The Math Behind the Unluckiest Moments in all of Pokémon

uh okay [Music] no way no way you just watched as a clip of a Pokemon Challenge called taizo Iron Man basically all you need to know is that the game is really randomized so whatever comes up on the starter table is completely random so what are the odds that all three legendary birds showed up on the table is it one over all the options cubed or is it more complex than that wait furthermore what's the unluckiest moment in Pokemon gameplay history is it the Cybertron willowist misses or maybe a bad critical hit in a speed run what about the luckiest moment in this video I'm going to show you the most unbelievable clips that you have never seen and along the way we're going to learn a little bit about the math behind them and who knows you might just walk away with a little bit of knowledge about probability Theory scary I know I have uncovered some of the most unreal Clips in not just Pokemon history but like all of speedrunning history too buckle up kids you're about to hear people say no way a lot and probably a fair few expletives here we go [Music] foreign [Music] whether it's encountering a Shiny Pokemon or just having something break out of a Pokeball these games thrive on random chance let's start simple let's say you're playing Pokemon emerald and you chose Mudkip as your starter first of all good job let's say we have a square whose total area is one now let's break that square up into a hundred smaller squares so each of those tiny squares have an area of 0.01 since they're 1 100th of the total area now imagine that each one of those tiny 100 squares represents one of the possible outcomes when we select tackle in battle five of those squares represent the possible misses the other 95 squares then must mean that's when tackle hits this is called a probability space where the area of a shape represents the outcomes possible in a situation so the total area of this square is all possible outcomes one the area of our five misses added together is 0.05 which is the same thing as 1 in 20. you can also represent this in your mind as sort of 1 20th of the square is shaded in you can think of this square or really any probability space as being like a dart board if you had an equal chance to hit any point on the Square when you throw your Dart neglecting the edges and the boundaries between the squares then each time you throw a dart is like clicking tackle in battle about 1 in 20 of your darts are gonna hit the red squares which is the same as clicking tackle and having it Miss but wait 0.05 percent these numbers seem related nice work dear viewer you've nailed it I'm about to blow your damn mind let's take the word percent we have perv for four and sent from the Latin word Centum which means 100 so literally the word percent means basically for every 100 probabilities when used like our 0.05 value are used as a ratio out of one where one represents all the possible outcomes like our big Square from earlier but decimals are like kind of hard for humans to visualize it's not very easy number to work with in the marketplace we multiply them by 100. this is the same thing as just moving the decimal two places to the right that's going to be our little cheat code for converting probabilities to percentages oftentimes the most useful way to use probabilities is to find out the odds of two or more subsequent events happening so instead of just missing tackle once maybe we miss it twice in a row the way to calculate your new probability is to multiply the odds of each individual event together since we've converted probabilities to percentages by multiplying by 100 we can't use percentages very easily for math on multiple subsequent events because if I multiply five percent for the first tackle Miss by five percent for the second tackle miss that gives me 25 percent which doesn't really make sense how can it be more likely to miss twice in a row than to miss once in a row so if we want to do math on multiple subsequent events happening we have to either use the ratio or the probability let's use the ratio 1 in 20 times 1 in 20 or 1 in 20 squared that square distributes in to both numbers in the fraction one squared is 1 and 20 squared is four hundred that means our new odds are 1 in 400. if we make a new big square with 400 tiny squares we only shade in one of them for the likelihood that we miss both tackles in a row all the other squares represent other different outcomes we have for example the outcomes where we miss the first tackle but hit the second one that's a few more then we have hitting the first tackle but missing the second one that's a few more and then the vast majority of outcomes where we hit both tackles okay now that you've got a primer for how I'm going to discuss these clips and sort of how the math Works behind them let's watch an unlucky clip and a lucky clip to set the Baseline oh boy howdy are there oh double Miss double double Miss I lose this game corveame is a speedrunner who primarily enjoys speedrunning the 3DS Pokemon titles she says they are good and or fun I don't know I don't really get it either she's doing an ALT main speedrun which basically just means instead of using the thing in the meta that's the fastest you use