View source for 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 (English)|Pokémon Stadium]], [[Pokémon Stadium 2]], the [[Generation III]] and [[Generation IV]] core series games, and [[Pokémon Colosseum]] use a 32-bit {{wp|linear congruential generator}}.

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: <code>''result'' = 0x41C64E6D × ''seed'' + 0x0000303B</code>
** This equation is run several times depending on the N64's Count register, then {{wp|exclusive or|XOR}}'d with another pseudorandom value
*Pokémon Stadium 2<ref>[https://github.com/Lincoln-LM/stad2/blob/main/src/math.c stad2/src/math.c at main · Lincoln-LM/stad2]</ref>: <code>''result'' = 0x0019660D × ''seed'' + 0x3C6EF35F</code>
*Pokémon Colosseum: <code>''result'' = 0x000343FD × ''seed'' + 0x00269EC3</code>
*[[Game Boy Advance|GBA]] and [[Nintendo DS|DS]] games: <code>''result'' = 0x41C64E6D × ''seed'' + 0x00006073</code>
*[[Distribution device|Pokémon Machine v2]] distributions: <code>''result'' = 0x41C64E6D × ''seed'' + 0x00003039</code>

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 {{pkmn|Egg}} will be available at the [[Pokémon Day Care]]

In [[Generation V]] and [[Generation VI]], the games instead use a 64-bit LCRNG as follows:

<code>''result'' = 0x5D588B656C078965 × ''seed'' + 0x0000000000269EC3</code>

===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:

<code>''result'' = 0x6C078965 × seed + 0x00000001</code>

This algorithm is used for the following:
* Restrictions on Shininess for the {{vg|Pokémon Ranger}} {{p|Manaphy}} Egg, Type 1 [[Wonder Card]] Pokémon, and [[My Pokémon Ranch]]'s {{p|Mew}} and {{p|Phione}} (currently all released with variable [[Nature]]s)
* 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 {{wp|Mersenne Twister}} 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===
{{incomplete|section|Better descriptions of each generation process and how the different forms of RNG interact in a given sequence}}
Found in [[Generation VIII]], {{wp|Xoroshiro128+}} 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 [[Pseudorandom number generation#Cryptographically Secure (CSPRNG or CPRNG)|CSPRNG]].

The following is a non-comprehensive list of instances where this algorithm appears:
* RNG advancements in {{g|Sword and Shield}}
* [[Symbol encounter]]s, [[hidden encounter]]s, [[fishing]], and  [[personality value]] and [[stat]] generation of [[wanderer]]s in {{g|Sword and Shield}}<ref>[https://gist.github.com/Lusamine/e17168d92019672c1f9dcc1a246d9818 Overworld RNG in Gen 8 (SWSH)]</ref>
* [[Pokémon Den]] and [[Dynamax Adventure]] generation in {{g|Sword and Shield}}<ref>[https://github.com/Admiral-Fish/RNGWriteups/blob/master/Gen%208/Raid%20Generation.md Raid Den Generation]</ref>
* Partial {{pkmn|Egg}} generation in Generation VIII<ref>[https://github.com/Admiral-Fish/RNGWriteups/blob/master/Gen%208/Egg%20Generation.md Egg Generation in Gen VIII]</ref>
* The spawning algorithm in {{g|Let's Go, Pikachu! and Let's Go, Eevee!}}<ref>[https://gist.github.com/Lusamine/c9c6be1287daa3aff2c5010a01d662f7 LGPE Spawning Algorithm]</ref>
* AI move decisions in {{g|Brilliant Diamond and Shining Pearl}}

===Xorshift===
{{incomplete|section|Better descriptions of each generation process and how the different forms of RNG interact in a given sequence}}
Found in [[Generation VIII]], {{wp|Xorshift}} 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 [[Pseudorandom number generation#Cryptographically Secure (CSPRNG or CPRNG)|CSPRNG]].

The following is a non-comprehensive list of instances where this algorithm appears:
* [[Trainer ID]] and Secret ID generation in {{g|Brilliant Diamond and Shining Pearl}}
* Pokémon generation in {{g|Brilliant Diamond and Shining Pearl}}

===Cryptographically Secure (CSPRNG or CPRNG)===
{{incomplete|section|Better descriptions of each generation process and how the different forms of RNG interact in a given sequence}}
Found in [[Generation VIII]], {{wp|Cryptographically secure pseudorandom number generator|Cryptographically secure RNG}} 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 [[Pseudorandom number generation#Xorshift|Xorshift]] or [[Pseudorandom number generation#Xoroshiro|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 {{g|Let's Go, Pikachu! and Let's Go, Eevee!}} and [[Generation VIII]]
* [[Trainer ID]] and Secret ID generation in {{g|Let's Go, Pikachu! and Let's Go, Eevee!}}, {{g|Sword and Shield}}, and {{g|Legends: Arceus}}
* [[Personality value]] generation in {{g|Let's Go, Pikachu! and Let's Go, Eevee!}}
* Non-overworld [[Legendaries]], [[Curry]], and scripted encounters in {{g|Sword and Shield}}
* {{pkmn|Egg}} seeding and individual rolls in Generation VIII<ref>[https://github.com/Admiral-Fish/RNGWriteups/blob/master/Gen%208/Egg%20Generation.md Egg Generation in Gen VIII]</ref>

==RNG abuse==
'''RNG abuse''', also referred to as '''RNG manipulation,''' is a procedure that manipulates the pseudorandom number generators in the main series games to obtain a desired Pokémon. 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 {{m|Hidden Power}} output (regarding [[Type]] and/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. {{game|Emerald}}'s initial seed is always 0. The [[Generation IV]] games use the [[Nintendo DS]]'s [[Days of the week|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 {{pkmn|Egg}} or a {{pkmn2|gift}}. 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|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 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 [[Appendix:Fan terminology#Legal|Legal]] values. In addition, Pokémon obtained through RNG abuse have been permitted at the {{DL|Play! Pokémon|Video Game Championships}}, 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.<ref>[https://gamefaqs.gamespot.com/boards/661226-pokemon-black-version-2/65249276 "Nintendo staff confirms RNG being allowed at VGC tournaments"]</ref> 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 [[Appendix:Fan terminology#Illegal|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==
* [[wp:Pseudorandom number generator|Pseudorandom number generator on Wikipedia]]
* [[wp:Mersenne twister|Mersenne Twister on Wikipedia]]
* [http://www.smogon.com/ingame/rng/emerald_rng_intro Smogon's explanation and guide on Pokémon Emerald RNG Abuse]
* [http://smogon.com/ingame/rng/dpphgss_rng_intro Smogon's explanation and guide on Generation IV RNG Abuse]
* [http://smogon.com/ingame/rng/bw_rng_intro Smogon's explanation and guide on Generation V RNG Abuse]

==References==
{{reflist}}

{{Project Games notice|game mechanic}}

[[Category:Game mechanics]]

[[de:Random Number Generator]]
[[es:Generación pseudoaleatoria de números]]
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[[it:Generazione di numeri pseudo-casuali in Pokémon]]
[[ja:乱数ポケモン]]
[[zh:伪随机数发生器]]