Game Theory: Mario’s LUNAR APOCALYPSE!! (Super Mario Odyssey)

Mr. MatPat, How many moons does it take to get to New Donk City? Let’s find out. a one! *crunching noises* a two-hoo! *more crunching noises* a three! Twenty minutes later… 46 47 48! 48 sugary moons. Now if you’ll excuse me, I don’t feel too well. BBLLEEEAARGH [intro music] [ding] [ding] [ding] [ding] [intro music] Hello Internet! Welcome to Game Theory, the funky mode to all of gaming’s most complicated issues. Today we’re gonna be strapping in and launching ourselves into Super Mario Odyssey, one of the most satisfying and confusing Mario worlds I’ve ever had to experience. I mean, you have a kingdom of Rainbow Forks right next to Nintendo’s version of Dark Souls. Then, because of Mario’s canon height of 5 foot 1 inch, the people of New Donk City are well over 10 feet tall, but of course Wario isn’t in the game, so I can’t prove once and for all that my calculations from four years ago weren’t as insane as they initially sounded, okay? But you know, arguably, the most fascinating part of this game has to do at the very last location you go to: The moon. Not because of the Dark Side stages or the boss rush, but because when you actually sit down and do the math, the moon is proven to be the single biggest threat to Mario. Nay, I say the entire Mushroom Kingdom! Forget Bowser and his petty little schemes to marry Princess Peach– That is nothing. This thing. This thing right here is a threat scarier than anything Nintendo has ever cooked up. We’re talking Majora’s Mask levels of planet-wide moon based catastrophe here, people. But to truly understand why this thing, the moon, is such a menace to Mario in this game, We’re gonna have to do some math, so get ready theorists. Let’s crack open some formulas and break out the TI-84s Yeah, 84s (we gotta bust out the big guns today) because here we go, off the rails to explore the great wide wacky world of Mario astrophysics. To begin, we need to first establish how large Mario’s earth and moon are and how far these celestial bodies are away from each other. Now, by this point you guys know how many headaches the Mario franchise causes me on the pixel measurement side. From shifting heights to wacky gravity, Mario isn’t fighting Bowser so much as he’s constantly fighting against my math. But determining the size of his planet in this game, this one. This was the straw that broke the camel’s back. I thought for sure that there would be a way to do it between all the maps and globes that are present in the game’s marketing and in the game itself. And let me tell you: I tried. I tried measuring pixels, but we had no consistent sized reference points. I tried measuring steps, but none of the stages allow you to truly see a whole continent We attempted Al-Biruni’s method. The Iranian scholar who determined the radius of the earth by observing the heights of mountains But without being able to reach a point on the horizon, we actually couldn’t establish a distance between anything. I examined the globes, the brochures, the start screen, the opening menu promotional materials for this damn game, so many different things, but damn it Nintendo you always have to make it difficult. So you know what I gave up. You heard that right. I just- I threw in the towel. To my knowledge There is no definitive way in this game to prove the actual size of Mario’s planet and his moon And I invite you all to try. Consider this the Mario Odyssey Challenge. If you figure it out We can do an episode dedicated to you and your math and no let me just nip this one in the butt right now you Can’t assume that the Hat ship on the overworld map is actual size that would make the proportions of this globe absolutely absurd and wouldn’t actually match up with what we see in game with actual hat ship or Bowser’s ship are much smaller relative to The actual size of the continents just throwing that one out there seriously, I feel like I tried everything here however just because I gave up on the measurement doesn’t mean that the theory itself was in the pooper. Doing this for as long as I Have I know that there’s more than one way to skin a Mario? Oh boy. That’s a gruesome image Sorry that didn’t come out right at all anyway The key to this theory is the Roche Limit. A theory concept first proposed by game theorist Reddit user JohnsonAndJohnCena For those of you who don’t know there’s a magical distance a moon has to be away from a planet to remain a moon. Now, what do I mean by that? Well think about it this way any planet or moon is held together by its own gravity, right? That’s why all of these things are balls. All the stuff in the planet is being pulled towards the center making it an orb IN SPAACE But remember everything has gravity. Big things like the earth, smaller things like the moon, even really small stuff like you or me We all have those gravitational forces that act on each other. For instance, the earth, under the influence of the moon’s gravity, has whole continents raised about 50 centimeters because of the moon’s pull on earth and Conversely the moon’s surface shifts by about five meters towards the earth in response to Earth’s Gravitational pull and to make those facts even more incredible Remember right now the moon orbits the earth at an average distance of about three hundred and eighty-four thousand kilometers or two hundred and thirty-eight thousand miles. That is how strong the force of gravity is. So that begs the question. What happens when you bring those two objects closer together? where the big object like the earth with lots of gravity is able to pull even Harder on the small object with less gravity like the moon? Well, something unexpected actually. The moon would get ripped to pieces because the Earth’s gravity is Stronger than the gravitational forces that are holding the moon together. You ever wonder how Saturn got its rings? This is believed to be why. A small moonlet happened to orbit too close to Saturn and was pulled apart by Gravity, with the pieces now orbiting the planet as rings and this, loyal theorists, defines the Roche limit: the distance away from a planet an orbiting body needs to be to not be torn apart by the planet’s Gravity. The