a different Pokemon just to sort of switch it up and add a fun New interesting route so in this clip maze driftlin misses Thunder and then walrene misses blizzard and then driftle and misses Thunder again and then walrane misses blizzard again and then driftlin misses Thunder again and then walrane hits blizzard and may loses isn't that wonderful an easy way to find out how likely something is to not happen is to do one minus the odds of it happening this works the other way too okay so the moves are all 70 to hit which is the same thing as 70 over 100 which we can simplify because fractions simplify so if we divide both of those numbers by 10 we get 7 in 10. those are our odds that the moves hit now 1 minus seven and ten three and ten those are the odds that any one of these moves can miss and we have five in a row so remember from the previous section of this video that all we got to do is multiply three in ten by itself five times and then at the end of course we gotta tack on the fact that the wall rain hit Blizzard at the end which is seventy percent this comes out to be about Seventeen and ten thousand Point 0017 this clip is weird because it's sort of unlucky but also sort of lucky I mean it ends unlucky but in the grand scheme of things it was kind of nebulously both [Music] wow what wait I don't understand the runner mock Wing just had a Caterpie break out of a Pokeball how unlikely is that I have Pokemon break out of pokeballs all the time well dear viewer while you go on living your little lives going about your day doing your chores just sort of typing away on those little keyboards and clicking away on your big old mice horrible problems for Pokemon speedrunners are solved every day by a terrifying website that looks like it was designed in the 90s introducing the Pokemon catch rate calculator so mock Wing is doing a Pokemon Fire Red Elite Four round two speed run basically they have to capture a bunch of Pokemon in the run to be able to re-fight the Elite Four at the end of the speedrun early game catches are great for this run since they're so likely in fact it's usually considered that really early game Pokemon like Pidgey or Caterpie have essentially a 100 catch rate especially at lower HP values so what does the almighty catch rate calculator say about this particular breakout well the Caterpie is level three we're throwing a Pokeball and we can estimate itself to be about 25 the actual HP value might be lower than this but this is close enough 99.994 to catch per ball 0.006 chance for it to break out that's about one in 17 000 just on catching a Caterpie you know when I set out to research this video I went into a bunch of communities and I specifically asked them did anybody have any super unlucky or lucky clips and something really really interesting happened almost nobody sent me clips of good things happening to them this is something psychologists and some probability theorists call negativity bias here's my friend average Trey to explain people are just hella lucky if they're not me we have a pretty powerful tendency to more distinctly remember negative events than positive ones I think this is why it's easier to Doom scroll on Twitter for four hours and feel terrible than it is to just text your friend and tell them that you love them it's also why 24-hour news cycles and journalists are constantly harping on you with stories about like there's been a murder in your neighborhood and they're not doing stories like local man is Happy the first one Garners a lot more clicks gets a lot more butts and seats and pays a lot more in advertising dollars I just think it's important to recognize that we oftentimes I liked the really crazy unlucky things that happen to us rather than the Myriad of crazy lucky things that happened to us every day I think if we all just serve to change our perspectives just a little bit could all be like a tiny bit happier and maybe also stop of the terrible 24-hour news cycle from ruining our parents generation anyway here's some more bad stuff okay thank you I think a kid there I what what I have bakaras [Music] pokerus you may have heard of it it's a pretty unlikely event in Pokemon basically it's about 1 in 21 845. at first glance this seems exceptionally lucky after all pokerus effectively halves the time it takes to train your Pokemon right isn't that good for a speedrun where you're using one Pokemon the whole time and you want to just obliterate everything well yes and no when a Pokemon is infected with pokirus it gains twice as many effort values or EVS per Pokemon fainted in battle EVS are a hidden stat at least until recent installments in the series that increase a Pokemon's individual stats based on what Pokemon you have defeated in battle I won't get too into the specifics here there are plenty of YouTube videos that try try to explain EVS but all you really need to know is that if fainting a Magikarp gives say one speed EV if you have pokerus you get two speed EVS instead there might be battles where this is advantageous but for the most part at the world record level Pokemon speedruns are routed all the way down to what EVs you get in the run for example let's say there's a fight later in the game that requires you to have a certain attack EV in