Hey there, gang! A great point has been made by many commenters, and I think I should address it! An infinitely long number with an equal distribution of all of the digits is not the *only* requirement for a number to be deemed Normal. There are other, more difficult to parse requirements that are more entrenched in number theory. I think that the requirements I stated in the video are still the most beneficial / easy to parse for an introductory youtube video on the topic, but for more info on what a number needs to be definitively Normal, please check the description for further reading resources. Thanks for watching and thank you for commenting!!!
most 9 year olds don't have tens of thousands of hours on their save file before beating the first trainer though. this pi fellow really sucks at pokemon
if anyone is curious back in stream 44 part 3 Pi was only a few steps away from May in route 103, but then at the 36:28 minute mark a 2 came by in the sequence of Pi, at that moment Pi was just over one of the ledges in route 103, tragedy followed and Pi has not recovered yet, May is still waiting in route 103 I commented it months ago in stream 313 part 3.
My mom teaches upper high school math and used to teach computer science back in the day. I’ve always loved Pokémon my whole life so she tried to join me with Pokémon go and has been playing that game ever since it released, so I showed her your channel since it basically merges two of her favorite things and she loves it so much!! She’s thinking about showing some of your statistics based videos to her stat classes haha. Thank you for making these! I forgot how cool math can be :”]
Pokerus is pretty easy to get through repetition. I've gotten it shiny hunting (in sapphire my battery is dead at this point so I can't soft reset and instead encounter and run away) and still never found a shiny pokemon.
@@solsystem1342"Pokérus has a 3 in 65,536 (or approximately a 1 in 21,845) chance of being generated on one of the player's Pokémon after a battle, making it rarer than encountering or hatching a Shiny Pokémon.". It's not pretty easy.
@@antoniocalado7101 Even if you consider it an average of 100 inputs for pi to get into battles, pi will get into around 70,000 battles which is far over the 3 in 65,536. Now that doesn't make it guaranteed by any means but it does make it so that you aren't lucky after getting Pokérus after 70,000 battles. Therefore, pi isn't lucky (at least not in that way).
I'm not doubting this is true but where do you see evidence of this? I thought it either had to say PKRS somewhere or show a smiley face to indicate it's already had it before
Basically got 2 super popular songs mixed up and thought "Stacy's mom" included a phone number, which it doesn't , that's a different song. But the joke still works cause it basically implies Stacy's mom is so promiscuous that everyone has her phone number for booty calls.@@diogomarques7479
To be fair, if the internet's brain rot hadn't massively accellerated in the last like, 8 years, this was seen as a thing so obvious it wasn't worth mentioning.
Normal number implies winning sequence is faulty logic because Sapphire is softlockable. It's very unlikely, but it would be amazing if gogols of digits from now, pi softlocks itself on Pacifidlog.
@@Noob-gb6bn fly to Pacifidlog, throw out pokeballs, enter the poke center, release your Surf and Fly users and any pokemon that can learn those. Congratulations! You can't leave without Fly or Surf, there's no way to buy balls with no mart so you can't catch a new HM user even if you picked up a Rod, and even if you black out you're gonna respawn in that pokemon center. You as a human with a console/emulator need an additional step, save the game, but Pi can't restart the game so it's stuck even without that. note: there may be additional conditions, the wiki mentions spending all money and throwing all items, but I'm not sure why since there's no Mart IIRC. Also in Emerald there's a guy that will trade your Horsea for a Bagon, which can Fly if evolved, but Horsea can Surf so you've released it already.
This is a great point that I didn't consider. There are actually several ways to softlock yourself in gen 3. And, if you're a pikasprey fan, there are *tons* of ways to *almost* do it too
10:54 Actually, this is exactly what is needed for pi to have a chance to succeed. The tile system in Sapphire can be thought of as the integer lattice, and a random walk on an integer lattice with unbiased directional movement is a known recurrent walk. This means that any infinite random walk is guaranteed to return to its starting point infinitely often. This is why pi spends so much time in littleroot town. It HAS to return back to the starting town every now and then because its dpad buttons are equally weighted. If we want to see pi beat the game in our lifetime, we need the walk to be transient, and the easiest way to do this is to introduce a bias in its directional inputs. This will give pi a positive average velocity in the direction of the biased input, but without this it will just waste too much time for us to see it win.
Do the walls in the game affect this random wandering's tendency to return to the starting/home tile? Mainly because running into a wall in game doesn't move you and effectively offset the movement? I'm assuming the theorem you cited is just for an infinite empty plane? Not that it doesn't have some implications for out experiment since we need π to randomly wander all the way over to evergrand city which is probably 200 tiles or more west of littleroot. Ultimately the fastest way to find the correct sequence would be to run this experiment in parallel with every possible mapping of 10 digits onto our 7 buttons. Presumably each mapping has its own "winning sequence" and thus we improve our likelihood of finding atleast 1 winning sequence instead of finding the only 1 for our test setup. Unfortunately 10 digits onto 7 buttons is going to be way too many perspectives for a twitch stream. (its atleast 70, you would definitely need a system for judging which ones were having the most success and only show the top 6 or so.)
Holy shit, it's so neat to see someone actually documenting this! Been following it on and off for ages and it's very funny how little progress it's made.
"if you read this whole thing, you're probably not a youtube commenter" WRONG i enjoy every bit u do in ur videos even if it is a split second explanation of an inaccurate joke that spans the entire page. it's enrichment in my enclosure.
