>>18866123Sort of this. The RNG in Gen 1 and 2 games is based off the console's processor clock.
To address the main point, let's first assume that the chance of encountering a shiny is 1/8192 and that each attempt is truly random (which it isn't, but let's assume it is).
The chance of NOT encountering a shiny then becomes 1 - (1/8192), 8191/8192. After n amount of attempts, the chance of not having encountered a shiny becomes (8191/8192)^n.
It then follows that the chance of having encountered a shiny is 1 - f(n), where f(n) is this previous function.
Attached is a graph of the function I'm talking about, namely, 1 - (8191/8192)^n.