order to have a high enough attack stat so that you can KO a strong Pokemon pokerus you might not have filled up as many attack EVS along the way because you might have doubled up on other EVS like speed or special defense when you didn't want to so was this lucky or unlucky well does his reaction give any clues crazy maybe you need to see somebody else's reaction here's another clip of this happening to my friend echi in a Pokemon Platinum speedrun really recently are you serious I have Pokemon no dude no no no no no no no no no no oh so this runs no no okay I mean one in 21 000 is pretty unlikely but plenty of people have seen pokerus before you think I'd stop at one in 21. come on really there's some really wet it's a big numbers coming remember that scene in The Social Network where Andrew Garfield's character Eduardo savern is trying to get into a finals Club at Harvard and he eventually pretty much almost gets into the Phoenix down okay it's just that's just me what do you think Eduardo's odds even were Harvard has an undergraduate student body of about 9 000 and about half of which are male and maybe a fourth of which are in the year in which you'd be trying to get into a finals club and maybe half of those male students are even trying so that leaves us with about 560 students even if the Phoenix only took one student every year which is ridiculous that would mean that your odds of getting in are about 1 in 560. those odds are nothing we just saw a man with long hair and a beard scream about one in 21 000 I know of an even more exclusive Club my club doesn't have one in 560 odds no no no my club has odds of 1 in 65 000. tell me this isn't about me getting into the Phoenix no Mr Sovereign this is not about the Phoenix this is about the back-to-back gen 1 Miss Club [Music] in these games a move's accuracy is stored in memory as a one byte integer so it has possible values of 0 to 255. one byte is made up of eight binary bits that means base two counting when a move is selected either by the player or by enemy AI a random number generator is called to generate a random number this RNG call is also to a one byte integer so it also has a possible range of values 0 to 255. this is all well and good but the problem is the function that compares these two a move in Generation 1 misses if the RNG integer is greater than or equal to the accuracy number because the code reads greater than or equal to if the RNG byte ever rolls the maximum of 255 the function compares the two finds them equal and returns that the move should miss to put it plainly moves that are intended to never miss under normal circumstances always have a 1 in 256 chance to miss we're talking about two gen 1 misses in a row which is 1 and 256 times 1 and 256 one in 65 536 now we're talking let's watch some clips of this happening to way too many people wow I got the fourth ration that I genuinely missed it I did it twice are you actually serious right now turn on bad it needs to be long ideally I just genuine I just doubled General and Mr Lear and perhaps my favorite member of the club a wild Moltres I mean I could go for packing if it criticaled it would get there wait wait wait wait wait wait wait did it just gentle on this attack on me you see that guy in the last clip that's Shenanigans underscore Chen for short that is not the last we are going to see from him we've seen a lot of unlikely stuff that's great but I'm getting tired of these tiny little once in a year numbers no no no let's move up a few orders of magnitude into the truly unlikely stuff let's revisit that clip from the beginning of the video now we can really stretch our probability muscles so for all three legendary birds to be on the starter table here are the odds for the first ball it can be any of the three of them so that's three in 386 since there are 386 Pokemon in Generation 3 and there's three legendary birds then for the second one we've removed one of the birds so that's two in 385 and then for the final one we just repeat the removal process to get one in 384. for the numerator obviously once we have one of the legendary birds we want the other two to show up so that's why three becomes two and then one but for the denominator why does that number keep going down there's still 386 total Pokemon in the Pokedex right well the algorithm that the randomizer program uses to generate the three Pokemon that'll be on the lab table prevents there from being repeats so once we've had one of the legendary birds the other two can't be that same Pokemon again so we decrease the denominator by one for each successive Pokemon now we just multiply all those probabilities together which gives us 1.05 times 10 to the negative seventh that's about 1 in 10 million so many of the clips I've already shown you and probably almost all the moments or Clips you thought of at the start of this video failed to represent the total number of attempts what all of those clips of back-to-back gen 1 misses failed to show you is the millions of collective battles that have been played and recorded by speedrunners in gen 1 over the years in which there were not two back-to-back gen 1 misses this is not to say that it's not still cool or that you shouldn't recognize the unbelievable odds of something