PandaJJ

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Mfw when I hadn't seen this untill now:

 
I'm tempted to make a thread in Bug Reports if the data collected by the OP is correct. I thought they had never stated the shiny encounter rate, but this shows they are just lying.

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Introduction
 
When breeding, you will have to catch the pokemon that you want to breed in the wild. However, many pokemon are not easy to find, and even more difficult to catch. These include rare safari zone pokemon such as chansey and miltank, or the starter pokemon such as bulbasaur and torchic. The best way to go about with breeding these pokemon is to catch a few, keep one that is decent, and then start catching pokemon of the same egg group that is easier to find and catch. This makes breeding much quicker and cheaper. The purpose of this guide is to show you where you can find these easy-to-encounter, easy-to-catch pokemon. The guide will contain two parts - the first part is a general breeding guide (for gendered pokemon), while the second part is a list of locations that contains the best easy-to-encounter, easy-to-catch pokemon.
 
Example:
Say you want competetive blissey. First you need to catch a chansey - they are rare to encounter, and incredibly hard to catch. When you finally get one, it turns out it has terrible IVs and a bad nature. Rather than going through the pain of trying to catch a new one, you should turn to breeding, the most useful tool in the game. Chansey is in the fairy egg group, so it can breed with any pokemon from that egg group. Hoppip is another pokemon that happens to be in the fairy egg group, and unlike chansey, it has a 100% encounter rate south of island 5, and a catch rate of 255 (33,3%). The best way to go about making a good blissey is therefore to catch hoppips, and then breed them together with each other/chansey while using braces to get a nice competetive pokemon.
 
 
Part one: Breeding
 
The current breeding system for allows us to completely manipulate the IVs of our offspring, or let luck decide for us. I prefer the former, so I put a lot of effort into breeding to get what I want. Manipulating the offspring requires braces and everstones, so it’s a costly business. However, if you are content with a pokemon with 25+ IVs instead of perfect 31s, the time and money spent on breeding can be drastically reduced. This section is a deviation of Gilan’s breeding guide, to teach you how to breed (imo) as efficient as possible. I will not consider how to breed genderless pokemon - see Gilan’s guide to breeding on a budget for the general way to go about this.
 
First let’s agree on some terminology. When I talk about a trait of a pokemon, I talk about its IVs and nature. A pokemon has exactly seven traits - the nature, the hp IV, the atk IV, the def IV, the spatk IV, the spdef IV and the speed IV. Now, in order to guarantee that the offspring has n+1 good traits, you will have to have two parents with n good traits, of which n-1 non-nature traits are overlapping. The parents are given braces/everstone to make sure that the non-overlapping stats are passed. In general, you will need 2^(n-1) pokemon with one good trait in order to make a pokemon with n good traits, and this process takes 2^(n-1) - 1 breeds and 2^n - 2 braces/everstones in total. The most common thing to make is a pokemon with six good traits (five good IVs and a good nature), which would require 32 pokemon with one good trait, 31 breeds and 62 total braces/everstones. The braces/everstones alone will account for 930k if we assume that everstones are 15k a piece - this is not accounting for the pokeballs needed or price for gender selection. As you can see, this form of breeding is extremely expensive and time consuming - however, it can easily be cut by 75%, as I will show.
 
So far, I have not defined the term “good”. If you define it to be 31 in all the relevant IVs, the method mentioned above is hard to improve. If, on the other hand, you define it to be 25+ in each relevant IV, it can be vastly improved upon. This is simply because pokemon with several “good” traits are now very common - the chance of a wild pokemon having at least three IVs above 25 is ~12.33%. If you want to improve on the method above, you can simply skip the part where you breed pokemon with one good trait together to get a pokemon with two good traits, since you can just catch pokemon with three good traits in the wild. To get a pokemon with 6 good traits now, you only need eight pokemon with three good traits each, you only need to breed seven times, which means that the 14 braces/everstones you need will be only 210k! Once again I have ignored the cost of pokeballs and gender selection, not to mention that I did not consider the fact that good natured pokemon with good IVs are rarer to find, but the point here is that the amount of time and money required is just a fraction of what it used to be. Now, you might question the amount of time spent on cathing the pokemon with three good traits - the interesting thing is that you are expected to spend less time catching eight pokemon with at least three IVs at 25+ than 32 pokemon with at least one IV at 31 - thus, you will save time here as well.
 
