Chapter 17 – Shiny Hunting: Full Odds, Full Throttle
Lots of mechanics to cover today, all Shiny-Hunting-related, so it'll be a boring chapter, folks. I've cut and relocated the absolute worst offender in this regard, the "Full Throttle" section (which is almost all math), to the bottom of the chapter.
When it comes to Shiny Hunting, "boring" is the name of the game 99.98% of the time. Literally. The most exciting and relevant part of this chapter is the final part of the non-cut content: "Color Coding". That's also the name of the game in Shiny Hunting: the only exciting moment is the very end, when you finally encounter a Shiny.
I won't blame readers who just read "Color Coding"... but be warned that "info-dumping" pervades even there. No mechanic being left behind or forgotten means chapters like this one, at least until I'm good enough to integrate them in more exciting ways. Remember, I've only been writing seriously for a few months. In the future, until I get sufficiently good, I'll continue to give heads-ups like this one whenever I feel like I've written a boring chapter, just so readers can know what to expect going in.
TL;DR: This chapter is info-heavy.
End-Game Content?
With the Rest Stop officially behind him, Ex turned his attention to his newfound goal. Well, it was newfound to him. His brain had been planning to do it all along:
Shiny Hunting. Attempting to find and Capture Shiny pokémon.
Ex wasn't taking the same steps he would've been taking if this were the video games, but the end result would hopefully be the same. His team, instead of battling, menuing, and running away from Wild pokémon, were simply keeping an eye out for sparkles while on Pickup duty. His Meowth had already seen two Shinies that way, so it seemed to work, which was exactly why Ex trained Charmander to do it too. With the aid of a shiny Nugget strapped to Bulbasaur, Charmander was slowly getting used to seeing shiny 'sparkles' moving through the Tall Grass. Hopefully. (Amber had offered to help Ex after he told her about Rattata and the moral reasons to Capture Shiny pokémon. It had taken her a bit of time to understand it all, but when she did, she didn't hesitate to lend a helping hand.) In short, Ex was currently Hunting Wild Shiny pokémon without engaging in any battles, which was a new experience for him.
In the games, unless you were using the Matsuda Method, you had to go to the Tall Grass – or Caves or Water – and enter battle after battle until the game's Random Number Generators output a set of values which corresponded to a Shiny pokémon. But grinding Wild battles wasn't the only thing you had to do if you wanted to Shiny Hunt.
Some Shiny pokémon required soft resetting to acquire. Software resetting, or 'soft resets', refers to the practice of saving just before specific encounters, especially Legendary encounters, then resetting the game's software (i.e. turning the game off and back on again) if it wasn't Shiny. You absolutely had to do this if you wanted to get Shiny versions of any Legendary pokémon without a cheat engine or being the luckiest person in the world.
Other unique pokémon, like the Starters of each generation, were sometimes hunted this way, but since most non-Legendaries could be hatched from eggs, the Matsuda Method was typically the preferred method since it lets players customize IVs and Natures and Abilities. Ex might eventually use the Matsuda Method, i.e. breed two pokémon from different nations together (here it's probably two different regions, if it exists at all), thereby boosting the chance of the hatched pokémon being Shiny by a factor of five (a x5 multiplier). But for now, Ex didn't have the resources to do that. The Matsuda Method was more of an end-game technique for this reason.
Well, Shiny Hunting in general is end-game content; many avid pokémon fans do it after they've beaten the game and they're waiting for Nintendo to release the next installment. But Shiny Hunting doesn't have to be end-game. Some players can and do Shiny Hunt during their first playthroughs. Those players are rare, however, because Hunting early means Hunting at...
Ex shuddered.
...Hunting at FULL ODDS.
Full Odds
Prior to Gen VI, the normal odds of encountering a Shiny pokémon were one in every eight thousand, one hundred and ninety-two wild encounters, on average. There were ways to improve these odds in later generations-
(His brain listed rather mechanically, The Poké Radar, the Masuda Method, the Cute Charm glitch, the Shiny Charm, the Friend Safari, Consecutive Fishing, SOS battle chains, the Ultra Warp Ride, Catch Combos, Lures, catching extra members of the species you want to be Shiny if you're playing Let's Go...)