I found this channel on my own a few months ago. And I busted into laughter after finding that, several years into the run, this project hasn't been able to even reach the first gym
As far as pi only having 10 digits, you could you bigrams instead, giving you 100 digits, which would allow you to "weight" certain inputs like assigning more bigrams to an input. Like giving B more than Start, so it spends less time in the menu
I mean, you already can do that, like adef suggested. U can see in the graphic, 0 & 5 are both mapped to Start. Winning Sequence could have easily put 0 onto B if they wanted to. Though, that leads to a different question. Even if pi is normal, for use as a random number generator it’s only pseudo-random. In the sense that, digits are the same each time you look at it. So, could a person look at the digits of pi in advance and *intentionally* assign each digit to a button to try and get pi to complete the game as fast as possible? Like, if you know the first two inputs required are both A presses, maybe you assign 3 and 1 to the A button. Or maybe not, maybe you find a different assignment that’s better in the long term?
Absolutely loved this video. I did expect this would be related to the pi plays sapphire stream, but I did not expect it to bring in the fire red blind and deaf challenge!
Just found your channel and instantly subscribed. I think this is the perfect channel to fill the hole that was left in my heart after BDG left Polygon, from the editing to the humor it's just (chefs kiss) 👌
I am a mathematician who is currently working a blue collar job and I want you to know unit videos have brought me a lot of joy. My brain craves the math.
For some reason it makes me so happy to hear someone else liking MartSnacks Pokemon blind and deaf video so much! It's such a great watch and i can only highly recommend it too! Also, this video has been just as entertaining as well, awesome job!!
You're genuinely one of the greatest. I have learned a lot and even refined understanding of things from your videos, all while you make them very entertaining. I look forward to watching your channel grow exponentially and wish you the best.
Hey I also love checking out winningsequence on occasion to see what's been happening and I'm super happy someone made a video about it! More than normality however, I think the bigger issue is that if you're doing a walk in a 2 dimensional plane (which Pokemon roughly is) with uniformly randomly likelihood of going in any one direction, then you are going to end up back at the beginning very often. I think this explains why the player is basically always at home. Because of this, I think picking a different normal sequence is just as unlikely to win. Great video!
Between this, the Flash/Surf/Fly videos, and the Wind Waker tricks explanation, you have earned yourself a sub! Always liked the shows you hosted on GDQ Hotfix as well.
adef.... please believe me when I tell you that youre seriously one of the funniest guys out here. Your content is phenomenal man and your sense of humor is impeccable.
@@erberor8007True but counter; it might be wrong, to be in love with Stacys mom. Besides Stacy doesnt seem yo be able to see. Although this could be part of what Stacy's mom has going on.
I was just checking the description and I noticed that one of your references is a bachelor's thesis from my university! And the first supervisor is actually my supervisor too! He insists on making all theses publicly available and I'm happy to see that that has achieved its purpose of making knowledge more easily accessible :)
Adef explaining number theory and how it relates to Pi beating Pokemon Me struggling to recall the one class on set theory from a semester of logic: nods along in agreement.
Since pi doesn't have the ability to restart the game, wouldn't it be possible that it loses all of it's "winning sequences" because it is starting on the wrong tile everytime ? Wouldn't we need to prove that there exists a sequence, however long it may be, that is able to complete the game starting from any tile, to prove that any normal number can eventually beat the game ? If there doesn't happen to exist such a sequence, could we maybe still prove that it is "almost certain" that pi eventually beats the game anyways as there exists a finite amount of tiles in the game, and an infinite amount of "winning sequences" that don't repeat periodically ? This has me scratching my head.
this is great, I loved the part where you're considering ways to make it more likely to win! I remember doing this myself at some point, ultimately I felt like I'd rather have a different mapping in battles to in the OW, like keep the OW movement the same, but in battles you do maybe 1-4 to pick your moves, 5 to pick pokemon, 6 to pick an item, 7 to run etc.. with some of those maybe being mapped twice?
@@TsadiqP that's ultimately why I didn't code a romhack even though Emerald is decompiled now, because I thought it kinda defeated the point if the win got handed to it. Repeat last D-Pad action seems like something that's a little more in the spirit though, you could also have one for buttons. It sounds kinda funny
What I find interesting about Champernownes constant is since it is counting up AND the concatenations will stretch multiple orders of magnitude, the digits leading digits in the concatenations should follow Benfords law with 1 appearing about 30% more likely as the leading digit in an infinite string. Thus one should be the most common digit at any point stopped (unless the sample only stopped on the last concatenation of all 9’s which would be increasingly less likely) But this number is also (and intuitively) proven to be normal with all digits appearing equally. It would be interesting to see the distribution of these numbers at a random number of digits in the millions. I’m assuming approaches a more even distribution as there are more and more digits. It would be interesting to see how long it takes for numbers distribution to even out. Infinity is just weird!
I assume it evens out when u hit a number that’s a string of 9s and then afterwards starts biasing towards 1, repeating that cycle with each order of magnitude
@@ffttossenz Yes it would even out only when a string ends with a concatenation of all 9’s, but this will become increasingly rarer. But the digits will become increasingly longer, so the leading digit will have less affect on total distribution. But the second digits will also have a 1 bias as well albeit less and so forth on the others as well. It would be interesting to see the affect of the Benford’s law with large numbers. I’m assuming it would deviate towards a more even distribution, BUT it would still skew with 1-9 in decreasing order. It would be interesting to see how quickly. My guess based only on hunch (and I could easily be wrong) is that it would happen slowly.
@@mikeallison5549 i disagree with the longer numbers having diminishing returns, since 1 extra digit means 10 times as many numbers, so even if the number is longer and thus diluting how much a single digit matters, you’re getting significantly more numbers of where the leading digit is a 1, 2, etc. in a row
@@ffttossenz first I really appreciate the discussion (wanted to state so this didn’t look like arguing). I do agree with you. The leading digit will have a decreasingly effect on the distribution as the number gets larger. BUT The second digit will also have a 1 leaning bias when counting up (but less than the first), but a one leaning bias as well, and so on down the line. So all digits will have a one leaning bias but the bias will decrease for each digit as the number gets larger AND the effect each digit will have on the total distribution will decrease as well. I believe it will tend to a normal distribution (as it has to as a normal number which this number is) I just think it would be interesting to see how quickly that happens. My hunch is even at 10,000,000 digits like the example adef pointed out in this video for pi, it would still have a significant skew to 1 and away from 9.