As mentioned, the chance of a wild pokemon having at least three IVs at 25+ is about 12.33%, meaning that about one in eight pokemon will have this property. You will need eight pokemon like this, which means that you should expect to catch about 64 pokemon. However, some of these poekmon will have stats that you don’t need - since the 12.33% chance is that any three stats are 25+, you might get a few with the one stat that doesn’t have to be 25+. I generally recommend catching about 60-120 pokemon (one to two boxes in your pc), which should be sufficient for this breeding method.
 
For those of you who have not yet figured out how to breed after this discussion, here is a list to sum it up:
 
1. Get a decent (one or more good traits) pokemon of the spieces you want to breed. If the pokemon is gendered, get one that is female (if it is not female, you can breed with ditto to change the gender).
2. If you want any egg moves on your pokemon, make sure to breed this onto it first (keep the offspring female, if gendered).
3. Catch one to two boxes (60 to 120 pokemon) of a compatible pokemon from the list in this guide. If needed, narrow the IVs of the ones that look good, release the ones that are bad. Remember to keep at least one pokemon with the nature you want on your competetive pokemon.
4. Figure out a way to breed the pokemon you cought in step 3 with the pokemon you cought in step 1 (or bred in step 2, if it has egg moves) to make its IVs better. If the  pokemon you cought in step 1 has n good IVs, you pair it with another pokemon with n good IVs, of which n-1 are overlapping. You repeat this process until you have reached the desired amount of good IVs. When you have reached the point where you have 4 good IVs on your pokemon, you will have to combine the pokemon from step 3 together to make a male with 4 good IVs as well. You might have to turn back to step 3 in case you did not catch enough good pokemon.
5. If the final pokemon has the correct nature, you're done. Otherwise, make a male pokemon with the desired nature based on the pokemon you kept in step 3 and breed for nature.
 
Sometimes, you will catch a lot of good pokemon in step 3 that you do not use to breed the specific pokemon you want. These can either be sold, or kept for later breeding. For this reason, it is a good idea to catch pokemon that belongs to multiple egg groups, as they will be more valuable when breeding.

I'm sorry to break this to you, but it seems (according to numbers given to me by matlab) that you have made a mistake. The number .0445575 is what I get by calculating P(k<2), because
P(k<2) = P(k=0) + P(k=1) = .0075743 + .0369796 = .0445539
The last two decimals do not match with your number, but I don't know what method you used to calculate that number (did you use the decimal approximation of p?) Of course P(k=n) might be a typo from your side, maybe you meant P(k<=n) instead. However the error arises when you calculate 1 - P(k<2), which is equal to P(k>1). This number is the probability of finding at least TWO shinies, so the number you found, 95.54%, is the probability of finding at least two shinies. The probability of finding at least one shiny is simply
P(k>0) = 1 - P(k=0) = .9924256
or 99,24% if you wish.
 
 
People who are saying that they have 3k playing time without finding a shiny are not really giving any useful information, because we have no idea what they spent that time on (likely not shiny hunting.) However, looking at information from other people, like PBC, gives us some evidence that the actual shiny encounter rate is not at all 1/8192.
 
Btw, I'm curious - who came up with the number 1/32000 in the first place?

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Introduction
 
When breeding, you will have to catch the pokemon that you want to breed in the wild. However, many pokemon are not easy to find, and even more difficult to catch. These include rare safari zone pokemon such as chansey and miltank, or the starter pokemon such as bulbasaur and torchic. The best way to go about with breeding these pokemon is to catch a few, keep one that is decent, and then start catching pokemon of the same egg group that is easier to find and catch. This makes breeding much quicker and cheaper. The purpose of this guide is to show you where you can find these easy-to-encounter, easy-to-catch pokemon. The guide will contain two parts - the first part is a general breeding guide (for gendered pokemon), while the second part is a list of locations that contains the best easy-to-encounter, easy-to-catch pokemon.
 
Example:
Say you want competetive blissey. First you need to catch a chansey - they are rare to encounter, and incredibly hard to catch. When you finally get one, it turns out it has terrible IVs and a bad nature. Rather than going through the pain of trying to catch a new one, you should turn to breeding, the most useful tool in the game. Chansey is in the fairy egg group, so it can breed with any pokemon from that egg group. Hoppip is another pokemon that happens to be in the fairy egg group, and unlike chansey, it has a 100% encounter rate south of island 5, and a catch rate of 255 (33,3%). The best way to go about making a good blissey is therefore to catch hoppips, and then breed them together with each other/chansey while using braces to get a nice competetive pokemon.
 
