Hey everyone! I wanted to get this video out quickly so I could also make people aware of Summer Games Done Quick. As a result I missed an error in the video. At 22:57, RNG(3) should be a^2*b + ab + b, not a^2 + ab + b, and RNG(4) should be a^3b + a^2b + ab + b. Apologies for the error!

Imagine seeing a 30 second clip and being like "huh, that's some good RNG" But secretly it was a culmination of three people using their mathematics PhDs to calculate exactly how they needed to do things

When you make a Paper Mario video for your college thesis

I... was not ready for number theory in a video game TAS.

RNG is my favorite topic for TAS because of how you can use black magic to get things to be in your favor.

“We’re gonna manipulate this ring to get a 1/46,000 chance” Me: Okay, seems reasonable... “Wasting only 2/10ths of a second” O_O

"No chance, no matter how small, is really impossible!"

"I went forward in time to view alternate futures. To see all the possible outcomes of the coming mega rush drops." "How many did you see?" "46,000" "How many was possible?" "....One."

Don't you love when wanting to complete a game as quickly as possible results in RNG manipulation that requires advanced calculus and coding skills?

I learned more about probability in these 40 minutes than I did throughout my whole stats class.

This is like catnip for computer engineering majors.

When stryder7x only uploads once every blue moon so you gotta get your paper mario fix somewhere else.

I love how the music changes over the video as you guys got closer to the solution. Starting with creepy, archaic, and kinda hopeless (and puzzle-y from where in the game the music was from) to triumphant and victorious. 10/10 math and 10/10 music choice

I think I know why text calls RNG! It causes the slight changes of pitch in the text sound effects, hence why all the text scrolling sound marginally different and not the same sound directly repeated. Presumably it'll do this even if the sound is printed automatically, and more importantly, even if the scroll sound is set to be silent like it is in menus. That's why the pause ment shakes up RNG so much. It's pinging to play silent sounds of dozens of characters printing.

"If you pause for just the right amount of time and jump three times"

those popoffs when you find time saves are heartwarming

At what point will there be college courses in Paper Mario?

When I first became a fan of TAS videos, it was the insane shit like this which got me hooked. I remember spending hours reading TAS submission notes, as TAS runs got more complicated over the years, and it was half the fun of a TAS for a fan like me. It's wild to see these explainations Pivot To Video, but I'm so glad they have. With the popularity of Very Specific Videos nowadays, I hope more people get sucked into these explainations. TTYD TAS hype.

It turns out RNJesus is a reverse engineer. Amazing stuff Malleo! Looking forward to hearing you at SGDQ!

I I think i'd like to go back my the diagnostics of an A press this seems too advanced for me

Brb, gonna go manipulate RNG to win the lottery

I'm getting "watch for rolling rocks in 0.5 A presses" flashbacks

Me: Expects a 10 minute video. Me: Sees that the video is 39 minutes. Me: A surprise to be sure, but a welcome one.

Wasn't expecting geometric series in a Paper Mario video

Watching this video puts into perspective how much effort is put into a TAS, it's mind blowing. Great video and I hope you keep it up!

If only my Finite Mathematics class were about Paper Mario instead. Maybe then, I'd actually understand it...

"Is it easy to get into speedrunning?" "Well...depends. What did you major in?" "Math." "It's a start, I guess...read up on coding first."

Is it bad that I don't want to watch the progress streams because I enjoy being surprised by all the cool tricks when it's complete?

I know a married couple. One is a huge fan of TTYD, and knows some rudiments of practical coding. The other is a huge fan of the number theory/conceptual/algorithmic sort of coding. So I sent them this, and they had a great time watching it together.

Can we give a quick round of applause for Nintendo's programmers? Imagine the work needed to make sure your game doesnt shit itself if someone figures out how to sequence break this hard. And all those percentages for one item. Jesus Christ. You did good too Mr. Mathematics, deconstructing and testing it. It just makes me realize how awful Nintendo games could be in lesser, more apathetic hands.

First 2 Paper Mario games are the most BIG BRAIN games in existence

Can’t wait to hear from you at sgdq

People don't appreciate the nitty and gritty that gets put into the makings of TASes and speedrunning in general NEARLY as much as they should. This was an absolute miracle and I can't hide my admiration for the effort put into this. You guys are fucking legends

Thank you Malleo for this video. I really love this probability stuff, and all the other math is cool to see being used in the TAS. Great stuff! btw at 23:57 you say "All over 1 over a" but you meant "All over 1 minus a".

i think this is a subtle reminder for me to keep learning math cuz i only got this by a small margin lol

23:32 I use exactly that to tell me how many cookies I'll need to buy n buildings in Cookie Clicker.

Is it considered cheating if I throw my Gamecube against the wall, causing a RNG bit to flip in my favor?

