In the last Smash Direct, did you notice the purple and yellow chairs in the background when Mr. Sakurai was talking? Most people think that that’s a hint that Waluigi is gonna be included in Smash, but I know better. I know the truth! Purple and yellow are both six letters long, and why chairs of all furniture? Because “chairs” is also six letters long. Together you have yourself 666. The devil’s number. The sign of the beast, and what’s another name for the devil? Satan, as in Mr. Satan, the true name of Hercule from Dragon Ball Z, a show starring the second most requested fighter for Super Smash Brothers, Goku! That’s right, you heard it here first ladies and gentlemen. Son Goku, Kakarot himself is confirmed for Smash Brothers Ultimate! I don’t know about you, but the proof to me seems undeniable. (Oh god why!) (Epic intro music plays as every loyal theorist rocks out.) Hello Internet! Welcome to Game Theory! Where true theorists, only use deep lore, math, and no items. Of the many amazing games that have come out for the switch, none have been as hotly anticipated as Vroom in the night sky. Waluigi: WAHAHAHAHAHAHAHA Where witches fly around on motorcycle brooms, in the night sky, very slowly. Oh so slowly. 10/10! Would vroom again! But if there’s a second game that people are excited to be on this console, well, it would be the latest installment of Super Smash Brothers. So while we all twiddle our thumbs waiting for Sakurai’s latest masterpiece to arrive on December 7th, can you all do me a favour? I have a short five or so question survey linked in the description. About what you watch or what you create on YouTube, and specifically about what characters in Smash you like to play as. So if you’d like to help me out with a future Game Theory on the psychology of Smash players, take literally a minute to fill it out. I’m not asking you to take a full-on Myers-Briggs personality test this time. This is all for an episode that’s gonna happen next month. Thank you so much for your help. And while you’re busy doing that, keep listening since for today’s episode, I decided to look into how many possible versions of Smash there actually are. 6. Thank you ladies and gentlemen, this has been Game Theory. You’ve been a great audience, make sure you don’t drink and drive. Have a great night. “BuT thAt’S juST a TheOrY!” Put your mocking MatPats down guys, of course I don’t mean the six official games that have been released. I mean how many different match combinations you can have within those games. A huge part of the marketing around this new game has been choice. Every character you could possibly want is there. Every stage you could possibly want is there. Every item etc, etc. When Masahiro put the word Ultimate at the end of this thing, he wasn’t joking because Sakurai doesn’t kid around. In a game where you can play practically any way you want, just how many ways to play are there? One:- Fox, Final Destination, no items. But in all seriousness just how infinite is Ultimate? Last time, I did an episode like this with Mario Maker, we invented a new number. The Marioplex. 10 to the 12,431st power. Which was more than the number of atoms in the existing universe. So let’s see what bonds of reality we’re able to break today. Does Smash offer us more variety than particles in all known matter? There’s only one way to find out! 1 2 3 4 Now if there’s one thing that math teachers are good at, its giving you really easy problems to explain concepts in class, and then giving you impossible ones on the test. So let’s do exactly that. Super Smash Brothers Ultimate is clearly our final exam, so let’s start with something a bit simpler by taking a stroll down memory lane, to the first ever Smash game for the Nintendo 64. The system where, apparently, I was holding the controller wrong the entire time. I only just learned this decades later! Now in the last paragraph, I mentioned calculating the number of match combinations that we’re gonna have in these titles. But that’s a bit misleading. I really mean that we’re calculating the number of permutations. Which are combinations, in which order matters. Think about it like a number lock, where the code to unlock it is, I don’t know, 6-2-4. If we’re talking about purely combinations, well then, any rearrangement of those numbers would unlock the lock. 2-4-6, 6-4-2, etc, etc. And that results in many fewer possibilities. Think about it this way, when position matters, you’re using permutations. So in the original Smash 64, there were 12 characters and 9 stages. Since multiple people can plays the same character, and they’ll all choose Pikachu, since he was totally overpowered in that first game, and looked just so darn cute in his little hats. We’re calculating what’s known as Permutations with Repetition. Just because a character was selected before, the next player can also select the same character. When it comes to