Earth’s Roche limit is eighteen thousand, four hundred seventy kilometers or about eleven thousand, four hundred and seventy miles That’s about one twentieth the Distance that the moon orbits at now so if it ever ventured within that eighteen thousand kilometer limit It would be pulled apart and the earth would suddenly have Itself some rings and that ladies and gentlemen is how humanity could finally achieve its final form by blinging out our own planet. We liked it and so we decided to put some lunar rings on it. Which brings us back to Odessy You ever stop to wonder why we’re collecting moons, instead of stars, in this game? Could it be that what we’re seeing here is early signs that Mario’s moon is being ripped apart because It’s orbiting within the Mushroom Planet’s Roche limit. You probably haven’t stopped and wonder that and for as absurd as it might sound it absolutely Seems to be the case here. Notice those huge chunks of space rocks scattered across the Mushroom Planet. We know for a fact that those are coming from the moon. Not only via their name, but also from seeing them on the moon itself But to truly know for sure we need to determine the Roche limit of Mario’s earth in the game and then see where the moon falls relative to it. Now, as you can imagine, that involves a lot of math So I’ll try to cut out anything that isn’t too interesting. Scientists are little MOON food sponsor of the day, but hey, that’s just a theor- I’m sorry Maybe I cut out a bit too much there. In all seriousness though the Roche limit of a planet is equal to 2.4 times the radius of the larger object times the cube root of the density of the larger object Divided by the density of the smaller object and as you can probably tell there is a lot of stuff in that equation that we don’t know. I mean, I just admitted two paragraphs ago to not being able to find the size of the planet so without that how do we have even a ghost of a chance of figuring out the radius of the planet let alone the density of the planet? And then we got to do the same thing with the moon. Well as it turns out We don’t actually need the exact distances as long as a common unit is used throughout all of these calculations So stick with me here, and let’s just base everything off of the moon’s radius. Give it a variable. Let’s call it little ‘r’ Now as you zoom out to the overworld map there are two frames where Mario’s moon And the planet are side-by-side and that’s important so perspective doesn’t distort their ratios. Taking pixel measurements from both of these frames We can see that the moon’s radius is about 30% of the radius of the planet. Now earlier when I issued you the Mario Odyssey Challenge I said that the ratios on the screen Might not be a hundred percent true But luckily we can also double-check this. In New Donk City, there’s a model of the earth and the moon on the ground in front Of city hall and wouldn’t you know it? But once again the math checks out in this model the radius of the earth is determined to be 3.3 moon radii and with that we can say that the moon radius equals little ‘r’ and Mario’s planet radius equals 3.3 times little ‘r’ Since we’re eventually working our way to finding density the next step is to find the mass of both Mario’s earth and Mario’s moon Which again seems like it should be impossible, but luckily we have another secret backdoor here. Gravity. You see, when it comes to finding the properties of planets and stars there are a Lot of different formulas that we can use since you know there’s no actual way for scientists to weigh a planet without using some form of math so here We can use gravity to calculate the mass by using the following equation mass equals acceleration times radius squared Over the gravitational constant. That acceleration right there. It’s as easy as finding out How fast mario falls after jumping. First on the Mushroom Planet and then again on the moon, something we’ve done a bunch of times here on the channel especially back in my episode Covering Mario’s performance at the Olympics, where we found that the Mushroom Kingdom’s gravity is more extreme than Jupiter. Anyway, for that all we need is the distance that Mario is falling and the time it takes him to fall. Plug those numbers into this equation and we get holy geez! on his home planet Mario’s normal jump has a downward acceleration of 70.16 m/s^2. That is well over seven times Earth’s normal gravity. It is three times Jupiter’s gravity, and it’s over double what it’s been in any other 3D Mario game. If you’re wondering why Mario feels heavier and falls faster in this game, well then, there you go. It’s not Mario packing in the cannoli It’s his planet putting on the poundage We do the same thing on the moon And we get an acceleration of 11.74 m/s^2. 1.19 g-forces Which is pretty incredible when you think about it. This right here? This is how much Mario would be able to jump if you were subjected to our measly gravity now with those Accelerations in hand we go all the way back to mass for both the planet and the moon This is just some basic calculations Let me just burn through this quickly by speeding things up Checking acceleration numbers making sure to leave 3.3 R for radius of the planet when calculating for Mario’s earth and just regular old little R When calculating for the moon and we get ourselves a mass of 1.14*10^13 r^2 kilograms for the planet and 1.75*10^11 r^2 kilograms for the moon. Now with the mass and radius of each body determined, determining the density, the final part of the Roche limit equation is a snap, Density, remember, is just a trip to the DMV. D equals M over V Mass of the object divided by the volume of the object The volume of the sphere, which applies to both the moon and Earth is calculated at 4/3*π*raduis^3. I won’t bore you with math It’s basically 150.53 r^3 for the earth and 4.19 r^3 for the moon Which leads to densities of 7.6*10^10 divided by the radius of the moon for the earth and 4.18*10^10 divided by the radius of the moon for the moon and that finally means that we have all the variables that we need for the Roche limit equation. As a reminder, the Roche limit of a planet is equal to 2.4 times the radius of the larger object