This is nothing short of amazing. The TAS community is lucky to have you, and I cannot wait to see your MKWii commentary at SGDQ 😁

You and stryder make some of the best glitch explanations on the internet, keep it up!

next video: "How i used RNG Manipulation on the lottery to win every time"

jdaster is a cool dude. Go play the TTYD Shufflizer mod he made, it's a total blast

I'm supposed to be sleeping and getting up in 4 hours to go to work, instead I watched this whole thing. Understood nothing but the amount of dedication you fellows have is out of this world.

2:38 "I must go, my people need me"

I wholly appreciate how much effort went into not only this video, but the RNG reverse-engineering overall for the sake of simply going fast. Massive props to everyone involved, and an additional thank you to you for making this video and bringing to light the complexity of TAS work :)

Me, before watching this video: I wish my RNG would improve, this boss is tough. Me after: *This is big brain time*

TASers, speedrunners and the entire community behind it are the most loyal fans there is for a game. Change my mind

nice! I definitely learned a thing or two, and the work that goes into TASes is just as cool as the runs themselves. okay, trivia time: Ocarina of Time and Majora's Mask both use an LCG (the a*x+b equation) as an RNG as well, so after adjusting the constants (a=1664525, b=1013904223), those scripts should also be applicable to these games, and surely others (Animal Crossing?). however, every time a new scene is loaded (Link goes through an entrance), these games directly set the RNG seed to the cycle counter of the main processor, so this form of RNG manipulation is limited to within scenes.

I apprecite you and your buddies' work and thank you for the entertainment!

The things people do to shave off a few seconds/minutes in a speed run. It's really neat you can manipulate something like this honestly XD

Can’t wait for this tas. Really is incredible how much work you guys put into it, I’m glad that I can see the result and some of the process.

Jesus Christ, this video is awesome. Love this channel, your style of making content is amazing, and you’ve done many great things for this community. Keep up the good work!

I've never even played this game and have no idea why this was even recommended to me but damn this is actually insane props to you three for getting this figured :)

I didn't understand half the maths in this, but I think I understood enough. I love long, in-depth videos like this! Thanks so much for uploading! Also, now that you can track & manage RNG, will there be more consequences to TTYD beyond 2 Mega Rushes?

I'm in love with all this crazy number theory, rng investigation, and coding to save five seconds in a ttyd tas (yes i know the route as a whole is like half a minute faster but this is still really amazing and i love it)

The probability of me understanding this is about 0.

I didn't understand most of this, but it was still really interesting! Keep up these cool videos bro!

so not RTA viable i assume?

Manipulating luck crashes Paper Mario: The Thousand Year Door.

Holy crap man. This is a fantastic video, I gotta say, if for no other reason than it shows how much effort can go into the most easily missed moments in a TAS. I love the concept of a TAS- pushing the game in ways that, no matter how lucky or skilled you are, no human runner could realistically be expected to pull off. But beyond that, as I see more and more often, it's also a championing of human effort. First, there's you, the guy who puts together the TAS. Then, there's the dozens of people who discovered every glitch you use to skip chapters and such. There's the guys who made the programs letting you manipulate the game with such fine controls. There's the guys who made the scripting engines that let you make quick codes to do brute-force testing. There's the guys who you chatted with in the making of this video to put together this thing here, that thing there, the value of this, the value of that, and eventually put it ALL together into one monumental run where everything falls away and there's just this perfect, impossible run. Days, weeks, or months of work can go into three seconds of gameplay. It's beyond astounding, and I love every bit of it.

This is incredible. Can’t wait to see the complete TAS.

I was there for most of the farm! That was such a hype moment and one I saw live which is rare, thanks for the huge opportunity

Holy crap you weren't kidding when you said this video was taking a lot of time 40 minutes!!! Also explains why I didn't understand wtf was going on in the moment

I wonder if displaying text calls RNG every frame because of jiggle… Some text in Paper Mario jiggles around randomly, so normal non-jiggling text might just have a jiggle scale of 0.

Your video reminded me that math is actually something I can look forward to learning about. Amazing stuff as always Malleo

Top notch. These kinds of finds are incredible.

I now have mad respect for game programmers and tas runners for being gods of the computer

It's amazing how excited you get over shaving seconds off a tasrun, and I absolutely love it.

bruh my brain is not big enough for this you guys are sick though thanks for the entertainment