I was about to suggest different bases of Pi right as you got to that point in the video The programmer in me wonders if it'd be possible to abstract out all of Pokemon Sapphire's logic such that an emulator was unnecessary, and we could actually test different sequences exponentially faster, without needing to actually emulate the game first...
I mean, you could rewrite pokemon sapphire to run faster with the the same behavior... most likely because it's unlikely the current code is the single fastest but, the "winning sequence" stream is more hypothetical/entertainment than anything else. Otherwise they would use emulator speed up tools already. Also, as you started trying to code speed golf you could easily introduce a bug that changes the result which would be aweful and there's really no way to test if code produces identical outcomes in all situations for such a complex game. You can't really remove anything complexity wise from the game though because it could be that pi ends up entering a contest, blending berries, or softlocking the game through some nonsense in pacifalog town😂
A sequence that takes the player to the end of the game from the start of the game is not needed, only a sequence that takes the player to all the locations eventually, for instance a sequence that gets you to the first gym leader is fine then PI could just do its thing for 100s of hours before randomly going off to the next gym leader then 100s and 100s of hours later go to the next etc. Beating the game bits and pieces at a time is far more likely than just one sequence that instantly walks the player into a straight line towards the victory condition like what the fire red blind playthrough is about.
Yeah, especially since you only need to do trainer battles once. After you beat one, you might wander away, but then it'll be done when you wander back.
I just found your channel and absolutely love what you do. I am a life long Pokemon player and a mathematician by trade (I am a probabilist/operator theorist)---your investigations are right up my alley. I think you did a great job discussing normality in this video (you were right to skip some of the finer points of the definition). Time to binge all of your content!
There may be no pokemon blind and deaf follow up by MartSnack, but a smaller creator has since routed a couple more games with the same restrictions in addition to an extremely impressive success of performing the original run on original hardware (much harder than it sounds)!
Here's my idea on how to redistribute the button weights: use two digits at a time. That way, there's 100 possible inputs instead of just 10, which leaves a lot more room to work with. So instead of only one digit per control pad direction, you can have fifteen or twenty and still have room for plenty of A-button presses and a few B-button and Start Button presses.
Going from reading "the intended audience for this don't read" and then hearing "pi is the number of star wars movies there should have been" in an instant was too much
I fucking knew it from.the community post. This is going to be good. Ive now watched the video, and you casually mentioning "base 13" having more digits shook my understanding of math.
Welcome to modules! More easily, consider a clock. That's an example of base 12 (although it doesn't start with a zero, but anyway). When you complete a cycle of a clock you start counting again from 1 and adding the previous cycles. It's way easier considering a series of power (but also I kinda suck to explain)
@@DrXtreme777 for real world applications, binary, which basically all computers use, is base-2, so there's a lot of use in understanding it. and historically, there were a few other societies and numeral systems that didn't use the decimal system/base-10, so it's helpful to understand if you're studying them
I'm extremely amused by the whole paragraph explaining the Stacey's Mom bit to avoid being eaten alive followed by immediately slathering yourself in virtual bbq sauce and hopping on a lit grill with a comment about Star Wars. XD 10/10
One of my uncles is so into math that on the 14th of every month he holds a "pie day party". Him and his siblings and friends all make and eat pie together. It's pretty wholesome
You could map the extra digit to each direction, and have the direction chosen be something like "if the next and prev digit are both odd go up; both even go down; if the prev if odd and next is even go left; if prev is even and next is odd go right"
8:00 I find it pretty funny that a bot doing nothing but translating numbers to in game inputs manages to almost perfectly mimic the movement behavior of the NPCs near it
What I find intriguing is that there are also some ways to softlock yourself in Gen 3 which means there are some sequences which never finish the game and we will never know the probability a random sequence runs into a softlock, or whether pi does
In order to play Pokémon you'll often need to hit the same button repeatedly - specifically the direction buttons to move (i.e. you need to walk twenty space to the right), 'a' to advance dialogue or attack, etc. I therefore think that looking for a run-length-encoding in Pi would be smaller in the number of digits, and so give a better chance of it occurring - something like (to use a convention of encasing the button in square brackets, followed by the repeat count) [a]5[up]10[right]6[a]12. A really easy way to encode this in Pi could be just to say that even numbered digits (3, 4, 5, 2, 5) are the button to push (3 being the 0th digit, and 0 is even!) and the odd numbered digits (1, 1, 9, 6, 3) the number of repetitions. if '0' appears as the repetition number it could mean 'don't actually press it, or press it ten times). If we want to press a button more than ten times in a row, just repeat it - e.g. 1919 would mean hit the button represented by '1' eighteen times in a row.
As I'm typing this, there is a new furthest point PI has gotten to. It managed to beat the first trainer in Petelburg Woods, but is now back in Littleroot Town lol
Ah I see the old "monkey with a typewriter" experiment. Eventually you will have the right combination of numbers to do it. The same way a monkey typing on a typewriter for eternity will be able to write one of Shakespeare's plays word for word.
I'm not really a maths guy so I was kinda worried this was a dumb question, a while ago on the live stream I asked if it will ever have the same number over and over again for a long time, I guess that was a more interesting question than I originally thought.
Something that came to mind that I thought was kinda interesting is that, in theory, the sequence could get all the way to the final text box of the game, then do something like press left several billion times in a row before finally pressing A to finish the run. Imagine the frustration if the stream ever did that.
