PokéBase - Pokémon Q&A
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I've never seen one, but you never know.

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Which one to choose??

Also, I believe a Meowth in Emerald was shiny
i answered 4 minutes earlier, just saying.

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Just like normal trainers can't have shinies, neither can Battle Masion trainers.
Shinyness is determined by IVs, and since the IVs for trainer Pokemon is programmed into the game, it idnt calculated randomly, unlike wild Pokemon.

Source - Bulbapedia didnt have any information about shiny Pokemon in the Battle Masion, and a Google search came up with nothing.
Also, the trainers in the Battle Maison are no different than normal trainers.

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edited by
1 vote

You can't

An opposing in-game trainer's Pokémon will never be shiny. This is because their Pokémon's data is always the same, it's not just chosen at random. And in X and Y none of the trainer's Pokémon are set as shiny Pokémon. So the chance is always impossible.
(Although some opposing trainer's Pokémon were shiny in Gen III.)

I hope I helped!

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edited by
Shiny Pokemon didn't exist in gen 1
Gen 2 had the 1st shiny