combinatorics, these are actually the easiest ones to calculate. Player 1 has 12 characters to choose from. Player 2 also has 12 characters to choose from. Same with Player 3 and Player 4. So that would be 12 possibilities * 12 possibilities * 12 * 12 or 12 to the fourth=20,736 possible character orders. It’s not bad for such a simple game. And each of those character permutations can be played on 1 of 9 different stages. So you just multiply the two together, and you get 186,624. I swear it felt like I had to play that number of matches to unlock Mewtwo back in Melee. And remember, that is purely off of simply the characters and stages. Multiply it by 2 because all of those versus matches on all of those stages have the option of either being a timed match or a stock match, which now gives us 373,248 possibilities. And here, you could actually get crazy in a hurry by adding in the different lengths of time and team matches and handicaps. But honestly the numbers are gonna get crazy without all of that. I’m just interested in the core essentials of what makes a Versus match a Versus match. Character, stage, type and of course Items, because what versus map selection process would be complete without someone insisting that the hammer be turned off because it’s so unfair. Or bombs because they’re too random, but you all know that you wanted the Beam sword back in the day because they used to be so good. In total, there are 15 items that you can turn on and off. You can also get their appearance frequency to six different levels:- very low to very high, or simply just none. Now that all might seem hard to factor together, but the math here is actually pretty easy. Is the Beam Sword on or off? Two options. How about the Home-run bat? Two more options. Hammer always off! No, just kidding, that’s another two. So you got 2 * 2 * 2, all the way down through all of the items, 2 to the 15th power or 32,768 new variations of game-play simply based on the items alone. Now we multiply that by 5 to account for the frequency settings, not 6 since the “None” option is actually accounted for in that last calculation, if all of them are set to “No”. So you wind up with a 163,840 different match types off of items alone. Multiplying that number with the nearly 400,000 match varieties we found through characters, stages, and type and we get ourselves 61,152,952,320 different playable options for your standard Versus battle, with four characters on screen. And that’s Important for me to point out, since this doesn’t take into account permutations with fewer than four players. I also didn’t differentiate between a human and computer-controlled character simply because I didn’t think to do all that until after finishing the math for literally the rest of this episode. *???* So just know that the actual total match varieties is slightly higher if you factor in all of that. Still, for four player matches only, it is a MORE than a decent number. But now with that baseline set, let’s jump ahead a few generations to Super Smash Brothers 4, to see what a huge difference adding a few more characters creates. SSB4 had a strong roster of 58 playable characters, half of which were from Fire Emblem. It also broadened the number of potential players in any given Versus match, from 4 to 8. So applying what we just covered with Smash 64, we know that it’s gonna be 58 X 58 across all eight of those potential players, or 58 to the 8th power to get ourselves the total number of possible character permutations in any game at one time. After we plug that formula into our trusty TI-83s or honestly, whatever online scientific calculator I can find today because my TI ran out of batteries, and I really don’t want to run the store today, we know that there are 128,063,081,718,016 possible iterations of character combinations. That is more Versus permutations than there is money in the entire world, or about 80 trillion US dollars. Even more impressive to me is that that is 6 billion times more character combinations than there were in the first game of the franchise. It’s crazy how times have changed. Assuming that each match takes around 3 minutes to play, it’s a total of 731 million years of game-play to play each of those iterations once. Fun fact by the way, this channel last year was watched for over 4 billion minutes, which is 7610 years of time! What’s crazy about that is that the oldest human civilizations discovered throughout history only cap out at about 7 to 8 thousand years. That’s right history books, you have the Greeks, the Romans, and the Theorists. *OH YEAH* Anyway, just a fun little statistic thought you’d get a kick out of. The rest of the calculations for Smash 4 are basically what we did with the original game. The Wii U version featured 55 total stages, but with the added wrinkle that now all the stages have an optional Omega form, which changed their layout to be similar to Final Destination. So that doubles our number and jumps us up to a 110 possible stage options. There are also now 3 main match types:- time, stock, and coin. And rounding out our calculations, 75 items that could all be cycled to low, medium or high. So that would be 2 to the 75th power * 3. Which, uh wow, 2 to the 75th power’s a lot bigger than I expected. Items alone are adding in 113 sextillion different options! 