible to know except by using another fun mathematical principle? We can get pretty close to estimating the number of levels we have to eliminate because they are simply invalid levels. I would say Within a million. Saying that made me feel like one of those amusement park wheels. Hey kid, I can guess your birth month, age, weight or the number of possible levels in Mario Maker. If I'm in the million, you won't get that giant SpongeBob plush made cheaply. Now, missing by a million seems like it would be a huge number. But when you consider how big the number is, we're dealing with a million it's actually a drop in the bucket, put it as a fraction on the calculator and it just rounds up. same to zero.

We are literally guessing a numberwhich when you put it in the calculator it says Infinity in the range of about a million, so honestly it's a pretty small margin of error. So how are we going to figure this out with little to no information to go off of? Using something called? Fermi's Estimate Enrico Fermi was an Italian physicist famous for a lot of things. Among them, the creation of the first nuclear reactor. That's a pretty impressive achievement. Fermi was a very smart guy, so he hears this: during the test of the first atomic bomb, he drops some sheets of paper into the explosion zone.

Sheets of paper, literal sheets of paper. He then measured the distance the sheets traveled due to the explosion and estimated that the first bombs weighed about ten kilotons. In reality, it was 20 kilotons. This is pretty close considering all he was using were pieces of paper thrown on the floor. Fermi estimation is based on obtaining 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 there are in Chicago or how many flights are in the air at any given time.

Basically, it's a skill you'll want to improve on if you ever interview for a job at Google because they love asking questions like that at the end of their interviews. If you were to create a stack of quarters as high as the Empire State Building, could you fit all of those quarters into a normal-sized room? No joke, that was a question I was asked at the end of one of my interviews at Google; The answer is Yes, easily. Fermi estimation is based on the principle that the overestimations that you are going to make in the process balance the underestimations, bringing you quite close to the correct answer.

So using Fermi estimation we can guess that of the randomly created levels, point zero zero zero zero one percent of them will be completeable. And of those that can actually be completed, let's say that only point zero zero zero Zero zero zero zero one percent will be fun. It's basically us saying that point zero zero zero zero zero zero zero zero zero zero zero one percent of the possible levels in Mario Maker are actually fun and complete. In case you missed it, it's a very, very small percentage. That's like a grain of sand in a percentage of the beach.

Running all those numbers through our high-precision calculator, we ended up with a final number of 1.8*10^12431 Ha. It barely made a dent. And that's why Fermi estimation works. We're taking such small percentages to say, "Wow, what if there's an incredibly small chance that all of these things will work together?" But you see that the number is still enormous. Overestimations are balanced by underestimates. When you enter that number into a calculator, it basically returns infinity. I mean, I did it with Google's scientific calculator and it literally spits out infinity. So think about it this way: this means there are more possibly fun Mario levels that could be created in the

universe

than you'll ever play.

In Super Mario

maker

, a $60 game with endless levels of fun possibilities. That's crazy! The only problem is that we never (A) have time to rate them all or (B) have enough space to store them. And i mean it; According to Universe Today it is estimated that there are between 10^78 and 10^82 atoms in the observable universe. There are more level possibilities in this little $60 game for the bad Wii U than there are particles in the entire observable universe. Wrap yourself in it. And there you have it, loyal theorists, the answer to a question that no one asked or wanted to know the answer to: How many playable and fun Super Mario Maker levels can you create?

In reality, it is a finite number: approximately 10^12431. A number so large that it actually has no name. The only number larger is a googolplex, which is one with a googol of zeros behind it and google is a one with a hundred zeros after it. It's a really big number or at least it didn't have a name until today. This is our chance, right? No one else has claimed this number. So, by the power that no one has given me, the number 10^12431. An unattainable number in this universe and almost as many universes as you can imagine, I call this enormous and strangely specific number MarioPlex™. .

Thus it will be written in the annals of history so that our children and our children's children will remember it. 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 theory of games. Thanks for watching. *music* *Mario plays*