How Many Encounters for a FULL Pokedex? (Red & Blue)

[@cwolf1221]

Good god Charlie, your dedication to getting that correct answer through all calculations is admirable

[@TheChiptide]

If it means getting a needlessly accurate answer to an objectively pointless question, there is no hurdle I won’t jump

[@GaybrohamStinkton]

....your hair is too long, what is the ideal length it should be.

[@GoldenTGB]

Well... if I remember correctly, you can glitch into the safari zone without the requirements, and encounter pokemon the old fashioned way, and that would make it easier. But... then you would need to use a glitch to get them, and that's not intended by the devs If you are going to the safari zone video, I recommend watching the video by "Lyra made a website" for the optimal way to get pokemon in the safari zone (which spoiler, is just throwing balls at them, and hoping you get lucky)

[@PfyscheStyx]

love ur videos golden

[@GoldenTGB]

@@PfyscheStyx thanks!

[@belodie]

From what I understand, the best strategy in the RB Safari Zone is just to throw balls. Because ADHD went brrr, I calculated the chances for the Safari Zone mons - here they are: Rhyhorn: Centre Area: 16.41% chance to flee after each turn, 23.77% chance to catch per ball Area 2: 16.80% chance to flee after each turn, 23.77% chance to catch per ball Tauros: Area 2: 54.93% chance to flee after each turn, 6.56% chance to catch per ball Area 3: 51.22% chance to flee after each turn, 6.56% chance to catch per ball Exeggcute: Centre Area: 21.83% chance to flee after each turn, 17.88% chance to catch per ball Area 1: 21.44% chance to flee after each turn, 17.88% chance to catch per ball Area 2: 22.92% chance to flee after each turn, 17.87% chance to catch per ball Area 3: 22.09% chance to flee after each turn, 17.88% chance to catch per ball Kangaskhan: Area 1: 41.80% chance to flee after each turn, 6.53% chance to catch per ball Area 3: 44.68% chance to flee after each turn, 6.51% chance to catch per ball

[@banditrests]

This is correct and yes, just throwing balls has been determined to be the best strategy for safari zone encounters

[@SvenSierra104]

@@banditrests It might be in gen 2, I forget.. but there is a programming oversight (Which does make me think it could be gen 1) with some Mons where you can get their flee chance to be a 0% chance. This method works on the rarer Pokemon, which means for those, specifically (if its gen 1) the best strat would be to just throw balls outside of those exceptions. I'm probably thinking of Gen 2 though 😅

[@ryananderson7335]

@@SvenSierra104do you mean the gen 3 pokeblock glitch? Gen 2 doesn’t have a safari zone

[@SvenSierra104]

@@ryananderson7335 Probably that then haha Was tired at the time of the comment.

[@Rendertk1]

I have to disagree with the decision to search most common to least common, I think the exact opposite approach would be required to minimise the number of encounters needed. Suppose we had a pretty common mon which has a 50% encounter rate on route A, this means it requires two encounters on average. Now suppose this same mon had a 30% encounter rate on route B, but there is also another pokemon on this route only found here and with a 1% encounter rate. In trying to catch the rare mon you are practically guaranteed to catch the common mon and even if you didn't you could always move back to search on route A after catching the rare mon. This means that the doing the encounter on route A first on average is adding just under two extra expected encounters unneccessarily.

[@TheChiptide]

I mostly did it this way because it was easier to calculate and better to explain in the episode, starting simple and working up in complexity. I thought about trying to find the most efficient way to find everyone, but ultimately I ran out of time. You’re right, though, that probably is a better way to do it!

[@brandonm8901]

This assumes that the rarest Pokémon on that route is unique to that route only. If the 1% mon is only available on that route then sure you have to make encounters on that route until that mon is found, but if it is found on many other routes then it is not optimal to search on that route only until completion. Routes should be ordered by the sum of the encounter probability of all Pokémon that are exclusive to that route. Simply starting with the lowest absolute encounter rates will lead to cases where you are encountering the same already caught Pokémon on the same route, searching for a mon that is available at the same or even a lower rate on another route where the other encounters would be new.

[@Rendertk1]

@@brandonm8901 Yes agreed. I did state the assumption for the scenario I was presenting. I was not intending to give the impression that the ordering should be from absolute rarest to most common with no consideration to other mons on the route ect. The main idea I was hoping to portray is the fact that deference should generally be given to rarer pokemon precisely because of their rarity. Even when available across multiple routes it may still be worth dealing with encounters with caught pokemon. For example imagine a rare pokemon that has a 2% encounter rate on one route and a 1% on another, grinding on the second route introduces another 50 expected encounters so it might very well be worth not parallelising other pokemon to save those encounters if they are also common elsewhere. Obviously a lot of this is dependent on specific details of the routes. I do like your idea that the sum of exclusive encounter rates be considered though that was an idea that I definitely missed.

