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Shininess is determined by a calculation involving the Original Trainer's ID number and secret I Dnumber, as well as the Pokémon's personality value.

>Technically, the formula used is (TrainerID xor SecretID) xor (PersonalityValue>>16 xor (PersonalityValue mod 65536)); the latter two values represent the first 16 and last 16 bits of the 32-bit personality value, respectively. More detailed information can be found at the personality value article.

The above formula can result in a number from 0 to 65535. If the result is less than 8, then the Pokémon is Shiny. This gives an overall probability of 8/65536 or 1/8192, exactly the same as in Generation II.

This can be found here and is it possible to calculate when a shiny Pokemon is going to appear? If so, what are the calculations I need to do?

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The formula that you provided is what the game uses to determine when a Pokemon you encounter will be shiny.

You are not able to use this formula to increase your chance of encountering a shiny Pokemon because you are not able to view your own secret ID and you cannot determine the personality value of a Pokemon. The personality value of a Pokemon is determined when you encounter it in the wild or when you receive it as an egg, thus shininess is also determined the moment you encounter it in the wild or receive it as an egg.

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