It’s been a while since I hunted a Shiny Pokémon so I decided to dive in head first with a Charmander starter in FireRed on the Gameboy Advance.
Per encounter, the odds of having a Shiny Pokémon appear are 1/8192, or 0.01220703125%, so I expected this to take a few hours a night over the course of a couple of weeks.
The only other Shiny hunt I have done which had the same odds was for Rayquaza in Pokémon Emerald – the Shiny appeared on Encounter 812 and was my first ever shiny Pokémon and also came to hold a personal record of encounters to odds ratio hitting less than 10% towards the total odds. I do remember a green Tangela when I first started playing the games and was unaware you could find the differently sprited rarities, so am fairly certain I did encounter one before, but Rayquaza was the first of many hunts to come.
Shiny #28, Charmander in Pokémon Fire Red after only 244 soft resets, less than 3% towards the total odds:
And yes, that is a bottle of vodka on the shelf below.