-but if the odds were not improved (such that all encounters were governed by the original rate of 1 Shiny per 8,192 encounters, or 1 S / 4096 e after Gen V), it was considered 'Full Odds' Shiny Hunting. If you don't change your odds from the base rate, you have Full Odds.
Some might wonder why anyone would ever hunt at Full Odds when they could improve their chances.
Originally, the answer to that question was rather simple. Prior to Generation V, there weren't many ways to improve your Shiny chances (and the ones that did exist were hard to use), and prior to Generation IV there weren't any ways to improve your odds. If you wanted to go Shiny Hunting back in the day, you had to hunt at Full Odds. Period.
Still, even now that it's possible to improve the odds, people do Hunt Shinies at Full Odds, even those that know all about the Shiny Odds enhancers... especially the ones that know about them. Most people that Hunt at Full Odds today are explicitly and extremely aware that they could be improving their chances, even by doing something as (relatively) simple as obtaining a Shiny Charm, a Key Item which doubles Shiny Odds, obtained after completing the National Dex. Those who ignore these Items and methods are making the conscious decision NOT to make Shiny Hunting easier for themselves. They are choosing to Shiny Hunt at Full Odds.
There was an interesting reason for this.
Hunting for Shiny pokémon, according to various avid Hunters, is similar to gambling, taking drugs, and thrill-seeking, all rolled into one. Every time you get a new Shiny, it's like getting a row of sevens on a slot machine or taking a puff of pot. In addition, encountering and trying to Capture a Shiny gives you a rush of dopamine and excitement like you might get when a roller coaster goes down its first big drop. And Full Odds is like the biggest, scariest ride in the park.
In the beginning, players might Shiny Hunt using easier methods – which would be like getting into street gambling, taking 'gateway' drugs, or riding the kiddy rides. But sooner or later they'll want a better 'fix', so they use fewer and fewer odds-improvers to drag out the hunts longer and longer, boosting the payoff at the end – like Evolving from a pot puffer to a coke smoker, or going from lottery tickets to horse race bets, or going from roller coasters that you ride for thrills to roller coasters that you ride because they have a reputation for literally being painful to ride, just so you could brag to your friends that you did it. And ignoring odds-improving methods entirely – going Full Odds – is like going from a coke smoker to a heroine hitter, or from betting on horse racing to gambling at casinos, or like riding the Drop Zone at an amusement park because free-fall is literally the only thing left that can get your adrenaline pumping anymore.
Shiny Hunters spend their time like a high roller spends money. A Full Odds Hunter might have 20,000 encounters without finding a single Shiny pokémon, which at 5 encounters per minute evens out to 66.6 hours of gameplay. That means a single person has done the same thing over and over again without getting any results for almost three whole days. The dopamine rush for those with the patience to wait this long is tremendous. The emotions are that much stronger when you finally encounter a Shiny at Full Odds because the stakes are so much higher.
Shiny Hunting has fewer detrimental side effects than other forms of addiction, obviously, but the underlying motivations are the same: the highs and lows of dopamine, the thrill of the chase, and being able to brag that you've done something difficult and painful.
In short, Full Odds is a hell of a drug. Or for a less extreme analogy, think of fishing with a fishing pole. (Ugh. Ex just now realized that Fishing here might be similar to fishing in a real world, which won't be fun). Like fishing, Shiny Hunting is a whole lotta nothing for hours on end, then a whole lotta fun and excitement all at once.
Some Hunters, on TOP of ALL THAT, also held the opinion that Full Odds Hunting is how real gamers hunted Shiny pokémon; only wimps boost their chances to make it easier, and any Shiny pokémon Captured at less than Full Odds wasn't worth owning. But Ex had never quite agreed with this, even if he could respect the sentiment.