Now imagine we stumble upon a sequence that gets up to the champion, loses, releases all it's mons except for a lv 3 Zigzagoon and goes back to littleroot
An interesting way to get around the input constraint would be reading each digit with it's following digit as a two digit number, and then subdividing 01-99 into 12 different buckets. The first number would be 31, then 14, then 41, then 15, 59, and so on and would translate to 3, 1, 4, 1, 7 and so on
Slight correction; a normal number is not just a number where the distribution of all of the digits are equal, that's a necessary but not sufficient condition. A normal number is a number where for any sequence of n numbers the probability for that sequence to occur tends to 1/b^n where b is the base. For instance 0.12345678912... would not be normal because for sequence length 2 we can find a sequence which never occurs such as 32, where a normal number would require that in the limit that occurs 1/100th of the time. Without this caveat the fact that every string can be found somewhere within the number fails (like in the 0.123.. case).
@@SaotomeLunaif you randomly select a number from the unit interval according to the usual probability distribution, the probability that the number obtained is normal, is one. That’s why it is called normal, because it is the sort of number you would almost certainly get if you picked at random.
Might be easiest to reinterpret Pi in hexadecimal so you could assign up to 16 total possible inputs. That'd allow you to put a higher weight on specific buttons. Having start assigned to a weight of 1:16 might help some with something like 2:16 for each direction on the d-pad (for a total of 8:16) which would leave seven values left over to split between A and B. (Or assign another value to each d-pad button and split the remaining three between A and B.)
One day we're going to use pi for something and its going to work flawlessly and then our sky dome will lift up and we're inside a big arena with the audience clapping and cheering. Our goal was just to figure out what pi is for
another thing that's worth pointing out is that the pokemon games are games where you can make negative progress -- for example, *releasing* your level 80-something sceptile. depending on the situation, this could potentially result in a soft-lock, or at the very least, *many* more digits required to undo those types of mistakes.
Hey there, gang! A great point has been made by many commenters, and I think I should address it!
An infinitely long number with an equal distribution of all of the digits is not the *only* requirement for a number to be deemed Normal.
There are other, more difficult to parse requirements that are more entrenched in number theory. I think that the requirements I stated in the video are still the most beneficial / easy to parse for an introductory youtube video on the topic, but for more info on what a number needs to be definitively Normal, please check the description for further reading resources.
Thanks for watching and thank you for commenting!!!
One of the very few instances where the "pop scientist" says that we do not know if pi is normal... very good!
Fun fact: my birthday is pi day😂
@@kaosoyuncular3954 Congrats my lad, you are a person of pie, or, should I say, you are a PI...sces... Sorry, I had to hahaha
Also, Daniel Avidan has the same birthday, just fun fact! A beautiful day to have a birth, muhahaha
Pi has mastered the strategy of every 9-year old Pokemon player: winning by overleveling your starter
Raw brute STRENGTH. Nothing else matters.
>b-b-but...
NOTHING. ELSE.
Who needs stat buffing moves? Just pure damage will do
most 9 year olds don't have tens of thousands of hours on their save file before beating the first trainer though. this pi fellow really sucks at pokemon
@@zeemgeemnah, he's just cheesing it
Speedrunners have taught us we were right all along: that is the most optimally way to beat the game 😂
I will be watching your career with great interest.
Thanks for sharing this Kyle! Made my day!
Omg, Kyle Hill, the award winning science educator! Hiii
The villain requires a new servant
crossover event of the century
A new hand touches the Beacon.
As an engineer I can tell you pi is exactly 3
Nah, by law it's 5
@@TheSoftwareNerdwhich rounds up to ten so pi is 10
Pi is actually 22.7
As a programmer I can tell you pi is exactly 1
As a math man I can tell you pi is the π button on my calculator
if anyone is curious
back in stream 44 part 3 Pi was only a few steps away from May in route 103, but then at the 36:28 minute mark a 2 came by in the sequence of Pi, at that moment Pi was just over one of the ledges in route 103, tragedy followed and Pi has not recovered yet, May is still waiting in route 103
I commented it months ago in stream 313 part 3.
I was curious, thank you for sharing
well, we done it now
@@norwatch_llamaassasin YES I SAW
@@norwatch_llamaassasin FUCK YEAH MY FRIEND
If anyone is looking for it, it's Stream 471 pt 2 where he finally finds May. Then the comments on that video should take you to the timestamp
pi plays pokemon like an NPC, staying in one place and doing the same thing over and over again
and like all NPCs it has a very few number of team members but they are leveled quite high
Would you say it's just running in circles?
My phone number appears in the first 200 million digits of Pi! I hope I haven't just doxxed myself to some super dedicated stalker.
Pi can be used to be dox anyone technically.
Oh, that was a mistake. Now everyone will find you.
Wow my reply was sent to the shadow realm lol
Lol same!
I got your coordinates from there too bye bye 🤫 🧏
My mom teaches upper high school math and used to teach computer science back in the day. I’ve always loved Pokémon my whole life so she tried to join me with Pokémon go and has been playing that game ever since it released, so I showed her your channel since it basically merges two of her favorite things and she loves it so much!! She’s thinking about showing some of your statistics based videos to her stat classes haha. Thank you for making these! I forgot how cool math can be :”]
This is wonderful! Please tell her she is more than welcome to use the videos for teaching!!!
@@adef everyone loves you so much man, you are going to be so huge one day
7:53 IT'S EVEN HAD POKERUS
Pokerus is pretty easy to get through repetition. I've gotten it shiny hunting (in sapphire my battery is dead at this point so I can't soft reset and instead encounter and run away) and still never found a shiny pokemon.
@@solsystem1342"Pokérus has a 3 in 65,536 (or approximately a 1 in 21,845) chance of being generated on one of the player's Pokémon after a battle, making it rarer than encountering or hatching a Shiny Pokémon.". It's not pretty easy.
