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Since the formula determining whether a Pokemon was shiny was changed, could this happen?

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No. A Pokemon that wasn't shiny will stay normal and a shiny Pokemon will stay shiny when transferred.

The base formula wasn't changed. The resulting number in the formula had to originally be 8 or less to become shiny. As of X and Y, the resulting number could be 16 or less resulting in a shiny. But that's for encounters on the games file, not from transferring.

If that were the case,all Pokemon you could transfer through generations could have a chance to turn shiny, which they don't. Ever. Unless you hack, of course.

EDIT: the only possible way this could happen that I can think of, is if your ID, SID, and OT were exactly the same in both games, and the formula calculated on the Pokemon had a result between 9 and 16. However,I'm not sure if the resulting number stays in the Pokemon's data or not. And I'm not sure if the blue pentagon on 6th gen Pokemon (or lack thereof in transferred Pokemon) effects anything in the formula results.

Hope I helped!

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I think he meant because the chance was reduced.
I'm aware. But that doesn't change a transferred Pokemon's chance of becoming shiny. The Pokemon wasn't found on your file of 6th gen, so the odds wouldn't matter.