PokéBase - Pokémon Q&A
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For example, if I had a Keldeo from the event, is there a chance it could be shiny?

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It is impossible to get a Shiny Mystery Gift Pokémon, UNLESS it is meant to be Shiny like the Pikachu-colored Pichu. This is because in the game's coding, there is a Shiny check function which prevents Mystery Gift from being Shiny by regenerating a new PID until the Pokémon isn't Shiny.

Credit to DA

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To add too Darkgokus answer Event pokemon that can only be obtained by going to a certain shp cannot be shiny either.
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I doubt it, because event Pokemon always cannot be shiny, except when the determined value makes it shiny (Shiny Rayquaza Event)

But is there a chance it could be?