@@antoniocalado7101yeah but the things been going for 2 years and has spent much of that doing wild encounters, it’s absolutely gone over those odds
@@antoniocalado7101 Even if you consider it an average of 100 inputs for pi to get into battles, pi will get into around 70,000 battles which is far over the 3 in 65,536. Now that doesn't make it guaranteed by any means but it does make it so that you aren't lucky after getting Pokérus after 70,000 battles. Therefore, pi isn't lucky (at least not in that way).
I'm not doubting this is true but where do you see evidence of this? I thought it either had to say PKRS somewhere or show a smiley face to indicate it's already had it before
"Normality is a remarkably difficult thing to prove" is such an unintentionally powerful quote.
I'm a commenter who reads, and I know what you did adef.
Me too, and I’m disappointed him SMH
I am confused. What did I miss?
he should definitely lose his career over this
Basically got 2 super popular songs mixed up and thought "Stacy's mom" included a phone number, which it doesn't , that's a different song. But the joke still works cause it basically implies Stacy's mom is so promiscuous that everyone has her phone number for booty calls.@@diogomarques7479
I shall pay for my sins.
I think i heard monkey ball music. Good job on the video gamer adef
Total respect for the addition of "if youre financially able to". Not many show that level of understanding/respect to their potential backers
To be fair, if the internet's brain rot hadn't massively accellerated in the last like, 8 years, this was seen as a thing so obvious it wasn't worth mentioning.
Normal number implies winning sequence is faulty logic because Sapphire is softlockable. It's very unlikely, but it would be amazing if gogols of digits from now, pi softlocks itself on Pacifidlog.
How to you softlock
@@Noob-gb6bn fly to Pacifidlog, throw out pokeballs, enter the poke center, release your Surf and Fly users and any pokemon that can learn those. Congratulations! You can't leave without Fly or Surf, there's no way to buy balls with no mart so you can't catch a new HM user even if you picked up a Rod, and even if you black out you're gonna respawn in that pokemon center. You as a human with a console/emulator need an additional step, save the game, but Pi can't restart the game so it's stuck even without that.
note: there may be additional conditions, the wiki mentions spending all money and throwing all items, but I'm not sure why since there's no Mart IIRC. Also in Emerald there's a guy that will trade your Horsea for a Bagon, which can Fly if evolved, but Horsea can Surf so you've released it already.
@@DeuxisWasTaken the game will not let you release your last hm users, you will have to put them both in the daycare and then teleport to pacifilog
@@Kambyday ohh that's how, thanks, good to know. I thought they only implemented that "can't be released" thing in ORAS.
This is a great point that I didn't consider. There are actually several ways to softlock yourself in gen 3. And, if you're a pikasprey fan, there are *tons* of ways to *almost* do it too
10:54 Actually, this is exactly what is needed for pi to have a chance to succeed. The tile system in Sapphire can be thought of as the integer lattice, and a random walk on an integer lattice with unbiased directional movement is a known recurrent walk. This means that any infinite random walk is guaranteed to return to its starting point infinitely often. This is why pi spends so much time in littleroot town. It HAS to return back to the starting town every now and then because its dpad buttons are equally weighted. If we want to see pi beat the game in our lifetime, we need the walk to be transient, and the easiest way to do this is to introduce a bias in its directional inputs. This will give pi a positive average velocity in the direction of the biased input, but without this it will just waste too much time for us to see it win.
Do the walls in the game affect this random wandering's tendency to return to the starting/home tile? Mainly because running into a wall in game doesn't move you and effectively offset the movement?
I'm assuming the theorem you cited is just for an infinite empty plane? Not that it doesn't have some implications for out experiment since we need π to randomly wander all the way over to evergrand city which is probably 200 tiles or more west of littleroot.
Ultimately the fastest way to find the correct sequence would be to run this experiment in parallel with every possible mapping of 10 digits onto our 7 buttons. Presumably each mapping has its own "winning sequence" and thus we improve our likelihood of finding atleast 1 winning sequence instead of finding the only 1 for our test setup.
Unfortunately 10 digits onto 7 buttons is going to be way too many perspectives for a twitch stream. (its atleast 70, you would definitely need a system for judging which ones were having the most success and only show the top 6 or so.)
Holy shit, it's so neat to see someone actually documenting this! Been following it on and off for ages and it's very funny how little progress it's made.
"if you read this whole thing, you're probably not a youtube commenter" WRONG i enjoy every bit u do in ur videos even if it is a split second explanation of an inaccurate joke that spans the entire page. it's enrichment in my enclosure.
I hope Pi can experience the entirety of Pokémon Sapphire one day. It’s a great game and all number sequences deserve to play such a fun game
0:16 If those kids could read, they’d be very offended!
I found this channel on my own a few months ago. And I busted into laughter after finding that, several years into the run, this project hasn't been able to even reach the first gym
7:20 Yep that's what I'm talking about
Pi: "Yeah, I got time."
This is a great video and I ALSO agree that the MartSnack video is one of my favorite videos of ALL time.
I had no idea anyone else alive remembered the "viewers like you, thank you" from PBS. Thanks for unlocking this memory for me
As far as pi only having 10 digits, you could you bigrams instead, giving you 100 digits, which would allow you to "weight" certain inputs like assigning more bigrams to an input. Like giving B more than Start, so it spends less time in the menu
I mean, you already can do that, like adef suggested. U can see in the graphic, 0 & 5 are both mapped to Start. Winning Sequence could have easily put 0 onto B if they wanted to.
Though, that leads to a different question. Even if pi is normal, for use as a random number generator it’s only pseudo-random. In the sense that, digits are the same each time you look at it. So, could a person look at the digits of pi in advance and *intentionally* assign each digit to a button to try and get pi to complete the game as fast as possible? Like, if you know the first two inputs required are both A presses, maybe you assign 3 and 1 to the A button. Or maybe not, maybe you find a different assignment that’s better in the long term?