[@Johncornwell103]

Taking the path of least resistance is always good advice to take to heart. Hell the universe itself strives on taking the path of least resistance. Subatomic particles will literally try every possible travel path but always pick the path of least resistance.

[@TheChiptide]

If it’s good enough for an electron, then it’s good enough for us! Real talk, though, that’s a big thing I learned in engineering school. If you’re doing something that’s super hard, it probably means you’re being dumb

[@QuentinCarrero]

Really good video! Not to be that guy but there is a *slight* technical innacuracy here. You actually need to have 54 pokemon instead of 53. While you correctly pinned down needing 2 Spearow for Farfetch'd, you did forget to nail down needing to catch a second Poliwag (or Poliwhirl, since it also maxes out at 50%) in order to trade for Jynx. Props for also correctly identifying not needing doubles to trade for Mr.Mime or Lickitung, since Slowbro is fully evolved and Abra can be brought at the game corner without random chance.

[@TheChiptide]

You’re totally right, for some reason I had it in my head that both Poliwrath and Politoed were introduced in Gen 2. So close!

[@daponagegoogenburg807]

As a small note, the gotta catch em all tagline hadn't been used since around gen 3. So, it hasn't been the slogan for like 2 decades

[@Nelsito99]

Iirc it was also an American only slogan for marketing Never used in Japan where the games are both from and made

[@sebasdgc14]

Uh, gen 3 came out 2 decades ago

[@cinnamintie]

as an addendum to the safari zone problem, there's also Abra who you can't reasonably assume can be caught first try since you get only 1 guarenteed turn to act.

[@TheChiptide]

Luckily, you can buy an unlimited number of Abra from the Game Corner, no encounters needed!

[@Sock-Monster-Simian]

This was an infinitely cooler question than I first thought. A lot of really fun/interesting math. Yeah, the math primer was definitely necessary at the beginning.

[@iconic-dx6js]

It's a good day when chiptide uploads

[@signalfirefly]

Actually, Route 10 is locked behind Cut, so you'd go to Route 11 first. Also, is the assumption that you're using Repel whenever you aren't actively looking for Pokemon? If so, did you account for unavoidable encounters, like before Repels are available? Does having to play through a large portion of the game multiple times for version exclusives or, say, three Eevees make a difference? (Not saying you necessarily should factor those things in, just curious.)

[@eliasstenbak5689]

If you save and reset you hit no encounters to beat the game, but your pokedex is empty

[@aneonfoxtribute]

Psh you math nerds and your numbers, I'm just gonna go out and do it myself! How hard can it be!

[@theinsanegamer1024]

For the Safari Zone, I would have just assumed the player is only throwing the Safari ball, not anything with the rocks or bait. Like an average player would. Then, take the chance to flee, and the chance to catch and compare. In x number of pokeballs, once there is a greater than 50% chance to catch, you catch it. If that number is below 50% once their chance to flee reaches above 50%, then it flees, and the numbers are added again, of encountering repeats, etc. However, you keep that same "X number of pokeballs thrown". Once the number of Safari balls needed to capture is greater than 50%, then you capture it. For example, lets say Kangaskhan has a 25% flee chance each turn, and needs 10 Safari Balls on average for a 99.99% chance to capture. Turn 1, 25% chance to flee, doesn't. Turn 2, 50% flee? Not greater than 50%. Doesn't. Turn 3? Yup, flees. You've used 3 Safari Balls, however. Next time you encounter? turn 1, turn 4 of pokeball, nope. turn 2/turn 5?, nope. turn 3 this battle/turn 6? It catches, since you act first in a turn. To calculate flee chance per turn, calculate with the above for the average number of turns, and from there you can calculate the flee chances per turn in that average number of turns. Sometimes it might flee first turn, five turns in a row. But you've got an average to work with, which makes this go from "impossible" to "Basically almost impossible."

[@cyndaquil8331]

Did you account for the game corner? Plus, please read about the expectation value of encountering an event BEFORE a certain number of tries. Another way to optimize is assuming that if you need x encounters to catch a 5% Pokemon and y

[@chrislebanion1662]

Haven’t looked too far into it, but I’d be willing to bet utilizing repel filtering would simplify this quite a bit. Also the safari zone fly/cinnabar coast surf glitch to bypass that headache.

[@TheChiptide]

I’m not sure “simplify” is the right word, but it would certainly lower the total number!

[@androidboyd]

Seems plausible it could turn something into a 1 that isn't a 1, for sure. At the very least would help the safari zone, I'd imagine.