113,336,795,588 -Thousand, Million, Billion, Trillion, TRILLION – 871,485,128,704 -WOO! FIRST TIME! Got it!- D-different options just based on items. Should finish that sentence. When you see these huge numbers, it’s really hard to read them backwards. So anyway, 128 trillion character options * 113 sextillion item options * 110 stages * 3 game modes. In total we’re talking Geez, just just put it up on the screen. If you could even fit it. No, no, n-no. You shrunk it too small here, just wrap it around the screen a bit. Yeah, make it a curve, make it curve around the screen, God, what even is this number? 36, 37, 38, 39. 39 total places! Okay. Apparently, you get yourself 5 duodecillion total match permutations! Let me put that in perspective:- The most accurate estimations right now say that the human body contains 37 trillion cells. Well multiply that by a 130 septillion, and you’ve got yourself the number of basic Versus matches in Super Smash Brothers 4, Wii U. 5 duodecillion! Alright. And yet despite all of this tremendous amount of variety, many of these options are never used in the professional circuit. Tournament play has grown a lot, since its beginnings with Melee. But in an effort to remain fair and competitive, much of the game has been thrown out the window for the sake of balance. So much so that Sakurai himself has come out voicing concerns over the growing gaps between casual and competitive players, and how he believes that competitive play is going against the original vision of the game. But to see just how concerned he really should be let’s take a look at Smashes Meta. No, I’m not talking Meta Like Doki-Doki fourth wall breaking Meta, but the strategies and limitations used by pro players that go beyond the game’s natural rule sense. Now obviously this fluctuates over time, as characters get rebalanced and the game gets patched. But as of the most current tournaments, out of the 58 characters available in SSB4 only 19 are generally used in competitive play by pros. That is less than a third! Of the 110 total stages, 48 tend to be banned, which remember is pretty much all of them, considering that there are only 55. The other 55 are just reskins of Final Destinations to spice things up a bit. They’re all 1v1 stock matches, and of course as we all know, items are sent to none, or maybe Smash Balls? Maybe? if you ask really nicely, pretty, pretty please? So plugging all those restrictions into our same calculations, We get 19 * 19, for the 1v1 match, * (110-48), to account for the thrown out stages * 1, for stock matches, * 1, because you’re not allowed to play with items, To get ourselves the grand total of competitive matches to BE:- 2 hundr- wow its actually less, it’s actually far less than I was gearing up to say. I’m like 2 HUNDR- uh, nope it’s not it’s 22,382. That is staggeringly low. That is- *Same MatPat* Geez, okay. I did this calculation but now I gotta actually read the number. That is 0.0000000000000000000000000000000004673% of the total actual playable Versus match options. That number alone explains why Nintendo has probably expressed some concerns with Smash tournaments over the years, and why they’ve tried so hard to make more of the maps and more of the items more inclusive in professional gameplay. I mean think about what this means. That is an infinitesimally small percentage of the game that’s being used here. It’s actually pretty fascinating. Looked at with those numbers, professional players eliminating most of the game in order to master a fraction of a fraction of a fraction of a single percent of everything that Super Smash has to offer. I’m not saying that as judgment or anything. I’m just reporting statistics. I have no skin in this game. I don’t care in the slightest. You play a game however you want to play a game. Is that a controversial view in 2018? Anyway, I just think it’s interesting to consider whether top tier players of this game are actually playing this game. And I totally get it, the Hammer is a ridiculous item. Meta Knight was completely broken. Bombs appearing out of nowhere resulting in way too many unfair kills and Pokemon Stadium’s constant changes are disruptive to serious strategies. It just begs the question, can a game filled with randomness also be competitive? Randomness also affects speedruns too, but those are still considered professional valid games. Anyway the solution to me, since no one asked for my opinion, is to create separate categories that test separate