times the cubed root of the density of the larger object divided by density of the small object. Therefore, the Roche limit of Mario’s plane is 2.4 times the radius of the larger planet Which is 3.3 ‘r’s. Since remember, It’s 3.3 times the radius of the moon times the cube root of that mess of densities that we just calculated. Don’t forget that when you divide a complex fraction you multiply by the inverse, so those little r’s hands cancel out There as well as those 10^10s. You got all that? No? Perfect. Don’t worry you didn’t miss a thing. Running through all of those numbers We see that the Roche limit is equal to 9.66 moon radii. In other words, thanks to all the math that we just ran through, we proved that if Mario’s moon is within 9.6 moon radii from the center of his earth, it will be slowly getting torn apart by Earth’s gravity which would give us the reason why we have hundreds of mini moons and moon rocks all scattered across the surface of Mario’s planet and You know what that’s exactly what’s happening here. You know how in the Moon Kingdom There’s a spot where you can see the earth not so far off in the distance Well, using that vantage point it seems pretty obvious that the moon is super close to Mario’s planet, so we could just assume it’s within that Roche limit But that’s not good enough for me or the standards that I have for this show so using that vantage point coupled with the in-game compass. You heard that right. Using the in-game Compass to measure actual angles it may seem unbelievable But it’s actually possible to determine the exact distance with trigonometry, chord lengths and good old SohCahToa But since this is the sort of math that I personally never wanted to show up in my life again I can only assume like three of you actually care about this type of nitty-gritty detail I’ll do it as a mini theory if enough of you and the comments are actually excited about that sort of thing suffice it to Say running all of those numbers you get the moon sitting just about 5.5 moon radii away from the earth confirming that It’s within the Roche limit and that it is getting eaten alive by the planet’s Gravity and remember this isn’t hypothetical this actually isn’t just a theory this is truly How Mario’s planet would be behaving relative to Mario’s moon It would be eating it alive.That is insane and while that goes a long way to explain Why moon rocks and multi moons are scattered everywhere it also spells out some dire Consequences headed straight to Mario’s planet. To give you an example consider this. When our Sun starts to burn out and turn into a red giant It’s predicted that our moon will be pulled out of orbit, and it’ll be pulled closer to earth crossing the Roche limit. At that point it’ll be torn apart. On the plus side it will give our planet a cool temporary ring. On the downside it will shower the planet with huge pieces of moon debris, destroying all sorts of land, throwing tides into chaos, and sending the planet into another wave of Extinction of space rocks crashing on the surface around the world because yeah while some of those chunks will orbit as pretty little rings most Of it’ll just get pulled down by gravity onto the Earth’s surface And that is the fate that Mario Odyssey has already started to allude to for the Mushroom Kingdom And that is the fate that is determined for it based on the science And it certainly doesn’t help that in the final battle Mario speeds this process along by destroying huge chunks of the moon’s core So enjoy running around to collect those moon rocks while you can Mario pretty soon You won’t have a choice as they hurtle Themselves towards you maybe that’s why in Kirby and the Crystal Shards Shiver Star’s a cold dead earth Maybe that’s why in Kirby super star you see Mario traveling the galaxy He’s looking for a new home who knows but all of that needs to be fleshed out in another episode Wow so that was a script full of numbers and speaking of numbers you know what numbers, I’m most excited by Money-saving numbers, or I guess that’s a stupid way of me saying numbers of dollars I’m saving when I make purchases And you know the easiest way to save money while making purchases online with our sponsor of the day, honey Honey is a free browser extension that automatically finds the best coupons on the web So you get the best prices on everything that you’re buying online without having to lift a finger It is free it takes two clicks to install and from that moment forward It’s gonna be saving you hundreds of dollars on the stuff that you’re buying online And I really do mean that a lot of other products would be like oh We only work on these obscure websites that you’re never gonna use, but that’s not the case with honey Honey actually works on all the biggest websites sending you money on everything from pizza to plane tickets to Literally anything that you buy on Amazon and unlike the fictional yet very exciting numbers that I went through on today’s episode each time you see honey’s numbers tick up that Is literally the money that you would have wasted without using it, it’s basically free money forever 21 Groupon Amazon Papa John’s, I mean this thing works everywhere Steph and I went shopping the other day for some new clothes on J-crew’s website, and it literally saved her $30 like that no extra effort It’s just like hey. You can save money. It’s like yes. I would like to save money anyway There is no reason to not add honey to your browser right now unless of course you just like wasting money But in that case I will glad take it off your hands or maybe you set fire to it Which is illegal, but would also be pretty badass anyway. It is super easy to install on your browser Just use my link so reward them reward yourself start saving money today That is not a theory it is a fact so remember It’s or smash that top line in the description and treat yo self to a guilt free shopping Trip enjoy now because in a few million years the earth is gonna Be destroyed by its own moon falling onto itself So you know don’t put that money to waste just a friendly reminder to let me know in the comments whether you’re interested in seeing All that trigonometry calculation, and I will see you next week


