Are the odds of encountering a shiny different for each Pokemon?

Are there different odds for different pokemon?

For example, say there was a 1/4000 chance of getting a shiny Bagon. Does that mean for every other pokemon in the game, is it a 1/4000 chance?

Solution 1:

Since randomness is only pseudo-random in video games and encounter slots (that is, which Pokemon you encounter) are generated in sequence with the PID (which determines shininess), it's technically possible for some shinies to be more or less common in the wild. This variance is comparatively low, though, and entirely unnoticeable when you're not using RNG manipulation/prediction.

On average, the base chance to encounter a shiny is 1/4096, regardless of Species. There are various methods to increase this chance, like the Shiny Charm, but they also don't depend on the Species.