How Many Different Possible Landscapes Are There In RCT2?
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- čas přidán 13. 10. 2021
- You can make a lot of different pretty landscapes in RCT2, but how many different possibilities are there? In this video we find out.
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Every RCT map is personalized (mathematically)
ok
get a new meme
Is this a mario iceberg joke? lol
_YOU WANT FUN?_
_MARCEL SHOW YOU FUN_
It's weird to think that somewhere in that incomprehensibly large stack of levels, there's one with your username and password written on the ground
And not just one, but more than a Googol of them. Assuming you write by raising the terrain up, you only need 58 tiles to have more than 10^100 different surface and edge combinations.
Well, how many different ways could you write it down on a sheet of A4 paper at a molecular level?
It's far "deeper" than this.
Every piece of information to have ever exist and that will ever exist is contained in this large stack of levels.
The same applies for the "Library of Babel". It contains all information that can ever exist. You just have to find it first :)
And there are many times more which are your username and password but a single pixel off.
*every piece of information that can be expressed in each combination, which is about 0.14 MiB. So not actually that much information on a modern scale
You know, while it might not be the best thing for ~engagement~, I really appreciate that you put the answer to the video titles in your thumbnail. I always watch the video because of it because I want to know how you get to that conclusion.
Sure beats a thumbnail of a rollercoaster that somehow has a :O face and a ton of ??????'s on it.
It might actually be better for engagement in some cases surprisingly. If people see a huge number in the thumbnail they will want to know how I arrived at that number, which causes them to click the video.
i too love anti click bait like this
It's like reverse clickbait, he gives you the answer but most of us don't want just the answer, so we click.
How's and why's are much more interesting than what's.
That read so much better in me head...
@@Captaintrippz It's a good phrase.
As a high school math teacher, this was one of your most enjoyable videos yet. How you keep coming up with these compelling topics on my favorite niche game is beyond me. Long live this channel!
Right? Every time a totally different video! I don't think I can ever get enough of it
*Arithmophobia Sufferer*
Recent thoughts:
_A big number looks too intense for me._
Never have I been so interested in information I will never have any actual real life use for.
I don't even play the game and I'm still watching these videos because of how well done they are
When you encounter a number like 10^365,565; use this for comparison:
The estimated total number of atoms in the observable universe is 10^80.
I was just wondering that.......................it seems I was wrong in my estimation!
That’s a little bit over a decimyrillion possible combinations
Most of these combinations are fairly unplayable -- it would be interesting to see how many landscapes exist that support some continuity criteria, e.g. lipschitz continuity!
The funniest kind of continuity
number of fun landscapes?
Fermi approximation - divide by Googol.
More than you can finish.
I want to see Marcel Livestream a playthrough on randomness park 😀
Not just some of them are unplayable, almost all of them are unplayable static.
it'd be interesting to see a randomizer scenario where every tile has a random landscape at the start and you have to make a park from it. Maybe even disable terrain changing if possible.
That sounds like a literal nightmare scenario.
Where do I sign up?
I love insanely huge numbers like this because they’re all just a minuscule rounding error compared to TREE(3).
Or even Rayo’s number!
I recommend a video called "List of Large Numbers" you will see words like "Googol" or "Giggol" or even "Boogol".
@@DarkstarArchangel
A googol is tiny compared to most of the end numbers in this video, and TREE(3) is so much unfathomably larger than any of these numbers.
Even your giggol or boogol are nothing compared to TREE(3). Pretty sure.
TREE(4) would definitely win though.
Rayo's Number (as mentioned by Samuel), however, has all these beat by margins that no number you or I could ever write with any notation could ever come close to.
@@OriginalPiMan That's why I mentioned the "List of Large Numbers" video and mentioned numbers like Giggol and Boogol.
...and yet TREE(3) is itself absolutely nothing compared to the Busy Beaver numbers (by definition, they grow faster than any computable number, and the TREE sequence is computable).
