Random number generators in games

[Chamale]

I know from experience (from making tool-assisted speedruns of Pokemon games) that the random number generators in Pokemon games are affected by user input. Obviously, there is some sort of formula that generates the random numbers. So... What is the formula, and how are the generated numbers applied? If there are any good hackers who know, please post here. If anyone here could find out, please do. Most of the pokemon speedruns are as optimized as they can get without knowledge of the RNG - but if we know how the RNG works, we can make much quicker runs.