8:50 There's no reason Pi needs to be restricted to 10 digits. You could use Pi base 12
Absolutely loved this video. I did expect this would be related to the pi plays sapphire stream, but I did not expect it to bring in the fire red blind and deaf challenge!
Just found your channel and instantly subscribed. I think this is the perfect channel to fill the hole that was left in my heart after BDG left Polygon, from the editing to the humor it's just (chefs kiss) 👌
The start button weight is crazy. It's probably a pretty large part of why overworld progress is so stunted.
I am a mathematician who is currently working a blue collar job and I want you to know unit videos have brought me a lot of joy. My brain craves the math.
your channel is somehow in the very center of my personal venn diagram of interests, I don’t know how you do it. great vid adef ✌️
For some reason it makes me so happy to hear someone else liking MartSnacks Pokemon blind and deaf video so much! It's such a great watch and i can only highly recommend it too!
Also, this video has been just as entertaining as well, awesome job!!
When dealing with infinites, unlikely is just certainty waiting its turn.
wow amazing video, original and interesting idea with a great execution, entertaining creator, and a bunch of hilarious jokes, loved it
HAPPY PI DAY.
Hap-pi day!
You're genuinely one of the greatest. I have learned a lot and even refined understanding of things from your videos, all while you make them very entertaining. I look forward to watching your channel grow exponentially and wish you the best.
0:16 Heard this as plural “Moms” instead of possessive“Mom’s” so I thought this was a joke about determining the number of Moms Stacy has
"we think Pi is a normal number" is such a wild statement out of context.
Hey I also love checking out winningsequence on occasion to see what's been happening and I'm super happy someone made a video about it! More than normality however, I think the bigger issue is that if you're doing a walk in a 2 dimensional plane (which Pokemon roughly is) with uniformly randomly likelihood of going in any one direction, then you are going to end up back at the beginning very often. I think this explains why the player is basically always at home. Because of this, I think picking a different normal sequence is just as unlikely to win. Great video!
Between this, the Flash/Surf/Fly videos, and the Wind Waker tricks explanation, you have earned yourself a sub!
Always liked the shows you hosted on GDQ Hotfix as well.
i’m so glad he mentioned one of the greatest and truly underrated videos on this platform, that shit is so beyond incredible to me
after 20 long years of searching, i’ve finally found it… my kind of autism….
lol
Thanks for all your hard work 🙏
I may not know her number, but I've heard Stacy's mom has apparently got it goin' on
She’s all I want.
And I've waited for so long
So Stacy can’t you see. You are just not the girl for me
I literally watched the blind and deaf playthrough right before watching your video! Crazy that you mentioned it!
THIS VIDEO WAS EXACTLY THE KIND OF VIDEO I LOVE. THANK YOU
another banger video, really loved the split second "pause to read the silly on screen" moments
adef.... please believe me when I tell you that youre seriously one of the funniest guys out here. Your content is phenomenal man and your sense of humor is impeccable.
This man’s talking has fixed my relationship with my father more than any therapist has💀 (we both enjoy watching ur pokémon vids much love 💜💜💜)
Stacy’s mom is only the target of the guy singing the song’s attraction. She’s not implied to be beloved by any of the other boys
Well, sure, but you really have to consider that Stacy's mom has got it going on. There's a lot of appeal there.
@@erberor8007True but counter; it might be wrong, to be in love with Stacys mom. Besides Stacy doesnt seem yo be able to see.
Although this could be part of what Stacy's mom has going on.
I'd argue Jenny has a more well known number
I was recommended this video by a viewer of the stream and loved it! Really gave me a new appreciation both for pi and the stream.
I loved this - thanks for adding some pi knowledge into pi day this year!
I was just checking the description and I noticed that one of your references is a bachelor's thesis from my university! And the first supervisor is actually my supervisor too! He insists on making all theses publicly available and I'm happy to see that that has achieved its purpose of making knowledge more easily accessible :)
6:40 lol my phone number is in the first 200m digits of pi
Adef explaining number theory and how it relates to Pi beating Pokemon
Me struggling to recall the one class on set theory from a semester of logic: nods along in agreement.
I choose to believe that Stacy's mom is canonically Jenny.
Since pi doesn't have the ability to restart the game, wouldn't it be possible that it loses all of it's "winning sequences" because it is starting on the wrong tile everytime ?
Wouldn't we need to prove that there exists a sequence, however long it may be, that is able to complete the game starting from any tile, to prove that any normal number can eventually beat the game ?
If there doesn't happen to exist such a sequence, could we maybe still prove that it is "almost certain" that pi eventually beats the game anyways as there exists a finite amount of tiles in the game, and an infinite amount of "winning sequences" that don't repeat periodically ?
This has me scratching my head.
i think every single one of your videos has been an absolute treat to watch
this is great, I loved the part where you're considering ways to make it more likely to win! I remember doing this myself at some point, ultimately I felt like I'd rather have a different mapping in battles to in the OW, like keep the OW movement the same, but in battles you do maybe 1-4 to pick your moves, 5 to pick pokemon, 6 to pick an item, 7 to run etc.. with some of those maybe being mapped twice?
or map a digit to "repeat last d-pad action". But these ideas, although increasing victory odds, maybe stray from the spirit.
@@TsadiqP that's ultimately why I didn't code a romhack even though Emerald is decompiled now, because I thought it kinda defeated the point if the win got handed to it. Repeat last D-Pad action seems like something that's a little more in the spirit though, you could also have one for buttons. It sounds kinda funny
What I find interesting about Champernownes constant is since it is counting up AND the concatenations will stretch multiple orders of magnitude, the digits leading digits in the concatenations should follow Benfords law with 1 appearing about 30% more likely as the leading digit in an infinite string. Thus one should be the most common digit at any point stopped (unless the sample only stopped on the last concatenation of all 9’s which would be increasingly less likely)
But this number is also (and intuitively) proven to be normal with all digits appearing equally.
