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FAQ:
>What are shiny pokemon?
Glad you asked! They're extremely rare variations of pokemon with different color pallets. There's about a 1/8000 chance of encountering them in the wild randomly without any RNG manipulation or methods that increase your chance of encountering one, so it isn't uncommon for some players to have never seen one before despite having played one or more games.
>1/8000 is too high! How do I get one easily?
The most common methods are the Masuda Method, Shiny Fishing, and PokeRadar Chaining, however there seems to be a higher chance of finding shinies in the Friend Safari as well. The three aforementioned methods are covered in the guides section in OP.
>What's the Masuda Method?
Named after Junichi Masuda, one of Diamond/Pearl's developers, programmed a little something special into the games that increases the shiny rate when breeding under certain conditions. Simply, a pokemon traded from a foreign country should be breeded with a pokemon from your cartridge. This increases the rate of an egg containing a shiny by 4x in DPPt (1/2048), and 5x in later games (1/1638). See the guide in OP for more details.
>What's a shiny charm?
A key item in Gen V that increases your chances of finding a shiny. 1/2730 in the wild, and 1/1024 when using the Masuda Method. It cannot be traded through games.
>Is the shiny rate higher in the Friend Safari?
The majority of /vp/ thinks that this is true, but there hasn't been a datamine of the X/Y ROMs so nobody can say for sure. The rate appears to be on par with the Masuda Method's probability of 1/1638. It should be noted that you aren't allowed to use the Pokeradar in the friend safari, so chaining isn't an option there.