PokéBase - Pokémon Q&A
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Im curious at the chances of finding any shiny Pokemon in black 2 and white 2. Also how would one go about catching one do you have to beat the elite four in order to hunt for shiny Pokemon ?

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The shiny chance is usually 1/8192, but I don't know all the ways to change it.

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You can find a shiny Pokémon at any point in the game, although the chances are 1/8192 per Pokémon. To find one, you just have to encounter Pokémon over and over again until you find a shiny. This can take a very long time and requires a lot of patience, but you can do it at any point in the game. Additionally, it’s recommended that you hunt in dark grass if you can, since they have a chance of giving you a double battle, which allows you to see more Pokémon in a smaller span of time.
In BW2, the only ways to change your shiny odds are the Masuda Method and the Shiny Charm. The Masuda Method is a breeding method that increases the chance of a shiny Pokémon hatching from an egg if the parents are of two different languages (1/1365 chance). The Shiny Charm can be received from Prof Juniper after completing the National Dex (excluding mythicals) and increases the shiny chance of every Pokémon encountered to 1/2731. The two methods can stack together for a combined chance of 1/1024 chance of finding a shiny.
However, keep in mind that Zekrom and Reshiram are shiny locked, meaning they are programmed to never be shiny. Additionally, there is a hidden guaranteed shiny in BW2 if you beat the game on hard mode; either Dratini or Gible depending on your version. You can also get a guaranteed shiny Haxorus in the Nature Reserve, which can be accessed by seeing all the Pokémon in the Unova Dex.

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Isn't there also a guaranteed shiny Haxorus?
Oh yeah, I’ll edit that in.