skill sets. One that limits the gameplay down, and tests pure mastery of control and strategy, like what already exists. And another bracket that opens up the door to more of the game’s elements, randomness and all. Which tests the ability to strategize, not just against your opponent, but also against the game itself, adapting on-the-fly. It’s a thought, heck, I just don’t want Sakurai sad. He works so hard on these things. That poor guy’s eyes are all red, for us. Professional play aside, we’ve got ourselves one last set of calculations. The one that you’ve all been waiting for. The Big Daddy Super Smash Brothers Ultimate. As we’re all very familiar with at this point, Ultimate has announced that “Everyone is here!” Which means as of me writing the script, there’s an astounding 74 playable characters available. Of which professional play will probably keep 5, as everyone else is going to be too unbalanced. However, as we all know not everyone is there. One tall, cool, purple glass of water is missing from our new Smash roster. *Cue sad music* Those of us in the cult of WAH have been pushing hard to get Waluigi added to the game. And because I’m an optimist, but more so because I simply like round numbers, I’m adding him into the roster, bringing playable characters to a nice round 75. That means that with character permutations alone, you’re looking at just over 1 quadrillion possible matchups. 50 billion times where this franchise first started out at the N64. Ladies and gentlemen, we’re not in Kansas anymore. There are also 103 announced stages for this iteration. But again at a better unite competitive and casual play, each of those stages not only has an Omega form, but also a Battlefield form. Meaning that they have all those little platforms that you just want to do an upward smash through. So that means 309 total stage options, but we are still not done. Ultimate apparently has the Stage Morph feature, where you select two stages and the game randomly flips between them to keep the fighters on their toes. Now, we all know that Smash players love to debate best characters and stages, but with this new feature, I think we’re gonna be able to create a level that all Smash fans will agree is the single worst stage idea ever fusing 75M with Pac-land. *NO BAN THAT* You hear that? Even before it’s confirmed possible in the game, I already hear it prebanned in competitive play. Anyway, this new feature adds in a whopping 95,172 possible stage options. Bringing the grand total to 95,481 and technically theres still even more here, because you can now turn on and off stage hazards, but since I don’t know which stages will and won’t have hazards, it’s not really worth guessing because, Holy Smash Balls you’ll easily have over a 100,000 stages to fight on. And finally when it comes to items, 85 have been confirmed via a combination of the Smash Brothers website, and from what we’ve been able to see from gameplay clips. And looking at the list of unconfirmed items, which includes the Home-run bat and Super-stars, I’d say that there’s a good 15 to 20 that are also gonna have a really good shot at being in there. So let’s just say that there’s gonna be 100 items in total. Remember that’s 2 to the 100th power * 3, for the frequency settings, or 3.8 nonillion combos off of items. Nonillion. 9- it’s up there. J-just egregiously huge. It’s just an egregiously huge number. And of course, there’ll be stock, time and coin matches because why not, it doesn’t matter, It’s multiplying by 3. It’s not gonna make that huge of a difference. So anyway, We’ve got ourselves 1 quadrillion characters, including Waluigi, * 95,172 stages * 3.802 nonillion item combinations * 3 modes *SHINK* for a grand total of *???* Lord, what is this? Okay. Okay, huh. 1 Sedecillion, 87 Quindecillion, 29 Quattuordecillion, 621 Trecillion, 867 Duodecillion, 929 Undecillion, 534 Decillion, 719 Nonillion, 356 Octillion, 228 Septillion, 316 Sextillion, 692 Quintillion, 480 Quadrillion (1,087,029,621,867,929,534,719,356,228,316,692,480,000,000,000,000,000) possible matches. I love it when I get to talk about numbers that have really weird names. That is nearly the number of nucleons inside the mass of Earth. If you took 3 minutes to play each of those possible matches, it would take 6 quattuordecillion years to play through all those possibilities. You know how long that is?! It is so long that I can’t even describe it using normal numbers. I mean the age of planet Earth is 4 and a 1/2 billion years. Playing all of those matches would be 1.3 undecillion times the age of Earth which, again, is equally meaningless. It would be 434 decillian times the age of the entire universe, again, a completely meaningless number. It is without question the single longest length of time that I’ve ever covered on any of the Theory shows. Over on Film Theory, I calculated the length of the longest Spongebob meme ever