 
Part one: Breeding
 
The current breeding system for allows us to completely manipulate the IVs of our offspring, or let luck decide for us. I prefer the former, so I put a lot of effort into breeding to get what I want. Manipulating the offspring requires braces and everstones, so it’s a costly business. However, if you are content with a pokemon with 25+ IVs instead of perfect 31s, the time and money spent on breeding can be drastically reduced. This section is a deviation of Gilan’s breeding guide, to teach you how to breed (imo) as efficient as possible. I will not consider how to breed genderless pokemon - see Gilan’s guide to breeding on a budget for the general way to go about this.
 
First let’s agree on some terminology. When I talk about a trait of a pokemon, I talk about its IVs and nature. A pokemon has exactly seven traits - the nature, the hp IV, the atk IV, the def IV, the spatk IV, the spdef IV and the speed IV. Now, in order to guarantee that the offspring has n+1 good traits, you will have to have two parents with n good traits, of which n-1 non-nature traits are overlapping. The parents are given braces/everstone to make sure that the non-overlapping stats are passed. In general, you will need 2^(n-1) pokemon with one good trait in order to make a pokemon with n good traits, and this process takes 2^(n-1) - 1 breeds and 2^n - 2 braces/everstones in total. The most common thing to make is a pokemon with six good traits (five good IVs and a good nature), which would require 32 pokemon with one good trait, 31 breeds and 62 total braces/everstones. The braces/everstones alone will account for 930k if we assume that everstones are 15k a piece - this is not accounting for the pokeballs needed or price for gender selection. As you can see, this form of breeding is extremely expensive and time consuming - however, it can easily be cut by 75%, as I will show.
 
So far, I have not defined the term “good”. If you define it to be 31 in all the relevant IVs, the method mentioned above is hard to improve. If, on the other hand, you define it to be 25+ in each relevant IV, it can be vastly improved upon. This is simply because pokemon with several “good” traits are now very common - the chance of a wild pokemon having at least three IVs above 25 is ~12.33%. If you want to improve on the method above, you can simply skip the part where you breed pokemon with one good trait together to get a pokemon with two good traits, since you can just catch pokemon with three good traits in the wild. To get a pokemon with 6 good traits now, you only need eight pokemon with three good traits each, you only need to breed seven times, which means that the 14 braces/everstones you need will be only 210k! Once again I have ignored the cost of pokeballs and gender selection, not to mention that I did not consider the fact that good natured pokemon with good IVs are rarer to find, but the point here is that the amount of time and money required is just a fraction of what it used to be. Now, you might question the amount of time spent on cathing the pokemon with three good traits - the interesting thing is that you are expected to spend less time catching eight pokemon with at least three IVs at 25+ than 32 pokemon with at least one IV at 31 - thus, you will save time here as well.
 
As mentioned, the chance of a wild pokemon having at least three IVs at 25+ is about 12.33%, meaning that about one in eight pokemon will have this property. You will need eight pokemon like this, which means that you should expect to catch about 64 pokemon. However, some of these poekmon will have stats that you don’t need - since the 12.33% chance is that any three stats are 25+, you might get a few with the one stat that doesn’t have to be 25+. I generally recommend catching about 60-120 pokemon (one to two boxes in your pc), which should be sufficient for this breeding method.
 
For those of you who have not yet figured out how to breed after this discussion, here is a list to sum it up:
 
1. Get a decent (one or more good traits) pokemon of the spieces you want to breed. If the pokemon is gendered, get one that is female (if it is not female, you can breed with ditto to change the gender).
2. If you want any egg moves on your pokemon, make sure to breed this onto it first (keep the offspring female, if gendered).
3. Catch one to two boxes (60 to 120 pokemon) of a compatible pokemon from the list in this guide. If needed, narrow the IVs of the ones that look good, release the ones that are bad. Remember to keep at least one pokemon with the nature you want on your competetive pokemon.
4. Figure out a way to breed the pokemon you cought in step 3 with the pokemon you cought in step 1 (or bred in step 2, if it has egg moves) to make its IVs better. If the  pokemon you cought in step 1 has n good IVs, you pair it with another pokemon with n good IVs, of which n-1 are overlapping. You repeat this process until you have reached the desired amount of good IVs. When you have reached the point where you have 4 good IVs on your pokemon, you will have to combine the pokemon from step 3 together to make a male with 4 good IVs as well. You might have to turn back to step 3 in case you did not catch enough good pokemon.
5. If the final pokemon has the correct nature, you're done. Otherwise, make a male pokemon with the desired nature based on the pokemon you kept in step 3 and breed for nature.
 