when it happens you absolutely should I'm just saying you know next time a shiny Hunter sees a full odd shiny and goes bazonko in Sano mode definitely be excited for them but also take a look at their attempt counter does it still feel that unreasonable news articles parents of Thanksgiving and Twitter blue users alike love to sensationalize things and saying that something is one in a million based on some study they claim to have read certainly helps them do that I don't mean to say that we shouldn't show off crazy Clips when they happen I just want you to start thinking a little bit more critically about probability and statistics in your day-to-day life so that you know when Uncle Billy comes over for family dinner and starts talking to you about the terrible 1 in 100 voter fraud that stole the election you can stop for a second and think hang on wait does This Racist guy actually know what he's talking about probably not okay now that I'm done proselytizing you let's talk about Chinese I didn't mean to like you know like make fun of shiny Hunters really I really do like shiny hunting I think it's really fun and it's pretty much the purest form of luck happening in Pokemon games there's really nothing simpler than just looking for a dangle Shiny Pokemon and it shows up and sparkles you go like oh my God this is the best thing that's ever happened to me it's so cool he's like apples anyway here's a clip of a guy seeing two full odd shinies at the exact same time so that you can be happy are you serious wait what the holy sh I've never seen that before Oh my god what the just happened holy two shinies on stream no way in Pokemon scarlet and violet which are video games [Music] one good thing that Pokemon scarlet and violet did do is introduce a king now putting aside that this is the absolute best Pokemon ever to exist dun dun sparse has a chance to be two segments or three segments long additionally starting in gen 8 there are something called marks basically there's a fun little chance that your Pokemon has cool little stickers the gamer you're about to see evolves a shiny Dunsparce into a shiny three-segment done spars and it has the coveted rare mark this one has wait wait this is like the one in one thousand Mark are you Martin [Music] oh wait based on the shiny hunting method used the shiny Dunsparce is about 1 in 683. the three segment done sparse evolution is one in one hundred and then the rare Mark is one in a thousand multiplying those together gives us a grand total of about 1 in 68 million good God I've danced around the issue long enough and yelled at you enough about the ethics of math and probability so here it is the unlikeliest clip I have ever seen the cool thing about this category is the RNG will never be the small white you actually do serious attempts huh it never will happen I guess whereas you just get them all yeah I'm getting wrecked by encountering it too it's pretty funny I've been looking for at least 10 seconds without an encounter no repels active this may be they're crazy this might actually be the craziest RNG that's ever occurred to me what is happening hello okay hold on hold on hold on this might be the least statistically likely thing that has ever happened in the Pokemon speedrun with this currently happening this oh my God this actually might be the least likely thing that's ever happened in a Pokemon speedrun nope I'm on pure encounter tiles I still haven't gotten an encounter it's been 200 steps in the Safari Zone I'm not I'm not exaggerating it's ten percent per step holy that was insane like any good wedding DJ trying to coax people away from the open bar and to the dance floor let's break it down there are some tiles in the Generation 1 Safari Zone that aren't capable of generating encounters because you know gen 1 but in this clip Shen isn't walking on any of those tiles the odds of any one step in any of the tiles Shen is walking through generating an encounter is 30 in 256. Shen takes by my count about 230 steps without generating an encounter so if our probability of generating an encounter on any one step is 30 in 256 then the probability of not getting an encounter on any one step is one minus that number then we just multiply that bad boy by itself 230 times from that we get a whopping 3.5 times 10 to the negative 13th we have just jumped from around 1 in 100 million which already seemed unbelievable to one in three trillion please let that sink in the Powerball which is the biggest lottery here in the United States has a grand prize that's around 1 in 230 million odds to win you are 12 000 times more likely to hit the jackpot in the Powerball than to do what Shen just did we may have all just watched the most unlikely thing we will ever see in any of our lifetimes and it happened in the Kanto Safari Zone and ultimately it doesn't really matter but it matters to us and that's all that matters thank you for watching I really genuinely appreciate it if you liked what you saw please consider subscribing and liking this video because I would love to make more stuff like this see you next time

Channel: adef

Views: 1,197,812

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Id: LynBpxaAcjc

Length: 24min 5sec (1445 seconds)

Published: Sun Jul 30 2023