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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 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: result = 0x41C64E6D × seed + 0x0000303B
    • This equation is run several times depending on the N64's Count register, then XOR'd with another pseudorandom value
  • Pokémon Stadium 2[1]: 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:

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:

Mersenne Twister (MTRNG)

Found in Generation IV and later, the 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

050Diglett.png This section is incomplete.
Please feel free to edit this section to add missing information and complete it.
Reason: Better descriptions of each generation process and how the different forms of RNG interact in a given sequence

Found in Generation VIII, 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 CSPRNG.

The following is a non-comprehensive list of instances where this algorithm appears:

Xorshift

050Diglett.png This section is incomplete.
Please feel free to edit this section to add missing information and complete it.
Reason: Better descriptions of each generation process and how the different forms of RNG interact in a given sequence

Found in Generation VIII, 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 CSPRNG.

The following is a non-comprehensive list of instances where this algorithm appears:

Cryptographically Secure (CSPRNG or CPRNG)

050Diglett.png This section is incomplete.
Please feel free to edit this section to add missing information and complete it.
Reason: Better descriptions of each generation process and how the different forms of RNG interact in a given sequence

Found in Generation VIII, 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 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:

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 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 Hidden Power 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. Pokémon Emerald'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 Egg or a 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 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 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.[7] 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

References

  1. ↑ stad2/src/math.c at main · Lincoln-LM/stad2
  2. ↑ Overworld RNG in Gen 8 (SWSH)
  3. ↑ Raid Den Generation
  4. ↑ Egg Generation in Gen VIII
  5. ↑ LGPE Spawning Algorithm
  6. ↑ Egg Generation in Gen VIII
  7. ↑ "Nintendo staff confirms RNG being allowed at VGC tournaments"
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