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With or without the Masuda Method, what would the chances be if it did effect breeding?

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As of Pokémon X & Y, it only works on Wild Pokémon and increases the rate from 1 in 4096 to 1 in 1365.3.

No, it does not effect the likelyhood of getting a Shiny Pokemon via Masuda Method.
In fact, it makes the wild shiny encounter rate increase to the same chance as using the Masuda Method.

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