For every pokemon you encounter on your adventure to become the world’s greatest trainer, you have about a 1 in 8000 chance of that pokemon being ‘shiny’, or a different color than normal.

Seeing a Shiny Pokemon is a 1 in 8192 odds or something along those lines, so seeing them in the anime is always a hype ...

During Pokemon Go's Deep Depths event later this month, players will have an increased chance of finding a rare and impressive Shiny Pokemon.