Later pokémon generations are slower – temporally, not technologically. Surfing from floor tile to floor tile in the Diamond and Pearl overworld, for example, takes twice as long as Surfing in Pokémon Platinum – essentially the same game – for seemingly no reason at all. Gen IV Surfing, even in Platinum, is much slower than Gen III Surfing, especially in Ruby, Sapphire, and Emerald. Even as the Nintendo gaming devices became more mechanically powerful over time (Gameboy to DS to Switch), the games themselves were programmed to move at slower paces than those that had come before, and this trend didn't stop at Gen IV.
In Gen V, pokémon sprites became fully animated, which took time to play out in every battle;
then they became full 3-D models in Gen VI, taking even longer;
the intro and closing sequences to each battle got longer;
menuing became slower despite the extra touch screen;
text wouldn't scroll as quickly;
the Mach Bike never came back after Gen III except in the ORAS remakes;
Gen VII speedruns take almost twice as long as speedrunning other generations;
speedruns of later generations in general take longer than speedruns of earlier ones;
the list went on.
All this resulted in longer Shiny Hunts in later generations, especially at Full Odds. It was slow even if a hunter had multiple gaming devices going at the same time. Later generations also had more expensive gaming devices – buying and running multiple Gameboys simultaneously was easier and less expensive than buying and running multiple Nintendo Switch consoles simultaneously, so Full Odds also became financially less viable over time. The addition of Horde Battles did help, since that was still technically Full Odds hunting, but only certain species could be found in Hordes. Ex had hunted at Full Odds himself, especially when that was all he could do, but when he saw methods for improving his chances to find Shiny pokémon without outright cheating, he naturally exploited them.
Unfortunately, many of the methods his brain mentioned earlier, like the Shiny Charm, probably wouldn't work here. Ex couldn't see how a lucky charm would increase Shiny encounters in a 'real' world. He'd looked it up on the Pokédex just in case, but the only results he'd found looked like scams. Even with that in mind, he didn't dismiss the idea entirely, but he had to table it for now.
The other odds-improving methods were in a similar state. Maybe the Masuda Method would work, but that involved lots of breeding, not wild encounters. The only thing he might be able to use right away was Horde Battle Hunting (five Wild pokémon means five chances for a Shiny), but he was currently avoiding those, and he would continue avoiding those until his team had some Multi-Target Moves... though in a real world like this one, the term "Area of Effect" might be more apt than "Multi-Target". Anyway, his team didn't have any AoE Moves, so he couldn't Horde Battle Hunt safely just yet.
In short, even though Ex knew about all the odds-improving methods, he couldn't use them. It wasn't a matter of choice, like the thrill-seeking Shiny Hunters choosing not to get the Shiny Charm. Ex was physically incapable of improving his chances using any of those methods.
Therefore, his best reference for Shiny Hunting, at the moment, was Full Odds Hunting – the 1/4096 of Gen VI and beyond, not the 1/8092 Full Odds prior to that... though maybe he should run the calculations twice, once with each fraction, since it wasn't guaranteed that the odds were 1/4096.
So he asked his brain to do the math...
(# See Full Throttle Section for the math.)
...and got two rough estimates: two hours and fifteen minutes per Shiny, or four hours and thirty minutes per Shiny, depending on the base odds.
And it wasn't long before those odds bore fruit.
Color Coding
Another Shiny Pidgey.
His first Capturable Shiny pokémon encounter turned out to be yet another Shiny Pidgey.
If Ex had been Hunting Shiny Rattata instead, this would be the third "phase" of the hunt. Most Hunters didn't like "phasing". It's the term they use whenever they encounter a Shiny pokémon they aren't actively Hunting at the time, like encountering three Shiny Pidgey in a row when Shiny Rattata is the target. Luckily for Ex, he wasn't "phasing" because he would take any Shiny he could get. His collection – his Shiny dex – was currently at 0/151.
He was about to fix that.
Blinky stood proudly before him with a golden Pidgey dangling by its feet, hanging from his teeth. Blinky had Fainted it with his last Hidden Power Electric, but first he'd Flinched it with his last Fake Out. And it was a good thing too. The Pidgey survived the first Fake Out on higher than usual health, meaning it just might have survived a Hidden Power Electric from Full Health. According to Ex's brain, anyway.