It would be interesting to see the distribution of these numbers at a random number of digits in the millions. I’m assuming approaches a more even distribution as there are more and more digits. It would be interesting to see how long it takes for numbers distribution to even out.
Infinity is just weird!
I assume it evens out when u hit a number that’s a string of 9s and then afterwards starts biasing towards 1, repeating that cycle with each order of magnitude
@@ffttossenz Yes it would even out only when a string ends with a concatenation of all 9’s, but this will become increasingly rarer. But the digits will become increasingly longer, so the leading digit will have less affect on total distribution. But the second digits will also have a 1 bias as well albeit less and so forth on the others as well.
It would be interesting to see the affect of the Benford’s law with large numbers.
I’m assuming it would deviate towards a more even distribution, BUT it would still skew with 1-9 in decreasing order. It would be interesting to see how quickly. My guess based only on hunch (and I could easily be wrong) is that it would happen slowly.
@@mikeallison5549 i disagree with the longer numbers having diminishing returns, since 1 extra digit means 10 times as many numbers, so even if the number is longer and thus diluting how much a single digit matters, you’re getting significantly more numbers of where the leading digit is a 1, 2, etc. in a row
@@ffttossenz first I really appreciate the discussion (wanted to state so this didn’t look like arguing).
I do agree with you. The leading digit will have a decreasingly effect on the distribution as the number gets larger. BUT The second digit will also have a 1 leaning bias when counting up (but less than the first), but a one leaning bias as well, and so on down the line. So all digits will have a one leaning bias but the bias will decrease for each digit as the number gets larger AND the effect each digit will have on the total distribution will decrease as well.
I believe it will tend to a normal distribution (as it has to as a normal number which this number is) I just think it would be interesting to see how quickly that happens.
My hunch is even at 10,000,000 digits like the example adef pointed out in this video for pi, it would still have a significant skew to 1 and away from 9.
Been following Pi plays Pokemon for a while now and its so cool to see it talked about
I was about to suggest different bases of Pi right as you got to that point in the video
The programmer in me wonders if it'd be possible to abstract out all of Pokemon Sapphire's logic such that an emulator was unnecessary, and we could actually test different sequences exponentially faster, without needing to actually emulate the game first...
I mean, you could rewrite pokemon sapphire to run faster with the the same behavior... most likely because it's unlikely the current code is the single fastest but, the "winning sequence" stream is more hypothetical/entertainment than anything else. Otherwise they would use emulator speed up tools already. Also, as you started trying to code speed golf you could easily introduce a bug that changes the result which would be aweful and there's really no way to test if code produces identical outcomes in all situations for such a complex game.
You can't really remove anything complexity wise from the game though because it could be that pi ends up entering a contest, blending berries, or softlocking the game through some nonsense in pacifalog town😂
we're slowing seeing it turn from math into pokemon to meth into pokemon
A sequence that takes the player to the end of the game from the start of the game is not needed, only a sequence that takes the player to all the locations eventually, for instance a sequence that gets you to the first gym leader is fine then PI could just do its thing for 100s of hours before randomly going off to the next gym leader then 100s and 100s of hours later go to the next etc. Beating the game bits and pieces at a time is far more likely than just one sequence that instantly walks the player into a straight line towards the victory condition like what the fire red blind playthrough is about.
Yeah, especially since you only need to do trainer battles once. After you beat one, you might wander away, but then it'll be done when you wander back.
That's kind of what he meant by how we could be in the winning sequence right now but not know it.
Starting fights 20 seconds in?? It's three.
Facts, phantom menace, attack of the clones, and revenge of the sith are all we need
@@lordfangar5671 now there's a hot take!
It’s definitely less than 7.
@@nablamakabama488I'd even go so far as to say it's less than 1
I just found your channel and absolutely love what you do. I am a life long Pokemon player and a mathematician by trade (I am a probabilist/operator theorist)---your investigations are right up my alley. I think you did a great job discussing normality in this video (you were right to skip some of the finer points of the definition). Time to binge all of your content!
There may be no pokemon blind and deaf follow up by MartSnack, but a smaller creator has since routed a couple more games with the same restrictions in addition to an extremely impressive success of performing the original run on original hardware (much harder than it sounds)!
Yess, those videos are awesome too! Their channel name is Tongy Bacala btw, the Leafgreen and the Johto videos are nice to get into it.
Damn, a video that mentions the death of the universe and still manages to stay positive. Props, man!
Here's my idea on how to redistribute the button weights: use two digits at a time. That way, there's 100 possible inputs instead of just 10, which leaves a lot more room to work with. So instead of only one digit per control pad direction, you can have fifteen or twenty and still have room for plenty of A-button presses and a few B-button and Start Button presses.
The best video on WinningSequence yet _and_ a shout-out to MartSnack's video? Well this is just delightful
Going from reading "the intended audience for this don't read" and then hearing "pi is the number of star wars movies there should have been" in an instant was too much
I fucking knew it from.the community post. This is going to be good.
Ive now watched the video, and you casually mentioning "base 13" having more digits shook my understanding of math.
Yeah! It's kinda neat. It's basically when you pretend that "10" is actually 13. So you would count upwards as:
1, 2, 3, 4, 5, 6, 7 ,8, 9, a, b, c, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 20
For example, in base 13, 6*9 = 42
Welcome to modules! More easily, consider a clock. That's an example of base 12 (although it doesn't start with a zero, but anyway).
When you complete a cycle of a clock you start counting again from 1 and adding the previous cycles. It's way easier considering a series of power (but also I kinda suck to explain)
Ty all for the help! What are the applications of this though
@@DrXtreme777 for real world applications, binary, which basically all computers use, is base-2, so there's a lot of use in understanding it. and historically, there were a few other societies and numeral systems that didn't use the decimal system/base-10, so it's helpful to understand if you're studying them
Joke's on you, I don't even know who Stacy's Mom is!