Something to note about text calling RNG. Everyone seems to be operating under the assumption that it must be because text the text rendering function requires some random element, but another thing it could also be is simply to keep things even more random. With a linear congruential generator, one of the things you have to be careful about is that when using one, the gambler's fallacy is true since all possible RNG values you can get are on a cycle that starts at the initial RNG seed. Suppose you want a particular RNG value that is on the cycle. If the LCG is good enough, it's not easy for a casual observer (e.g. a casual player) to know where in the cycle that RNG value will be. However, what is true is that as you progress along the cycle not getting the RNG value you want, you know that your chance of getting the desired RNG value sometime soon increases, since you cannot get the same RNG value twice until you've looped around in the cycle. You're getting new RNG values each time and so by process of elimination eventually the desired RNG value will be the only one that can be picked as the next RNG value. However, this flaw is really only useful if RNG advances in a reliable and predictable way to the casual observer. To avoid this flaw, you want the calling of the RNG function to be highly erratic. That is, you want when it is called and how often it is called to be very hard to manipulate. And what happens to be true about text in this game? How many text characters are on screen in any given frame can vary quite a bit, and how many frames you keep text on screen is something that's virtually impossible for a human player to control reliably. This will also help to prevent human-possible RNG manipulation in general, not just the gambler's fallacy issue. While it is possible that some aspects of text rendering, such as certain text effects, really do require randomness, it would not surprise me at all if making RNG hard to manipulate was also a motivating factor, especially in instances where there is obviously no random element to the text, such as when it is displayed in menus.

My name is Jeff crashes Paper Mario: The Thousand Year Door

Didn't think this was going to be how I was spending my night, but holy am I glad I sat down and watched this.

You guys are amazing. Not only with the math but also with the coding. Very nice work

Really liked the selection of music you used

this whole class sounded like RAW anime w/o subs i'm so confused i can't understand anything that all those numbers and letters said but whatever it means i'm glad it worked out.

When you understand how the RNG works in a game, and have a reliable means to manipulate it, the sky is the limits, especially for a TAS run where human error is not a factor.

Awesome teamwork to make this happen!

Heh, the minecraft community has been doing stuff similar to this for a while now. (Our RNG is a 48 bit linear congruential generator). I don't have time to watch your entire video atm, so sorry if I am telling you what you already know, but was curious if you guys noticed the applications lattice reduction algorithms have to the reversal process. (in brief, about 10 months ago I noticed, after moving a point to the origin, the vectors ,,,..., form a basis for a lattice containing all n-tuples of possible consecutive seeds. After applying your favorite lattice reduction algorithm, simply iterating over integer linear combinations of these vectors near the region where your seed tuple must lie is often sufficient.) In minecraft, we have used this to find rare seeds (1/trillion in some cases), and more recently obtain a bedrock item by manipulating a certain 1/3000 chance in a process virtually identical to what you do here. Of course, since your LCG is only 32 bits, this might be overkill.

This is amazingly cool that the rng was reverse engineered like this and I remember watching the stream back when you were brute forcing rng for fence skip and wondering whether something like this would be at all possible for this game or if the rng system was just too complex. That leads me to wonder, is it possible to use this reverse engineering method of finding the right rng at other points in the run where brute force and test methods were used in order to possibly waste less frames getting the desired rng or to get slightly more optimal rng than was achieved? Not that you will go back and do that in this TAS but maybe in the next TTYD TAS if/when that ever occurs.

13:23 "Oh my God the video is not even half way over yet! Guess I'll order some takeout."

Unbelievable work, nothing else can be said. Hats off to you all.

And i thought i'd never see derivations again after school... Really makes me wonder if i ever asked my teacher "am i ever gonna use this in real life?"

What an awesome story and collaborative effort! Can't wait until there is a non-tas strategy for manipulating RNG next, ha ha.

This is awesome! I'm so hype for this tas

"I didn't feel happy." -> freaks out on cam

To be honest,because of my lack in knowledge of calculus i didnt understand the whole thing but like 95% of it which is pretty good. this seems crazy hard to me. Awesome job!

Can't wait to see this in the next WR

Godly video. Really makes me want to get around to making a TAS of a specific, obscure game. There’s Dreamcast emulators for that, right? Also, Infinity War jokes about the odds and Endgame jokes about JDAster holding up his finger

This is simply amazing . Tas speed runners are truly masters of the art of making playing a video game even a greater waste of time ( by oddly playing slower then faster ) .

Not gonna lie, getting some PTSD from Discrete Math class.

This makes me appreciate shit that happens by sheer unmanipulated chance much more, and stuff that occurs via manipulated chance WAY more.

Holy shit that's awesome o: Nice to see how so much goes into all of this ^^

Man, I thought learning about parallel universes was tough, but trying to understand this video really hurts my head.

Hey malleo i really liked ur stream, and im really glad u answered some of my questions! :) can't wait for the new TAS TTYD! -tootiefruty

about to watch the video - i hope u mention HOW LONG we spent trying to get it before reverse engineering RNG.

This is why I love TAS'es, you can see it and it's pretty much spectacular yeah, but the story behind them can be insane

Weird way the world works, Fatguy and jdaster together, and malleo and jdaster together. Small world

Seriously incredible

Once I take number theory, i’ll be sure to use this video as study material

Ngl I would love for 'When Luck Just Isn't Enough' to be a full series, going over the trails and tribulations speedrunners and tassers have to overcome in various games to get RNGsus to submit to their will.

What a video :O Thank you!