But forget all that. It wasn't time for calculations, it was time for science!
A Fainted pokémon was at his feet, and it was time to test his first theory. He tapped it on the head with an empty pokéball. Nothing happened. Maybe it needed to be thrown. He tossed the empty pokéball from short range so he wouldn't miss. The ball bounced off the Pidgey, bounced on the ground a few times, then came to a complete stop. It had not opened to admit the Fainted pokémon. Ex walked over, picked it up, and sighed. Capturing comatose creatures didn't seem to work, unfortunately.
Oh well.
On to Plan Two.
First, Ex called back his entire team using his Pokédex's Pokéwhistle.
Second, while he waited for his team to return, he checked their summaries and PP.
Third, when everyone was back, he had them all surround the Fainted Pidgey in a circle.
Fourth, he instructed them to attack if the Pidgey tried to flee.
Fifth, he used a Revive.
The Pidgey did try to flee.
His team attacked.
Pidgey Fainted. Again.
There was also a bit of friendly fire, requiring Oran to heal.
Ex sighed. Again.
On to Plan Two point Five.
He went through the same steps as before, but this time he made sure his team stood in a semi circle around the Pidgey, so they wouldn't be in each other's lines of fire. While they were getting into position, he laid out the five different Status Berries in front of the Pidgey. He also had his team Faint a nearby Rattata, in case Pidgey had a Nature without a Flavor preference, or preferred meat.
Then Ex used a Revive – his last Revive. (Fingers were crossed this would work, otherwise he'd have to wait until the Pidgey woke up naturally, or until his team Picked Up another Revive.)
When the Pidgey stirred this time, it did not flee immediately, instead glancing nervously at the pokémon around it.
Then it noticed the food.
The Shiny Pidgey quickly ate the Berries, starting with the Rawst (ugh) and leaving the Aspear alone, meaning it was probably Gentle.
Blinky – the pokémon who had caught this Pidgey, his brain pointed out – was Gentle too, which was a massive coincidence: a 1/25 * 1/25 = 1/625 chance. But then again, coincidences happen all the time; if his brain hadn't known about Natures, it wouldn't've even noticed. Besides, Nature guesses have a low probability associated with them anyway. In Shiny Hunting livestreams, where the chat fills with Nature guesses at the sight of a Shiny, it's rare that anyone actually guesses the correct Nature in advance, even with more than ten people guessing on the same pokémon.
After Pidgey had finished the Berries and moved on to the Fainted Rattata, pecking curiously and clearly distracted, Ex saw his chance and threw his ball. An Ultra Ball.
His Pickup Party had found one Ultra Ball, two Great Balls, and many normal Pokéballs at the Rest Stop. Ex didn't like letting good Items go to waste and he didn't want Pidgey to escape. If he'd used a regular Pokéball against a level 5 Pidgey at 50% health, he would've only had a 73-78% chance of Capturing it, depending on which generation's Capturing algorithm this world followed (if any). But using an Ultra Ball would guarantee a Capture under these circumstances... unless this world ran on the first generation's algorithm, in which case a Great Ball would ensure Capture, not an Ultra Ball. But given how messed up the Gen I Capturing Algorithm could be sometimes, neither Ex nor his Brain thought that was likely.
The ding of the Ultra Ball alerted Ex to a successful capture. He walked over and picked up the Pokéball, looking at the yellow pattern in satisfaction.
Of course, Capture chance hadn't been the only reason he used an Ultra Ball. Ex also liked matching colors and themes of Pokéballs to colors and themes of pokémon. Since he was Capturing a gold Pidgey, he used a gold Pokéball. Well, a yellow Pokéball, but that was close enough. He also Captured his future Pidgeot just now, and the strongest of three Balls fit thematically with the strongest of three Evolutionary stages. If he Captures another Shiny Pidgey, he'll be Evolving that one into Pidgeotto, so he'll use a Great Ball, and a third Shiny Pidgey will stay a Pidgey, so it'll get a regular Pokéball. That is, of course, unless his team happened to find more Ultra Balls before then. At the end of the day, Ex preferred matching colors over matching themes.
