PokéBase - Pokémon Q&A
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Because The chances to find a shiny Pokemon have been doubled for friend safari, horde battles, and breeding. The Shiny Encounter rate must be lower then all the other shiny encounter rates like breeding for a shiny is 1-8,192.

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Double for horde battles? Really? I thought it was 5 times as much. Since, y'know, there's 5 pokemon.
Then maybe's it's ten times as much...  Doubled chances times five Pokémon :)