Pseudorandom number generation in Pokémon

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.

Linear Congruential random number generator (LCRNG)
Pokémon Stadium and games in Generation III and Generation IV use a 32-bit LCRNG.

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:
 * This equation is run several times depending on the N64's Count register, then 'd with another pseudorandom value
 * Pokémon Colosseum:
 * GBA and DS games:

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 encountered 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

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

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:

This algorithm is used for the following:
 * Restrictions on Shininess for the Pokémon Ranger Egg and Type 1 Wonder Card Pokémon (currently all released with variable Natures)
 * Determining the species of a Pokémon swarm
 * Determining the Pokémon in the Great Marsh
 * Determining the Pokémon in the Trophy Garden

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

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 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. '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 Pokémon fandom, RNG abuse is slightly controversial. Proponents note that RNG abuse does not require a third-party device and that the Pokémon obtained through RNG abuse can be obtained through normal gameplay. In addition, Pokémon obtained through RNG abuse have been used at the, an official tournament. They also say that RNG abuse is very complicated, and not as simple as typing a cheat code. However, some players believe that RNG abuse is cheating, as the action of picking a Pokémon's characteristics is similar to using a cheating 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.