Pseudorandom number generation

A pseudorandom number generator is an electronic device or software's attempt at creating a random number. Just as rolling a die is not 'random' (being determined by factors such as force and angle of the throw, as well as friction), computers cannot be truly 'random'. In order to generate 'random' events in games and other forms of software, they must get as close to looking it as they can. There are limitless ways of accomplishing this. The degree of apparent randomness depends on the ability to predict the next result of the algorithm.
==Mechanics==
First, the generator must have a seed, a number to start with. This number is usually a date and time referring to the first time that the algorithm is called during the usage of the device or the software's active session. Seeds are also occasionally derived from user input, as it is highly improbable to do the exact same thing more than once, making it appear 'random'.
This number is put through a complex algorithm, and the result is formatted according to the needed context. The raw result then becomes the seed for any subsequent uses of the random generator. Therefore, the nature of the generator is a recursive algorithm.
==Algorithms==
===Linear Congruential random number generator (LCRNG)===
Pokémon Stadium, Pokémon Stadium 2, the Generation III and Generation IV core series games, and Pokémon Colosseum use a 32-bit .
Below, seed is a number between 0 and 0xFFFFFFFF. If the generator has been called previously, seed is the result value from the previous call to the generator.
*Pokémon Stadium: result = 0x41C64E6D × seed + 0x0000303B
** This equation is run several times depending on the N64's Count register, then 'd with another pseudorandom value
*Pokémon Stadium 2stad2/src/math.c at main · Lincoln-LM/stad2: result = 0x0019660D × seed + 0x3C6EF35F
*Pokémon Colosseum: result = 0x000343FD × seed + 0x00269EC3
*GBA and DS games: result = 0x41C64E6D × seed + 0x00006073
*Pokémon Machine v2 distributions: result = 0x41C64E6D × seed + 0x00003039
In Generation III and Generation IV, this algorithm is used for the following:
* Encrypting Pokémon data in the save file
* Generating the personality value of a wild Pokémon
* Generating the individual values of a wild encountered Pokémon in Generation III and Generation IV
* Determining the species of a wild Pokémon
* Determining the Pokémon Lottery Corner lucky number
* Determining if an will be available at the Pokémon Day Care
In Generation V and Generation VI, the games instead use a 64-bit LCRNG as follows:
result = 0x5D588B656C078965 × seed + 0x0000000000269EC3
===Alternative pseudorandom number generator (ARNG)===
The Generation IV games also use a different algorithm to alternate, reroll, or modify a previously randomly generated value. The algorithm works in the same nature; however, the equation changes to:
result = 0x6C078965 × seed + 0x00000001
This algorithm is used for the following:
* Restrictions on Shininess for the Egg, Type 1 Wonder Card Pokémon, and My Pokémon Ranch's and (currently all released with variable Natures)
* Determining the species of a mass outbreak
* Determining the Pokémon in the Great Marsh
* Determining the Pokémon in the Trophy Garden
===Mersenne Twister (MTRNG)===
Found in Generation IV and later, the is another type of random number generator that produces 624 random numbers at once. These random numbers are then stored and used when needed. When all 624 numbers are used, another set is generated.
This algorithm is used for the following:
* TID and SID in Generation IV
* Egg PIDs in Generation IV
* Friendship change calculations
* Sprite animations in Generation V
* Individual values in Generation V
* AI move decisions in Generation V
===Xoroshiro===
Found in Generation VIII, is another type of random number generator used, however this is not the sole form of RNG used, as it is used in tandem with CSPRNG.
The following is a non-comprehensive list of instances where this algorithm appears:
* RNG advancements in 
* Symbol encounters, hidden encounters, fishing, and personality value and stat generation of wanderers in Overworld RNG in Gen 8 (SWSH)
* Pokémon Den and Dynamax Adventure generation in Raid Den Generation
* Partial generation in Generation VIIIEgg Generation in Gen VIII
* The spawning algorithm in LGPE Spawning Algorithm
* AI move decisions in 
===Xorshift===
Found in Generation VIII, is another type of random number generator used, however this is not the sole form of RNG used, as it is used in tandem with CSPRNG.