I'm extremely amused by the whole paragraph explaining the Stacey's Mom bit to avoid being eaten alive followed by immediately slathering yourself in virtual bbq sauce and hopping on a lit grill with a comment about Star Wars. XD 10/10
as someone who goes by "Pie" online, this video was deeply uncomfortable to watch
I don’t have enough disposable income for the patreon but I left a like because I’ve been enjoying the videos. Keep them up!
If Pi is infinite...
Next video: "Finding Pokemon Sapphire in Pi!"
One of my uncles is so into math that on the 14th of every month he holds a "pie day party". Him and his siblings and friends all make and eat pie together. It's pretty wholesome
You could map the extra digit to each direction, and have the direction chosen be something like "if the next and prev digit are both odd go up; both even go down; if the prev if odd and next is even go left; if prev is even and next is odd go right"
8:00 I find it pretty funny that a bot doing nothing but translating numbers to in game inputs manages to almost perfectly mimic the movement behavior of the NPCs near it
I didn't get much of the nerdy references or the math behind any of this, but dude this video was awesome. Great stuff
Another absolute banger. God I love this channel
Pokémon blind and deaf challenge mentioned! Glad that video and related ideas are getting some more attention
I thought I was the only acoustic out here celebrating Pi Day today! This is awesome to see
With this videos I have watched every video you have made so far, I need more, it's addictive
Good video. I love how easily he explained everything so complicated.
This channel is wildly underrated, hope you blow up someday
What I find intriguing is that there are also some ways to softlock yourself in Gen 3 which means there are some sequences which never finish the game and we will never know the probability a random sequence runs into a softlock, or whether pi does
In order to play Pokémon you'll often need to hit the same button repeatedly - specifically the direction buttons to move (i.e. you need to walk twenty space to the right), 'a' to advance dialogue or attack, etc.
I therefore think that looking for a run-length-encoding in Pi would be smaller in the number of digits, and so give a better chance of it occurring - something like (to use a convention of encasing the button in square brackets, followed by the repeat count) [a]5[up]10[right]6[a]12.
A really easy way to encode this in Pi could be just to say that even numbered digits (3, 4, 5, 2, 5) are the button to push (3 being the 0th digit, and 0 is even!) and the odd numbered digits (1, 1, 9, 6, 3) the number of repetitions. if '0' appears as the repetition number it could mean 'don't actually press it, or press it ten times). If we want to press a button more than ten times in a row, just repeat it - e.g. 1919 would mean hit the button represented by '1' eighteen times in a row.
As I'm typing this, there is a new furthest point PI has gotten to. It managed to beat the first trainer in Petelburg Woods, but is now back in Littleroot Town lol
Ah I see the old "monkey with a typewriter" experiment. Eventually you will have the right combination of numbers to do it. The same way a monkey typing on a typewriter for eternity will be able to write one of Shakespeare's plays word for word.
I'm not really a maths guy so I was kinda worried this was a dumb question, a while ago on the live stream I asked if it will ever have the same number over and over again for a long time, I guess that was a more interesting question than I originally thought.
I doesn’t need one long winning sequence, just many small ones, once a gym has been beaten it can be unbeaten
Something that came to mind that I thought was kinda interesting is that, in theory, the sequence could get all the way to the final text box of the game, then do something like press left several billion times in a row before finally pressing A to finish the run. Imagine the frustration if the stream ever did that.
Now imagine we stumble upon a sequence that gets up to the champion, loses, releases all it's mons except for a lv 3 Zigzagoon and goes back to littleroot
An interesting way to get around the input constraint would be reading each digit with it's following digit as a two digit number, and then subdividing 01-99 into 12 different buckets. The first number would be 31, then 14, then 41, then 15, 59, and so on and would translate to 3, 1, 4, 1, 7 and so on
it was about time I got PBS'd by this channel, love the content and keep it up!
I was literally JUST talking about this to someone earlier today. That's creepy.
Slight correction; a normal number is not just a number where the distribution of all of the digits are equal, that's a necessary but not sufficient condition. A normal number is a number where for any sequence of n numbers the probability for that sequence to occur tends to 1/b^n where b is the base. For instance 0.12345678912... would not be normal because for sequence length 2 we can find a sequence which never occurs such as 32, where a normal number would require that in the limit that occurs 1/100th of the time. Without this caveat the fact that every string can be found somewhere within the number fails (like in the 0.123.. case).
Ah, normal, the word that means "typical and not at all unusual" being used for only the weirdest numbers. Mathematicians are so weird sometimes lol
Thanks for adding this, I was about to make this comment as well but you beat me to it 😊
@@SaotomeLunaif you randomly select a number from the unit interval according to the usual probability distribution, the probability that the number obtained is normal, is one.
That’s why it is called normal, because it is the sort of number you would almost certainly get if you picked at random.
Might be easiest to reinterpret Pi in hexadecimal so you could assign up to 16 total possible inputs. That'd allow you to put a higher weight on specific buttons. Having start assigned to a weight of 1:16 might help some with something like 2:16 for each direction on the d-pad (for a total of 8:16) which would leave seven values left over to split between A and B. (Or assign another value to each d-pad button and split the remaining three between A and B.)
One day we're going to use pi for something and its going to work flawlessly and then our sky dome will lift up and we're inside a big arena with the audience clapping and cheering. Our goal was just to figure out what pi is for
another thing that's worth pointing out is that the pokemon games are games where you can make negative progress -- for example, *releasing* your level 80-something sceptile. depending on the situation, this could potentially result in a soft-lock, or at the very least, *many* more digits required to undo those types of mistakes.