  1. Using a bit of maths on how to figure out the surface area thanks to the fact isle delfino appears on the map, and then figuring out the radius using that, i got a grand radius off… 1974.2km! Smaller than mercury, larger than pluto.
    Thus it has a density of 0.43kg/m^2 using your weight calculations.

  2. the moon pieces wouldn't make it to earth because of the force pushing the out so it doesn't

    collapse the moon doesn't have enough speed to go past the outwards force

  3. 13:34 You see, that bothers me. The sun is said enter its red giant phase in about 5 billion years. C02 levels in our atmosphere will drop below what's required for C3 and eventually C4 photosynthesis to happen in about 900 million years, resulting in the death of all plant life. Because plants account for a massive part of the food chain, this alone would result in mass starvation of marine, avian, and terrestrial life. Not only do plants make up the foundation of the food chain, plants create oxygen. These plants dying would rid Earth of basic food for animals and oxygen for future generations. Being generous, only the most resilient of microorganisms (like Tradigrades) will live for another 300 million years on a planet being bombarded by 12% more solar radiation than right now, with all oceans completely evaporated, completely void of oxygen, and lacking of a life sustaining atmosphere. Maybe your point in saying this is that the tearing of our moon would result in catastrophic mass extinctions and bombardment of lunar pieces, but saying that the moon crashing into Earth because of the sun's expansion into a red giant is invalid. Firstly, despite its appearance (increasing size) and condensing elements, the sun would actually be loosing it's outer layers, making it lighter and, as a result, expanding our planet's path of revolution around the sun, which contradicts theories that the sun will engulf Earth, which would have nothing to do with this issue if it weren't for how you said that the sun entering its red giant phase would cause the moon to be torn to pieces by our planet's roche limit. The moon happens to be moving about 1.2 cm away from Earth every year. *Away*. It's predicted that we will loose our moon in about 500 million years, which will cause differences, but wont spell the end of life as we know it. And even if the moon hypothetically were to reenter Earth's gravitational influence or even remain in it's influence throughout the death and suffering of life on Earth and the death of our sun, life (including the relatively extremely resilient tardigrade) would cease to exist and be exterminated by the explosion of our lunar neighbor. That being said, I doubt many people will read through this or like this comment, but if you could see this and five me some clarification, that would be amazing. You obviously don't have to, but in any case, I really appreciate the trouble you go through to make these videos. Thanks for not being a Noughtpointfourlive and having 15 midroll ads, and thanks for all the great theories you've put yourself through hell to conceive. You deserve the life you live, and keep it up 👍

  4. I know this is a year late and Mat may never see this but what of you where to use the mushroom kingdom gravity and compare it to earth's and see the ratio.(x/y=?/y) then basically I guess compare everything to earth after using that….

