PokéBase - Pokémon Q&A
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i am going to get Pokemon y soon and I neeeeeeeeeed to know!

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Same as the usual Gen VI shiny rate - 1 in 4096.

However, since five Pokemon appear at the same time in a horde, it can be increased to 5/4096. Which can be quite helpful!

Though you can always use chaining methods to get the chances to 1/200, if you want to get a shiny. :)

Hope I helped. :)
Source: Experience

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1/819 cancelled down :P
^Maths and stuff
Got my first shiny pokemon ever in pokemon y (vanillite) in frost cavern while using sweet scent! :D
I never have gotten a shiny in gen vi yet. :S
It's okay, !*•~Indigo~•*!, neither have I...
I was just running through grass without a repel and I was almost out when a horde battle started. Great I thought, but as I looked closely I saw a hint of purple within the black masses of murkrow.  A solitary shiny murkrow within a horde. True story.
I got a shiny poliwhirl in a trade with one of my spiritomb.

But it wasn't actually that exciting. Its much better if you get one yourself. I'm yet to do that.