I feel like you just had a university lecture about this and decided to make a video how many different possible parks in total there are. Then you realized it's way to complicated with rides and scenery, so you went with how many different possible landscapes are there :D
At least that's how my thought chain would go! Love the content :)
I've felt the same after doing my combinatorics course.
I've since then forgotten almost all the formulas and proofs.
I did the same thing after learning the binomial coefficient. First thing I did was check the probability of winning the lottery.
Conclusion - don't play the lottery.
What are you talking about? This is high school math.
It's all basic concepts, just with big numbers.
@@choo_choo_ You get high school math at university too.
@@607 Yeah, in remedial classes. Doesn't make it college math.
Someone needs to line up an interview with you and Chris Sawyer. I think that would be an awesome interview, and I think that Chris would actually enjoy talking to you.
As much as I and many others would love to see that, from what I've heard you have a better chance of running into a wild pack of unicorns than actually getting a hold of Chris Sawyer.
Every time I hear or see Chris Sawyer I think of Rush
I second this
There's a documentary on Rollercoaster Tycoon by a CZcams channel named Noclip where they tried to get in contact with him (Marcel even features in it). He very much just wants to leave it as a part of his past.
@@TomDolby I find that crazy, but I am not him so I don't know how he feels, but man what an amazing man and an amazing accomplishment.
I've always loved how Marcel uses different colorations to highlight things in his videos. Using the game itself as part of the editing adds a lot of charm to the video!
I also love math, so this video was music to my ears!
Marcel is my go to for when I’m having a panic attack. His videos are so calming and nice
Even when he’s talking about ludicrously large numbers
ghci (the haskell terminal) can calculate (possibly infinitely) large numbers, I typed 10^1000000, and it worked, although it takes a while to print such a large number. It does give exact answers instead of scientic notation though. But it is probably quite easy to find a haskell program to calculate such numbers in scientic notation seconds with haskell.
Marcel: A man of torturing guests, a devout follower of the RCT Gods, and a mathematician of incomprehensible numbers.
My goodness.
so basically a cthulu cultist?
@@xionkuriyama5697 You could say that, yes
My mind has melted thank you Mr Vos
When I was younger, I wanted to know "how many images can there be", like, how long would it take to refresh a monitor with every possible combination of pixels that it could show. I very quickly realised that it would be incomprehensible, and this video just reminds me how my brain is incapable of comprehending just HOW incomprehensible this kind of number truly is 😅
Placing a toilett makes my park very unique.
Ok so, here's what I propose:
1.342e365565 shall be named Landscapeplex
1.915e496495 shall be named Cogwheelplex
and the theoretical number of total RCT2 parks (over 1e1000000) shall be named RCTplex.
I considered naming one of these the Marcelplex (or Vosplex, but that sounds kinda lamer), but I wasn't sure which.
I know its only been a few hour but, underrated comment
Am I the only person who watches the "hello, everyone, and welcome to another video" line on repeat a few times before starting to watch the video? I mean, this man's got a great voice and accent, it brings me so much peace.
Probably yes.
Yeah you might be.
You must also like Anton Petrov's "Hello Wonderful Person, this is Anton . . ."
I usually say the line whenever I see a Marcel Vos video, it is indeed an iconic voice, accent and way to start the video.
It's like FailRace. Has used the same intro line with the same inflection since his very early days, maybe even his first video.
Even if every single person in the world were to generate one different terrain every second, the universe will end before we even get close to all possibilities… 😬
Dude you don't know when the universe will end quit trying to sound smart
@@user-wk4np7fh2v quit being a jerk you ignoramus. It's called hyperbole.
Plus, ever hear of the "heat death of the universe?"
@@user-wk4np7fh2v I don't think you understand how large these numbers are...
@@user-wk4np7fh2v The heat death of the universe is calculated to occur in roughly 10^100 years
A quick google search tells us there's roughly 10^80 atoms in the observable universe
So doing the math, if every atom in the observable universe generated a new landscape for every second the universe has or will exist, we get... 3.1536×10^187. Which is not even close.