As for why he would bother Capturing multiple Pidgey in the first place... well, that part wasn't Ex's idea.
Ex threw the Ultra Ball in front of him, releasing the Pidgey from its Ultra Ball, a Potion and a Rawst Berry already in his other hand. The lively Pidgey trilled happily as its wounds were healed, nibbling on the Berry with surprising Gentleness. Its beak didn't touch his skin at all.
Ex's brain, throughout all of this, was thinking, That's 1/3, and 1/150 (or 1/151). 2 more Pidgey and the Pidgey line will be complete.
His brain, ever the perfectionist, wanted to complete a LIVING Shiny Dex, which is more difficult than completing the standard sort of Shiny Dex, which itself is FAR more difficult than completing a normal Pokédex. And keeping in mind how much time and dedication it takes to complete a normal Pokédex legitimately, one might consider his brain's goal impossible... and it probably would be. If this were the games, it definitely would be.
For a normal Shiny dex, like a normal Pokédex, so long as you've owned a Shiny version of a pokémon at one point in time, it counts towards completion of the Shiny dex. Even if you Evolve or Release it later, the checkbox has already been ticked. But for a LIVING dex, the checkbox next to each species only remains ticked as long as you actually have that species in your PC. Your living dex isn't complete until all 150(/1) Kanto pokémon are accounted for. For a living SHINY dex, you need at least one SHINY member of every species in your PC at the same time. In practice, this means Capturing multiples of each Evolutionary line (and also giving up if you're playing the games, because good luck getting Shiny-locked pokémon legitimately). It means Capturing three Shiny Dratini, three Shiny Charmander, three Shiny Pidgey, two Shiny Spearow, four Shiny Eevee (for Kanto), and so on, keeping at least one of each unEvolved.
Ex, at this point, had thought of objecting to having a living dex here, due to the morals involved with forcing pokémon not to Evolve. After all, Ex wants his pokémon to be able to choose for themselves when to Evolve, and a living dex requires unEvolved pokémon. But in this case, his brain pointed out a loophole. So long as Ex didn't train his Shinies to the level where they would Evolve, he didn't have to worry about what they would choose.
This wasn't the case with his Meowth. Ex plans on keeping the Pickup Party going for a while, which means keeping it going in dangerous, high-level places like Victory Road, the Pokémon Mansion, or even just Lavender Town Tower, which is a level 20+ zone (in the games) and would require level 20+ Meowth (or Persian if they decide they want to Evolve).
Shiny pokémon are a different story. Ex's brain doesn't intend to fully Evolve most of them, or even train them all that much in terms of Levels and Experience. It'll train them a little so they have a better chance of surviving in their original habitats (not that they need it, being Shiny and all), but it'll only train the fully-Evolved ones more than that. In short, it was clever use of morality mechanics, which Ex just barely let slide.
All other moral reservations he'd had about collecting pokémon had gone out the window when he'd learned what happens "in the PC". If they get sent back to their habitats, there was nothing inhumane about capturing as many as he felt like, so long as he didn't abuse them.
Ex stared at the Ultra Ball in his hand, then at the Pidgey.
Having learned his lesson from last time, he did not immediately put her (thanks Amber) in the Pokédex's Pokéball Scanner. This time he would wait until after reaching Viridian to register her as his, allowing him to start training her in the meantime. He had a five-day grace period before he absolutely had to registered her, according to the Silph website. He would have to be careful to keep her ball with him at all times and not confuse it with any of the other Pokéballs in his backpack, but since it was currently his only Ultra Ball, that would be easy.
Over the course of the next two days, along the main path of Route One, he Captured a total of five Shiny pokémon, including...
2. A Shiny Rattata, Nature Adamant, Ability Guts (which was insanely lucky)
4. Another Shiny Pidgey, Nature Rash, Ability Unknown
5. Another Shiny Rattata, Nature Timid, Ability Run Away
He and Amber had decided to stick to the easiest 'path' of Route 1, so he didn't encounter any other species in the Tall Grass (though he did encounter one other species somewhere else). They were sticking to the easy path partly because Amber had requested it and partly because Ex wanted the Route to stay predictable. The other species would become available over time; no need to rush things.