[@banditrests]

Just a fun Pokémon catching fact, because of the way the catching formula works in Gen 1, ultra balls are not always better than great balls, depending on the catch rate of the Pokémon. Gen 1 gonna Gen 1.

[@TheChiptide]

I started to read up on the Gen 1 catching formula for this video, and it honestly made my head hurt!

[@banditrests]

@@TheChiptide it’s a genuinely ridiculous formula and also pretty buggy, in part because of the way all calculations in Pokémon get truncated. They fixed the catching mechanics in later generations but all decimals are STILL TO THIS DAY floored. Might be an interesting thing to talk about, the way the hardware limitations made early gens weird and glitchy and some of them still haven’t been addressed for some reason. Like you can cause speed under flow to move first in trick room still in Gen 9

[@skalty9868]

It isn’t been the slogan since the beginning, it WAS the slogan at the beginning and hasn’t been for over two decades

[@silasary]

I disagree with excluding all trade Pokemon. We can only exclude those that require a fully evolved Pokemon. Farfetch'd requires a Spearow, which means it either requires adding a second spearow or a fearow. Same goes for Mr Mime's abra. Jynx needs a Poliwhirl. Lickitongue on the other hand needs a Skowbro, so it doesn't require a reencounter.

[@TheChiptide]

I did try to only exclude trade Pokémon that utilize fully evolved pokemon, that’s why I had to account for the 2 spearow. You can get Abra from the Game Corner, so you don’t actually need to catch any of those. Though I’ll admit, I did totally thing Poliwrath was gen 2 for some reason, so I did forget that one!

[@harrisonverhine6218]

Love both this and Numberphile's original video. I have an idea for an alternative approach. I feel like this problem could be modeled with a Markov Decision Process. The state space would represent your Pokedex progress. Each route (or generally, each encounter table) would be represented by an action in the MDP. Then the transition function would describe the odds of making progress for a particular route. I think you could tie your rewards to making Pokedex progress. Then finding the optimal policy should result in best routing through the game. Once you have that, you can find the average number of transitions through the resulting reduced Markov process. Curious if others think this would work and could be feasible to implement. I'm wondering if we'd arrive at the same number or if there are different assumptions baked into these approaches.

[@Kahadi]

So... A bit of a spin-off idea. A minimum battle run of Pokemon is when you go through the game with the fewest total battles possible. In a normal playthrough, this means every mandatory trainer battle, including gyms and the Elite 4 but also trainers you cannot avoid walking in front of without glitches, as well as the fewest number of wild Pokemon encounters necessary to use all of the HMs needed to progress, assuming you can't manage with only gift Pokemon. But this stipulation can be tacked onto other challenges, like solo runs and randomizers, which might adjust the minimum number of battles because of the HMs needed. That (poor) explanation aside, what would the fewest number of encounters be for a minimum battle Pokedex completion run? Now you need to calculate what would give fewer encounters and battles, evolving a Pokemon or catching the evolution? Which would also have encounter levels as a factor. If you catch Rattata on Route 2, it will be a very low level and thus require fewer battles to just catch a Raticate later. But if you catch a Rattata on Route 16 or Route 21, you can catch it at a high enough level that a single Rare Candy will evolve it, thus requiring only one encounter for both Pokemon. But both of those routes also have Raticate just available to catch, so you need to compare if the encounter rate difference between the higher level Rattata and the lower level Rattata makes it more worthwhile to just catch a Raticate. Finally, you need to factor in the potential experience gains of the mandatory battles and the number of available Rare Candies, since Rattata might still be better off caight at a low level and evolved into Raticate simply because the mandatory battles will be enough to get it there or if its better to catch a higher level one and use a Rare Candy or gain that single level with a battle to save the Candy for something that has a slower growth rate or higher evolution level or even just catch the Raticate to save both the mandatory battles and Candies for Pokemon that you can't catch the evolutions of that require far higher levels and thus far more experience. And you need to factor in things like how many mandatory battles would be over by the time that Pokemon becomes available and thus what Pokemon are available earlier that should get that experience instead. That would be an insane thing to calculate. I don't expect you or anyone else to do it, but I'm now genuinely curious to the answer...

[@TheChiptide]

I actually did something similar to this not too long ago, when I tried to find the luckiest game of Pokemon possible!

[@GaybrohamStinkton]

16...mans int taking trainer battles into account. Also, you are highballing everything, the game can be restarted when an inoptimal spawn is found, if its not 100% its 50%, restart till the 50% is the 100% you need. Its all binary innit

[@TheChiptide]

I was thinking more in terms of real life time, not encounters that the game recorded. So even if you save scum or something, you still had to get the encounter

[@HandsomeLongshanks]

3:30 potentially wrong. You need 1 encounter for every trade you make. So, unless you're giving away pokemon you don't need anymore, you'll need replacements for the ones you trade away.