@@splatter_proto It’s crazy because that number is still virtually nothing compared to the total possibilities…
My brain had already melted out of my ears by the 10 second mark.
"I want to get off Mr. Marcel's Wild Calculator"
-34,726 guests
I genuinely never thought I would find a video about math so entertaining. I don't know why, but seeing numbers that huge in a video game, especially a game like RCT2, makes me bust out laughing. They're just so big!
As if I didn't get enough choice paralysis when playing RCT
Finally! Vos answering the hard questions. Keep at it bro
This is the hard hitting journalism I subscribed to
One of my favorite rct2 videos so far, but then again, I love numbers. I thought you did a really good job of breaking down binomial expansion and factorial without getting too in depth with the math. The number of possible parks are intimidatingly huge. Every extra factor of random blows it out of proportion again. The names of the rides, the names of the guests, the locations of the various guests, music choice, color of Rollercoaster including individual tile customization..... All things considered, I don't think you'd be as big as G64 - Graham's number, but definitely larger than g1.
This sounds like some marketing blurb someone would put on the back of the box. “Over a trillion different landscape combinations!”
Now that we know how many combinations of Rollecoaster Tycoon landscapes there are because of Marcel Vos
and how combinations of Minecraft Worlds there are because of Ant Venom
(though that video is a bit dated now because that was on a older version)
now we all we need is Decino to make video on how many combinations of Vanilla Doom Maps using the stock assets only are there
Great Video! Thanks, Marcell I never miss your videos. I've been playing RCT since it first came out in the 90's. OpenRCT2 breathed new life into an addictive game.
Youre effectivly officially the SpiritOfTheLaw of Roller Coaster Tycoon 2! xD
These numbers, when they get this high, are very difficult or even impossible to visualize or compare to one another. I think it's because our human brains just weren't meant, nor ever evolved, to have a need to ever deal with them; who could gather that many berries, or have that many tribe members? Looking at a sandy beach all the grains of sand become one to us, not separate entities.
I once calculated how many possible different Minecraft worlds there could be (most of them would be just chests filled with random coloured shulker boxes filled with random sized stacks of random items, every other kind of world would be a rounding error). The number was so incomprehensibly large that it could no longer even be expressed as scientific notation, but only as a power tower: approximately 10^10^10^10^159
That number has too many digits to even enumerate how many digits it has!
@@tylisirn If you have the time, I'd suggest watching "What is the largest number?" by CZcams mathematician Sharkee. Very interesting. Have a good one!
"Ginormosity" is an excellent word and I will try to use it more often in my own life. Also I giggled like a small child every time you read out those powers of ten. When even your exponent is incomprehensibly large, you know you're into uncharted territory!
This is probably my favorite video you’ve ever done. Brilliant work.
Who needs cosmic horror when you have numbers like these to make you feel insignificant?
Insane how quickly the numbers get huge. Probably >99,9% of the parks end up unplayable but the theoretical possible combinations are nearly endless. I know it sounds cheesy but something to think about when looking at planet earth; out of all the random possibilities we have this planet with functioning life on it. Look outside at nature and there seems not much random. It's like choosing one of the random parks and then ending up with the Marcel Pixel art one.
And then look at all the other planets that can't support life and realize it only looks like that because we couldn't have formed on a planet we couldn't have formed on.
This is madness! Good job.
I didn't even know about factorials until today. Thanks for this very informative video.
These videos get better and better, also probably my favorite music from the game :) and loving the online community! ❤
Big numbers makes me happy!
wow what a sick nice math video. the numbers are serious sick for suth a game.
awesome video Marcel Vos, ik vind je video's geweldig. ik leer zoveel dat ik echt snel beter wordt in RTC, mega veel dank voor al je video's
keep up the awesome work, can't wait for the next video you post.