Interestingly, both Pidgey had been level 5 prior to Capture and both Rattata had been level 1.
Ex hadn't encountered any level 1 Rattata – or any level 1 pokémon in general – prior to that point. Assuming all pokémon hatched at level 1, he should have encountered plenty of level 1s by now... but the level 1 Rattata were much smaller even than level 2 Rattata, so maybe level 1 pokémon could hide more easily. Or maybe... maybe being level 2 was an indication that a pokémon had won (i.e. survived) its very first battle. In Rattata's case, that would be a battle against a hungry Pidgey.
But a Shiny Rattata wouldn't need to survive any ambushes and could probably sustain itself on Berries alone, given its size. The article had said that Shiny prey species used their Shininess to avoid getting eaten, which probably means they avoid getting attacked in the first place. On the flip side, Shiny predators dull their Shininess to help ambush prey, meaning that his Shiny Pidgey would naturally be good hunters, and would have risen to the top of the local level range. They also wouldn't need to fear getting eaten themselves if they Fainted in a failed ambush, so they'd get the luxury of trying again and learning from their mistakes.
All this was only rudimentary guessing at this stage, and even if he wasn't on the right track, he did ultimately have two level 1 Rattata and two level 5 Pidgey, and he had a very good idea for what to do with them. Two ideas, actually. He originally thought he'd have to implement the ideas at level 2, but level 1 was even better. And step one was to not level his Rattata at all.
Chapter over, below is the math.
Full Throttle
In order to estimate current odds, Brain needed to reference prior odds.
Back with handheld devices, Ex had been able to find, look at, and run away from 5-6 Wild pokémon every minute on an individual gaming device, depending on the generation. Naturally, this hadn't been enough for him.
The most dedicated Shiny Hunters will typically have multiple games and multiple game devices running side-by-side to increase the amount of Wild pokémon they can encountered simultaneously, thus increasing their odds of finding a Shiny. Most dedicated Shiny Hunters will have anywhere from 4 to 6 gaming devices going at the same time.
With 8 Game Boy Advanced SPs lined up side-by-side, with 4 Nintendo DSs on a raised platform just behind them, with eyes as keen as a Skarmory's, and with fingers as precise as a pianist's,* Ex definitely qualified as "dedicated". His encounters per minute per device dropped from 5 to 4 when using this method, but with 12 devices running at the same time, that put him at a total of 4*12 = 48 e/m (encounters per minute).
This particular set-up was specifically meant for Full-Odds Hunting; most odds-boosting methods required dedicated attention on a single game and couldn't be performed on multiple devices at the same time. And since Full-Odds was the best assumption Brain had for how this world worked, it used data from the 12-device set-up, not from any of the other ways Ex had Hunted Shinies.
Odds of encountering a Wild Shiny under normal circumstances: 1/8192 S/e (Shiny per encounters)
Wild encounters per minute: 48 e/m (encounters per minute)
Wild Shiny encounters per minute: 48 e/m * 1/8192 s/e = 48/8192 s/m = 24/4096 s/m = 12/2048 s/m = 6/1024 s/m = 3/512 s/m (Shinies per minute)
Minutes per Wild Shiny encounter: 512/3 m/s = 170.666 m/s (minutes per Shiny)
(What's more, Ex's full-odds Shiny encounter rate was even higher if he stuck only to the fastest generation, i.e. Gen III Ruby/Sapphire/Emerald, where he could have sixteen Gameboys going at the same time, giving him a Wild encounter rate of 64 e/m. However, doing that restricted his Hunting to the Hoenn region. He used that set-up for Safari Week and a few specific hunts – Absol, Chimecho, Bagon, and other rare Gen III encounters, catching any other Shinies he encountered along the way – but it wasn't something he'd typically do more than once or twice a year.
