Meta Rate My Team PokéBase - Pokémon Q&A
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That is really unfair, because in Pokemon Black is there a chance of 1/8192.
Or not?

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Yes its true!

Now you'd think with a Pokémon this rare, it has to have good Individual Values and such. That's no longer the case. Shiny Pokémon are always going to end up with the same odds of good stats as normal Pokémon. They used to have set IV's in the Metal generation where it had 0 HP IVs, random Attack IVs and IVs of 10 in Defense, Speed, Special Attack and Special Defense, but since then and until XY, it has been based upon the hidden PID of the Pokémon. As of Pokémon X & Y, it is a 1 in 4,096 chance of finding a shiny Pokémon.

Gen VI - This generation slightly changed how Shiny Pokémon are determined. While the basic formula is still identical to Generation III and all games since then, the value the formula returns now only has to be less than 16 to result in a Shiny, rather than less than 8. This results in a probability of 16/65536 or 1/4096, double the previous probability.

Gen II-V the chances of finding a shiny were of 8/65536 or 1/8192.
Gen VI the chances increases to 16/65536 or 1/4096.

With Shiny Charm use:

Gen V - 1/2.730,6 chance. Masuda Method - Increased it from 1/1,365.3 down to 1/1024.
Gen VI - Increases 1/4096 to 1/1365,3. Masuda Method - Increased it from 1/1365,3 to ~1/400.

In Serebii it says ''It is not known if it affects breeding'', but I think it does works.

Source and Source
Hope this helps.

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Note: Shinies did not exist in Gen 1.
Ok, thanks!
Add the proballity with shiny charm
Ok [Editing].