I want to see Marcel play a scenario where the terrain has been randomized and has to make a park out of it.
I guess you could say that it's....INCONCIEVABLE!
You keep using that word.
If you think that's big, try looking in to graham's number. Then, when you've recovered from that, look into tree(3)
My favorite number is TREE(TREE(G64))
Come for the RCT2 guides, stay for the combinatorics.
Mind Blown!
I love it when Marcel does math videos. I really liked the launched coaster g-forces video too.
If you start taking symmetry into account, you no longer have 19 tile formations, but only 6 (flat, one corner raised, 2 adjacent corners raised, 2 opposite corners raised, 3 corners raised, 1 corner raised by 2). The top height only admits flat, the second-to-top admits 5 formations, and all below admit 6. This gives a total of 180 different height formations (instead of 567). When we check height with its possible water combinations, the total number of land + water combinations possible is 2616 (instead of 8281). Adding the 56 terrain options, the total combinations on a single tile would be 146496.
The point is that bringing in symmetry in your calculations can make for an easier time. The second point is that the group-theoretical approach of problem solving is fun - for me :)
Of course, a park with a certain tile changed (e.g. north corner raised instead south corner raised) is physically a different park, but you can now describe them in 'classes', which makes it a lot easier to describe them.
The symmetric arrangements of individual tiles don't really make a difference though, because if you take a park, and rotate one tile, it's a different park. For symmetry, you'd have to consider the entire park at once, and the difference from the assymetric calculation would be division by some number less than 8 (because each park can have up to 4 rotations + 4 mirrored rotations, but some parks will actually already be symmetric so they won't have all 8 possibilities, meaning that the average must be less than 8.)
I guess someone was good at math! Haha, cool video man!
If I learned something from watching Marvel's videos, it's that there's a lot mor math in rtc then yih would expect!
This park is really incomprehensibly variable!
random rct2 trivia is exactly what i need after pulling an all nighter in a techno club. thank you marcel
For reference, there are something like 10^18 grains of sand on earth, 10^50 atoms in earth and 10^80 atoms in the known universe. There literally is no way to make the number comprehensible. You could remove one variation for each atom in the universe, each second for the entire time the universe has existed and the number would barely change.
Marcel Vos our RCT2 Mathteacher :D
That's some nice pixel art.
This means you can encode information as RCT2 landscapes at about 18.8 bits per tile, so a 254x254 map could hold about 150Kb of data.
You could save a small RCT2 map as a bigger RCT2 map!
Amazing!
YES, new video!😀😀😀
Hey, you've basically ended up performing
Statistical Mechanics-style calculations in trying to do this. If you're having trouble finding sensible calculators online, I'd highly recommend taking logarithms and using Stirling's approximation; that way you can keep track of these insane numbers by hand :) .
It is estimated there is around 4.65 x 10^185 *Planck Volumes* in the observable universe
Numbers so big you could scientifically notate your scientific notation.
10^10^6
"Some are lovely landscapes, some are works of art and most are completely random"
This is literally a working version of "give enough monkeys enough typewriters and enough time, one of them will write Shakespeare"
Interesting. And this is just from a 90's computer game. Makes one wonder about the seemingly infinite variables and possibilities in real life and the universe.
There are an estimated 10^80 atoms in the observable universe...
When math finaly makes fun ;)
To put this into perspective, according to the many worlds interpretation of quantum mechanics, there are "only" somewhere on the order of 10^500 parallel universes in our multiverse
To put that into perspective There's only 10^80 atoms in the observable universe
Assuming perfect compression ( which is not the case, but close ) the complexity, or number of possible permutations, for a park of a given size with a given number of items, should, in theory, be similar to your file size. So, if your file size 10 bytes, that's 256^10 possible permutations. If the save file is 1MB, that is 256^1,000,000 permutations. That logic similarly applies to other games as well. On that note, Vsauce has an amazing video on the topic of what "all possible permutations" really means, and it's absolutely crazy, I believe it's his episode about whether we will ever run out of new music.