  5. To find the radius of the earth you could see how big Mario's footstep is and then see how big the moon is from there. And after that you can find the radius of earth by halfinf it and going r3.3×2

  6. Hay mat pat the moshrom kingdom is on earth that,s in a difent universe so you can look up the size of some continit or crater and walla youv got the anser

  7. I think I’ve figured out a way to figure out how big Mario’s earth is,we use the moon.we can see the full moon in the game,so we find out how big it is,and make it bigger until it covers the Mario earth in the game perfectly

  8. Oh MatPat Mario will never be 5'1 again. If he went on the moon he would start to get taller because of spine expansion. I'm just gonna throw that out there.

  9. MatPat: mentions SohCahToa

  10. What would happen if a Moon was bigger than a Planet? Would it still be a Moon or a Planet or some other thing?

  11. Couldn’t you just measure the gravity and calculate the size of the mushroom planet? (Assuming it has the same density of our earth)

  12. If Mario's earth somewhat like our earth, is there a way to measure the distance traveled into space in which the ship stops burning up in the atmosphere?

  13. Can't you just use the mass of Jupiter and its gravity compared to the gravity of the mushroom planet to come up with the mass of that planet? It seems to me that if the mass of Jupiter makes its gravity 3 times less than the gravity of the mushroom planet then its mass should be 3 times more than jupiter and then you can use the plaza floor to do the same with the moon. Please let me know if I'm wrong

  14. You could count the gravity to determine the mass of the planet and then compare that to the earth’s mass compared to its size to finally take that equation for the earth (mass divided by volume) and then apply it relatively to the mass of the planet and do M (mass of the mushroom kingdom) times the result of the equation for the earth to finally find the volume of the planet in Odyssey. You can do the same thing for the moon. The planet in Odyssey seems pretty close to the earth, so this would be the most precise way to count it

  15. I would have been happy to see the dog shots trig. That is one of the reasons I love this channel. The math and science are great.

  16. Is it just me who thought of BEN drowned when I saw the thumbnail.. I got excited and then saw because I'm obsessed with that elf

  17. Mentally preparing myself for next year’s math class by binge watching game theory in hopes that something will stick

  18. Mr mat pat how many moons dose it take to get to new donk city
    Let's find out A 1 A 2eooo A 3
    20 min later
    46 47 48 48 Surgery moons

  19. Doesn’t that mean the game with the moon falling in Zelda is also not possible(not a Zelda fan sorry)

  20. You can already see the moon is too close by just looking no math needed

    That is if they were earth sized and had the same mass

  21. What if you take the average sizes of all the worlds and moon. From biggest measurements to the smaller measurements to have a conclusive number for now to finish the size? Until confirmation of actual size.

  22. Me: Yes grandpa matpat, teach me about 600 bc old school counting with black bricks to solve Mario

    My REAL grandpa: it’s called a cauculator son

  23. Anyone ever jus like stop in the middle of a video to realize agian and agian just how smart matpat is😂 I mean I ligit learn more about science and math from this channel then school, highschool this year here I COME

  24. If the moon shreds to peices while entering the earth then y didn't the moon in majors mask get destroyed while entering the was the atmosphere

  25. No mario is the biggest threat. Don't believe me? Well you will believe THIS!

  26. Take the size of the Lost Kingdom (This one because it's the smallest island) and figure it out by laying Mario Jumpman Mario's size across it at a clear point that can be seen from the globe, and put that size around the globe, then find the other axis by rotating 90 degrees and the again for the third. Then make the sphere. Find the amount you need to size down for the moon. Done. I'm not good with debug modes, so I can't do it. But someone else proficient with editing data values and that stuff can..

  27. Why don’t you see how long the it takes the ship to travel to the moon and then calculate how long away that is then use that for the ruler to measure the moons size

  28. 12:53

  29. Not to add another layer of terror but…due to what we determined to be the gravitational pull of the mushroom kingdom in the mario olympic theory wouldn't the roche limit be farther that our own planets. Which means with how close that moon is now it should already be spelling out the apocolypse for Mario's home. If not in progress.

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