[@delibirdite]

Late response but you might be able to make it easier to calculate if you also include the repel strat where you use a certain level pokemon to force certain encounters

[@BVCake]

I think I am the only 11 yr old who watches and is genuinly interestid in the chiptide show, and I am proud of that

[@Elix111]

I'm 12 so nah frfr

[@BVCake]

@@Elix111 Well 12 is not 11 so yeh frfr

[@GoldSayaProductions]

It's a Pokemon channel. I'm sure lots of eleven year olds. Most of them just don't advertise

[@BVCake]

@@GoldSayaProductions Im talking mainly about the MATH part, cuz im a nerd

[@wootmasterzorsx]

See, there’s one shortcut to cut that answer even further. Find the biggest Magikarp fan on the planet with a full Pokedex in their game, trade 69 Magikarp to them for all the stuff you need in terms of evolution lines and version exclusives and get the remaining 5 Static encounters, and you finish in roughly 74 encounters. All this as a joke “if we allow trading, we can just get the Pokémon we need from any encounters and trade with someone with a completed Pokedex.” The math and work in this video for a REAL answer is really impressive. I just wanted to be cheeky. …And I still feel like I messed up my counting along the way, lol. I’ll leave the for real math to you.

[@Emberloid]

this gave me flashbacks to stats class and retraumatized me

[@matercan5649]

This one's an interesting topic love to see it with persona and other jrpgs tho and then compile it to a new video for sleeping viewers

[@jadedcode8953]

I love your videos!

[@cycloneofsouls]

My good sir, you forgot to account for how many encounters it'd take to get the experience required to evolve all of the baseline pokemon into their final forms! based on the average amount of xp you'd get per battle on each route, and the amount of rare candies you get in the game! The biggest shortcut ahhhh lol

[@TheChiptide]

I just assumed you’d battle the elite four a bunch of times instead of grinding on wild pokemon

[@cycloneofsouls]

@@TheChiptide are those not encounters?! (obvs im not being serious, just being a goof)

[@vizzzyy190]

thank you for your service

[@RM-um9xx]

Counterpoint: save scumming

[@TheChiptide]

I mean, you still had to get the encounter, even if the game doesn’t remember it

[@Mustafa_AhmedPGH]

You poor man.

[@Jackledaman]

Awesome video :D

[@zivronen9539]

I didn't expect to have an introduction to bayesian networks today. And I was right, this is like second, maybe third course assignment.

[@TheChiptide]

This will all be on the test

[@brandonm8901]

Does this assume that any route can be reached with no encounters? Starting by Surfing on R19 then reaching Diglett's Cave and only counting that as 2 total encounters? This isn't assuming starting a fresh game where certain routes are prerequisites to other routes

[@ChosenOne41]

In the safari zone I would just throw safari balls until it worked instead of trying to figure out how the rock and bait options work

[@TheChiptide]

Honestly, I think that’s the best strat anyway

[@kenji6492]

Idk if it would have been less expensive but through *cough cough* TOTALLY LEGITIMATE MEANS you can install the Gen 1 Virtual Console releases on a 3DS.

[@youtubeuniversity3638]

Now we need Min. and Max..

[@PhoenixShadow13]

Good afternoon everyone!

[@notLord0]

Don't you need 3 Eevees?

[@TheChiptide]

You do, but Eevee is a gift Pokémon so you don’t need to encounter it. You just need to play through a significant portion of the game to get it!

[@satsujin-shathewitchkingof6185]

44.04 technically

[@TheChiptide]

You right, gotta remember those sig figs

[@satsujin-shathewitchkingof6185]

@@TheChiptide I just liked how many 4s there was

[@dtsnelson]

Im early say something funny.... gotta catch em all.

[@tysmith211]

For the algorithm

[@CaptainKrby]

Safari zone my behated

[@TheChiptide]

I don’t know what sick person at game freak came up with that idea, but I swear they need to be locked up asap

[@DennisComella]

So once you've caught all 53 Pokemon, how will you level them up? You need to add the expected encounters to find a MissingNo and duplicate rare candies on the Cinnabar coast, then subtract the total experience gained from required trainer battles (optimally distributed to maximize level ups, factoring in the expected level of each limitedly available caught Pokemon by the time each battle occurs, PLUS the probability that you later encounter (and catch) a higher level of the same species (or an evolved form)). Then you'll know the true number of encounters! 🫠

[@TheChiptide]

I assumed you’d just battle the elite four over and over to level up, but MissingNo could work too!