Sometimes, you will catch a lot of good pokemon in step 3 that you do not use to breed the specific pokemon you want. These can either be sold, or kept for later breeding. For this reason, it is a good idea to catch pokemon that belongs to multiple egg groups, as they will be more valuable when breeding.

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

Part two: Catching pokemon
 
The catch rate in this game is a/255, where a is approximately
a = ((3*HPmax - 2*HPcurrent)*rate*bonusball*bonusstatus)/3*HPmax
The value a/255 is however calculated by a completely different formula in the game (it actually calculates the chance of a ball shaking four times). The in-game formula has a major rounding error, so in reality every value of a larger than 200 gives a 100% catch rate. Furthermore, the formula for a has some rounding errors, so here is what I have found is required to have a 100% catch rate out:
 
-For pokemon with a catch rate larger than 200, you need to reduce their hp to 1.
-For pokemon with a catch rate between 75 and 200, you need to reduce their hp to 1 and put them to sleep.
-For pokemon with a catch rate between 35 and 75, you need to reduce their hp to 1, put them to sleep and use an ultra ball.
 
The list of easy-to-catch pokemon will be sorted by egg groups, and then by what I think is the best area. Each area on the list will be on the following format:
 
Area (Collective Encounter rate): Pokemon 1's name (encounter rate, catch rate), Pokemon 2's name (encounter rate, catch rate), and so on
Comment: comment
 
A pokemon's name will appear in boldface if it belongs to more than one egg group - these are the most desired pokemon to catch. Furthermore, several areas will be listed together if they have exactly the same encounters. Here is an example from the human-like group:
 
Human-like
Mt. Ember (50%): Machop (50%, 180)
Comment: This area also contains 50% geodudes
 
Generally, what you are looking for are high level pokemon that have a 100% encounter rate and 100+ catch rate. The high levels help you narrow IVs. For genderless pokemon, you will have to simply catch dittos.
 
 
The list
 
Field
I might have missed a place or two, but field pokemon are generally easy to come by. Whismur is nice because it’s also the best monster breeder.
 
Rusturf tunnel (100%): Whismur (100%, 190)
 
Diglett's cave (100%): Diglett (95%, 255), Dugtrio (5%, 50)
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
 
Monster
 
Rusturf tunnel (100%): Whismur (100%, 190)
Comment: Whismur in this area are level 5-8, which means you have to do some leveling to narrow their IVs.
 
 
Human-like
Human-like pokemon are unfortunately one of the few types of which you can’t find 100% of the time. Spinda is arguably the best pokemon due to its secondary egg group, field, while also having the highest encounter rate. If you are however breeding machamp/hariyama, you might as well just catch machop/makuhita.
 
Route 113 (70%): Spinda (70%, 255)
 
Mt. Ember (50%): Machop (50%, 180)
 
 
Water 1
There are a ton of places where you can farm only water 1 pokemon, these are just a few possibilities that are out there.
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Route 104 (100%): Wingull (95%, 190), Pelipper(5%, 45)
 
Surfing in Route 6, 22, 23, 25, Viridian City, Fuchsia City (100%): Slowpoke (50%, 190), Psyduck (50%, 190)
 
Surfing on Island 4 (100%): Wooper (35%, 255), Marill (35%, 190), Psyduck (15%, 190), Slowpoke (15%, 190)
 
Surfing in Ruin valley (100%): Wooper (50%, 255), Marill (50%, 190)
 
Surfing in Route 120 (~95%): Azumarill (~66%, 75), Surskit (?%, 200), Mudkip (?%, 45)
Comment: Exact encounter rates not known.
 
 
Fairy
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Surfing in Route 114 (100%): Azumarill/Marill (100%, 190/75)
 
 
Flying
 
Surfing in Route 104 (100%): Wingull (95%, 255), Pelipper (5%, 45)
 
Route 103 (Altering cave) (100%): Zubat (100%, 255)
(Depending on the cycle)
 
Bug
 
Mt. Moon (100%): Paras (100%, 190)
 
Pattern bush (100%): Various
Comment: This place has a lot of different pokemon, all in the bug group. The encounters vary by night/day cycles. I just put this here because the pokemon here are higher level than the paras.
 
