It depends on the pokemon.
The chances of finding it in the wild are 1/8192 (.001220703125%)
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1/8192 is the appearance rate for any shiny pokemon. The odds are no different with legendary pokemon.
Yes, however the odds that the Pokemon you pick is shiny are 1 in 8912 and there is no way to reduce that without cheating.
It depends on luck. when catching a magikarp, you have a 1/8000 chance of shiny.
Every time you battle or hatch a Pokemon you have a 1 in 8192 chance of finding a shiny Pokemon. While this is an extremely rare occasion there are ways of increasing your chances of finding a shiny Pokemon.Pokemon whose parents are from games of different languages are approximately 4 times more likely to be shiny (odds of 1 in 2048)Chaining with the PokeRadar increases your chances of finding shiny Pokemon with each successive Pokemon chained. Odds on a maximized chain of 40 are 1 in 205.
You can obtain a Shiny Stone by winning first place in Bug-Catching Contest. However, being first place in Bug-Catching Contest could land you with any stone.