The following is a non-comprehensive list of instances where this algorithm appears:
* Trainer ID and Secret ID generation in 
* Pokémon generation in 
===Cryptographically Secure (CSPRNG or CPRNG)===
Found in Generation VIII, is another type of random number generator used, however this is not the sole form of RNG used, as it is used in tandem with Xorshift or Xoroshiro.
Notably, this type of random number generator is not possible to RNG abuse due to its nature.
The following is a non-comprehensive list of instances where this algorithm appears:
* Initial seeding in and Generation VIII
* Trainer ID and Secret ID generation in , , and 
* Personality value generation in 
* Non-overworld Legendaries, Curry, and scripted encounters in 
* seeding and individual rolls in Generation VIIIEgg Generation in Gen VIII
==RNG abuse==
RNG abuse, also referred to as RNG manipulation, is a procedure that manipulates the pseudorandom number generators in the core series games to obtain a desired . It is commonly used to obtain Shiny Pokémon, Pokémon with high individual values, Pokémon with a specific set of individual values that yield a particular output (regarding Type or move Power), or Pokémon with certain Natures.
In games where the initial seed (on startup) is predictable, the subsequent "random" numbers are predictable as well. 's initial seed is always 0. The Generation IV games use the Nintendo DS's date, time, and delay between starting the game and pressing "Continue" to generate the initial seed. Generation V games use the Nintendo DS's date, time, keys currently pressed, and other entropy data to create a seed moments before the Nintendo logo appears.
The random number generator is used to determine a Pokémon's personality value and individual values when it is encountered or received as an or a . By searching for initial seeds that satisfy the characteristics required, the player can then hit the target seed and advance 'frames' to receive their target characteristics. There are several methods used to influence a Pokémon's characteristics — for instance, a bred Pokémon and a stationary wild Pokémon's characteristics are generated through different methods.
In Generation III and Generation IV, there are some limitations. As a player's Trainer ID and Secret ID numbers determine a Pokémon's shininess, Shiny Pokémon generated through certain methods can only have certain individual values. Due to Wonder Card gifts using a timer register to create personality values, it is not possible to manipulate a gift's Nature. In Generation V, this is no longer the case as the individual values and personality values are determined from two different RNGs.
===In the fandom===
In the Pokémon fandom, RNG abuse is slightly controversial. RNG abuse largely does not require third-party devices or custom firmware, and the Pokémon obtained through RNG abuse can be obtained through normal gameplay, with only Legal values. In addition, Pokémon obtained through RNG abuse have been permitted at the , as the rules do not explicitly disallow Pokémon obtained in this manner, with some participants reporting that event staff permitted their use even with admission of having performed RNG abuse."Nintendo staff confirms RNG being allowed at VGC tournaments" RNG abuse also requires a degree of preparation, effort, and skill, as the player is required to learn and use various tools and programs to calculate how to obtain a Pokémon with specific attributes, whereas using a cheat device or editing software can grant a Pokémon with specific attributes nearly instantly, and unlike RNG abuse, would permit Illegal values.
However, some players believe that RNG abuse is cheating, as the action of picking a Pokémon's characteristics directly is similar to using a cheat device. Opponents of RNG abuse claim that it gives those who can RNG an unfair advantage, however the proponents say that with RNG everyone can have the best stats, and therefore no one will have an unfair advantage by catching a Pokémon that happens to be better.
==External links==
* Pseudorandom number generator on Wikipedia
* Mersenne Twister on Wikipedia
* Smogon's explanation and guide on Pokémon Emerald RNG Abuse
* Smogon's explanation and guide on Generation IV RNG Abuse
* Smogon's explanation and guide on Generation V RNG Abuse
==References==
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