 
Grass
 
Memorial pillar (100%): Hoppip (100%, 255)
 
Mt. Moon (100%): Paras (100%, 190)
 
 
Water 2
Depending on what second egg group you want, you should catch either Wailmer (field) or Magikarp (dragon).
 
Super rod in Slateport (100%): Wailmer (100%, 125)
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Super rod in Route 118 (100%): Carvanha (95%, 225), Sharpedo (5%, 60)
 
 
Mineral
Mineral pokemon are another unfortunate example of which there is no 100% spot. The vast majority of mineral pokem are admittedly genderless, so you will not need these too often. You can also hunt them while hunting human-likes.
 
Team magma hideout (70%): Geodude (55%, 255), Graveler (15%, 120)
Comment: This place contains 30% torkoal, which are not very useful since they are only field and has a catch rate of 90.
 
Mt. Ember (50%): Geodude (50%, 255)
Comment: This place contains 50% machop.
 
Also, Rock Smash in many places (Island 1) may be a way to have a 100% spot.
 
 
Amorphus
Most of the amorphous pokemon are ghosts, which means they are not affected by false swipe. To make matters worse, shuppet is immune to sleep, making it fairly hard to catch. Although slugma is far away from a pokemon center, so is Mt. Pyre, and Pokemon tower has a very low encounter rate overall, so slugma is arguably your best option. (Note that you can use foresight to bypass the false swipe immunity.)
 
Mt. Ember (Ruby path) (100%): Slugma (100%, 190)
 
Pokemon tower (91%): Gastly (90%, 190), Haunter (1%, 11.8%)
 
Mt. Pyre (100%): Shuppet (50%, 190), Duskull (50%, 190)
 
 
Water 3
 
Super rod in Petalburg city (100%): Corphish (100%, 205)
 
Surfing in Kanto (100%): Tentacool (100%, 190)
 
 
Dragon
 
Surfing in Sootopolis (100%): Magikarp (100%, 255)
 
Old Rod in Vermillon (100%): Magikarp (100%, 255)
 
Ditto
Dittos are hard to come by, but I don’t think there is any other place than the mentioned tone worth mentioning.
 
Desert underpass (50%): Ditto (50%, 35)

I'm sorry to break this to you, but it seems (according to numbers given to me by matlab) that you have made a mistake. The number .0445575 is what I get by calculating P(k<2), because
P(k<2) = P(k=0) + P(k=1) = .0075743 + .0369796 = .0445539
The last two decimals do not match with your number, but I don't know what method you used to calculate that number (did you use the decimal approximation of p?) Of course P(k=n) might be a typo from your side, maybe you meant P(k<=n) instead. However the error arises when you calculate 1 - P(k<2), which is equal to P(k>1). This number is the probability of finding at least TWO shinies, so the number you found, 95.54%, is the probability of finding at least two shinies. The probability of finding at least one shiny is simply
P(k>0) = 1 - P(k=0) = .9924256
or 99,24% if you wish.
 
 
People who are saying that they have 3k playing time without finding a shiny are not really giving any useful information, because we have no idea what they spent that time on (likely not shiny hunting.) However, looking at information from other people, like PBC, gives us some evidence that the actual shiny encounter rate is not at all 1/8192.
 
Btw, I'm curious - who came up with the number 1/32000 in the first place?

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.

Take care Panda.
 
Guys, remember when over 100k people played one pokemon game on twitch? Someone made a video with the top 10 moments and it is a must see:
https://www.youtube.com/watch?v=WziMRN9WoVk

You are just mad because you couldn't get pageking

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.

I'll miss you handsome
 
[spoiler] still waiting for your name [/spoiler]

Not you too :( Thanks for all your effort with the team and the gym, stay in touch buddy <3

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.

Hey guys. I don't know how to better put this than to quote my good friend:
 
I knew that this was true all along, but shit just got serious. I'm going to hold back on my long-ass goodbye post, because I'm not about that life. In short, I'm thankful that I met and spent time with so many nice people here. I was planning on spending a lot of time on our gym, but life just got in the way. Luckily I designed a system that does not depend on me playing this game for the gym to exist, assuming this team is not dead. This thread and the gym thread should be taken over by a shared account anytime now, so my presence will no longer be needed. Feel free to send me a PM if you want to talk with me about anything.