which wound up being, 8.7 octillion years. To play the entirety of Super Smash Brothers Ultimate would be 689 quadrillion times that amount of time. Sure it might not be more matches than particles in the entire universe, like in the Mario Maker episode, but the universe will have been born, matured, and gone through its own heat death, millions upon millions upon millions of times over, while you still grind away playing zero suit Samus versus Belmont on Wiley’s castle fused with Hanenbow with only Beam swords and Star rods. My only regret with this whole episode is that we weren’t able to get into numbers that were big enough to name, like I did in the Marioplex episode. I really wanted to name something after Sakurai, for putting in this amount of work. This man deserves it. Wait- There’s Smash Down and Tourney mode? As well as all those other character combinations, and handicaps, and times and stocks? Hmm, maybe we’ll come back to this one on another day. Sakurai, I’m gonna name a number after you. I swear it. But until next time, remember, that’s just a Theory, a Game Theory! You know, we’ve talked about a lot of big numbers today, but I’ve got one last one for you:- 23,000. Sure, that might not seem like much when compared to the reality breaking figures of Smash permutations, but it is a huge number, once you consider that it’s the number of unlimited classes available to you with Skillshare. Who’s not only our partner for today’s episode, but has been a long-term and trusted partner for this channel. A service that is literally used by everyone over here on Theorist HQ to improve and broaden our skills. But I’ve already talked about all the classes that we use over on the Film Theory episode about Superman, and about all the journalism classes that he should be taking over there. Instead today I want to focus on you, because it’s not just us using Skillshare but its loyal Theorists like you. In fact, so many of you have already started using Skillshare, that we asked them for some statistics to see what classes you guys are most interested in, and I gotta say the results are really fascinating. My friend Jazza, who’s an artist that I met at VidCon, Australia. Actually has the most popular class with you guys:- “Stand out and make money on YouTube!”. Seems up your alley. Now, if there’s someone you can trust the advice of, it is definitely Jazza. He’s an incredibly smart and talented guy. And speaking of artists, A lot of you have also taken “Digital Landscapes: Painting Environments with Photoshop”, which I’m sure is why we’re getting so many incredible pieces of fan art these days. Then, in the number three most popular spot for you guys is one that I actually took for myself:- “Video Editing with Adobe Premiere Pro 2018 for Beginners”. I actually watch a lot of these editing tutorial videos across all different skill levels, because no matter how long I’ve been doing it, there’s always something I learned. And yeah, sure we work with editors now, but it makes me a better director and producer of a YouTube show if I’m able to communicate with them, and know the limitations of the programs that we’re working with. And lastly, rounding out the number 4 and number 5 slots, “C++ from Beginner to Expert” and “Comprehensive Essential Japanese for Beginners” both skills that, honestly, I might have to follow your guys’s lead on, because I’ve been wanting to beef up my programming and language abilities for quite some time. I’ve never actually carved off the amount of time that I need to do it, but in one of these days. I do want to teach Oliver a new language. I do want to teach him programming too. Maybe we could take them together. Still a bit young. I wonder if there’s a “Programming for Babies” class. Anyway, so that’s the Theorists top 5, which is honestly a great list. I love how diverse it is. Just like all of you watching. Rainbow. So whether you’re setting up for a new hobby, getting ahead for school or building up your resume for a dream job, Skillshare wants to help. The first thousand people who sign up using our link in the description, get two months completely free! After that it’s as low as 10 dollars a month. No college in the world is gonna be able to beat that. Probably learn more practical skills too. So geez, go ahead it’s:- skl.sh/gametheorists2 You’re supporting the channel, you’re supporting independent, online educators who made these videos, and most importantly of all you’re supporting your own brain. You can literally learn something in the time it takes to watch one of these episodes, so go do it! Just watch the episodes first. That’s:- skl.sh/gametheorists2 Or you know, the links down in the description. You’ve watched YouTube long enough, you know where the link is. So in the words of Safiya Nygaard, Shmash it! Alright, and most importantly of all, remember, that was all just a theory, a Game Theory! Thanks for learning.