The reason he hadn't gone even further BEYOND was that sixteen devices at a time was pushing even his limits. The more devices he had going at a time, the lower his encounters per minute per device, or e/m/d. Sixteen Gameboys was the sweet spot for his Full-Odds Shiny Hunting. If he tried to use more than that, his attention would be so divided and his encounters per minute per device would decrease so much that his overall encounters per minute would actually decrease, even though he had more devices running. In short, it was a problem of Diminishing Marginal Returns.**)
When it was done calculating, Brain stated its findings.
We averaged out to one Shiny pokémon every 170 minutes and 40 seconds. That's one Shiny every 3 hours, or 2 per day (on average) when we dedicated 6 daily hours to it. But even using the most accurate Shiny odds available, there's still a major problem with equating video game Shiny Hunting to this world.
I figured, thought Ex. What's the difference, and what's the damage?
The numbers aren't simple here, to put it bluntly, thought Brain. They aren't as clean or easy to crunch. And the outcome won't be as accurate either, because a real world has more variables:
We don't have a standard e/m because encounters themselves work differently.
I have to estimate everything based on how many pokémon you, personally, can see per minute.
Meowth, being shorter than you with a worse vantage point, might see fewer pokémon than you can.
Or they might be able to see more than you because they're deeper in the Tall Grass, where all the pokémon are.
Location in general might affect frequency of encounters, or even frequency of Shinies, so average time per Shiny HERE might not be the same as other Routes.
Finally, Meowth might be distracted by Pickup, but hopefully the eye-catching aspect of Shiny pokémon will negate this when it matters.
Not to mention all the OTHER variables that probably exist but I don't know about.
And don't forget human error.
In short, assign a low weight of confidence to any estimates I give. Also, I need to know how many pokémon YOU can see per minute to run the calculations.
Ten minutes later, after averaging out a simple n = 1 sample size of data, Brain had a very rough guess. (N = 1 is statistics jargon, typically used in medical trials where a drug or technique is tested only on one individual. More generally, it means you've only collected information from a single person/source, in this case from Ex himself.)
Ex, if he kept an eye out and up, not down and focused on his Pokédex, could see about 5 pokémon per minute – the equivalent of 5 e/m. If Meowth could see about the same amount as him, that meant he and his party had an encounter rate of 6*5e/m = 30 e/m. Once Charmander was trained in Shiny Hunting, that would mean 7 pairs of eyes on the lookout, making it 7*5e/m = 35 e/m. Actually, since Ex's eyes would be mostly on the Pokédex, it would be 6 pairs of eyes, lowering it to 30 e/m again.
With full odds of 1/4096 s/e, that worked out to...
30 e/m * 1/4096 s/e * 60 m/h = 1800/4096 s/h = 900/2048 s/h = 450/1024 s/h = 225/512 s/h
... two hundred and twenty-five Shinies every five hundred and twelve hours. When you flipped the fraction and reduced, that was about two hours and fifteen minutes for every one Shiny. Better than his old Full Odds hunting back in the other world, surprisingly enough... unless the odds here were 1/8092, in which case it would take four and a half hours per Shiny, which was worse than his 12 device setup, but still wasn't that bad. Even in the worst case, Ex should encounter three to four more Shinies before reaching Viridian if he dedicated eight hours each day to Shiny Hunting.
Fingers were crossed that he and his brain hadn't messed up the math somewhere along the way to reaching this estimate.
* 8 Gameboys and 4 DS's is the setup of YouTuber YourFriedBread. He found 22 Shinies in Safari Week 2020 this way, which was the highest out of any individual Shiny Hunter this year during Safari season. Check out that video ("Safari Week 2020 YourFriedBread") if you want to see the setup, not just read about it. It's pretty impressive, and seeing it is much more impactful than having it described for you.
** Replacing 'the worst argument in the world' on my profile page, I've included a blurb on Diminishing Marginal Returns. Any current AP Microeconomics high school students might want to check it out, but it's open to all. You shouldn't need any prior knowledge on economics to understand it. I've also included my own attempt at solving the Diminishing Returns problem. If I've already removed the 'Diminishing Returns' notes by the time you get there, you can PM me for a copy if you want to see them, same as last time.