TLDW version: A lot
I love the music. I saw the link to the outro music--it's amazing. Is there a link to the full length background music anywhere? I love how meditative it is and would love a longer version (like your background music).
That's... a lot of zeroes.
Didnt understand one single calculation or any outcome but it sounded big, and thats cool
I want toget off Marcel Vos' wild mathmatical ride
This is existentially terrifying.
Perspective: There are estimated to be 10^78 ~ 10^82 atoms comprising the entire known universe.
Roller Coaster Tycoon 2 is more advanced in maths then the calculators folks, You learn something new each week with Marcus.
Need to add mowed grass and unkept grass to the terrain combinations. /s Excellent video!
This makes me feel like I'm watching MatPat calculate the number of possible Mario Maker levels all over again...
Great work on your calculations and presentation!
My brain hurts. I loved the video! =D
Next episode: Marcel gets a government supercomputer to calculate the total number pf possible park permutations.
This is the kind of video I want to see 😀
Very good video, and well done with the maths. The formulas seem to be correct if I remember my maths right.
One slight thought about the terrain (see 3:15), or more specifically the edge textures:
If a specific tile does not have any visible edges, can we really include those edges in the formula?
On the one hand, the information about the edges are in the game, indicating that it should be included.
On the other hand, the difference between two variants of invisible edges are not possible to detect by purely looking at the terrain, indicating that we should exclude invisible edges.
However, the maths required to exclude edges that are invisible would be so extremely complicated that it would probably be pointless to even try to include in the video, so I would like to say that you did the right choice of formula.
I think we can say that the possible amount of different park layouts is close to infinity? When numbers get incomprehensibly big like this, there is no other way to put it.
It's not even close to infinity. As a matter of fact, most numbers are bigger than this one. It's a below average sized number.
@@Lemon_Inspector :(
Good video to show how even when we can see that number of possibilities are obviously limited, it doesn't mean that our efforts in creating something within them are futile.
Most of possibilities are gibberish, unlike our creations, and what you create still has incomprehensibly low chance of existing somewhere else.
be very affraid numbers are attacking here!
alot of realy large numbers.
pretty entertaining video as per usual offcourse
Now that's a lotta damage!
After talking about scenery: How about a little more?
excuse me, that random park landscape you flashed on screen for about 5 seconds is a thing of absolute beauty
competition idea: each contestant has to build a park on their own randomly generated landscape
Great video. Your cogwheel example assumes that the maximum number of scenery items must be used. If you count the combinations where less the maximum number are used, you would go up by at least another 10^100,000,000
When I downloaded RCT2, I never imagined it would be the game that would get me to lay in bed thinking of all the possible land decorations that outnumber the age of our universe... And how I can try and work that into a themed roller-coaster that's good value!
Marcel does math again!
I feel like Randall Munroe would love this video.
My scientist friend: You have no idea how large the figure 1.342*10^365,565 is. Me: Well I know. It would fill up with "0" in more than 100 pages in Word Document.
Different water height feels like cheesing it
a new RCT video from Marcel always brighten a boring day.
The fact that there wasn't a calculator strong enough to handle the calculations you had to do was great.
Me watching the video: I like your funny words magic man
Insanity!
Now we need to know the numbers for rct1 and rct3, transport tycoon deluxe, and the rest of the saywer games to find out how big 1 Sawyerplex is
I thought you said Factorio & i got excited
I didn't realize how much I wanted to see Marcel make some Factorio content until just now.
Mathematician: Welcome to combinatorics! Enjoy your stay!
According to some cursory research, there are approximiately 1.33 x 10^82 atoms IN THE ENTIRE UNIVERSE. So yeah, 10^365,565 is literally incomprhensible. WolframAlpha says that it is 10^10^5.5 (yes, exponent within exponent) times larger than the number of atoms in the universe.