PokéBase - Pokémon Q&A
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Before I embark on a hunt to catch a legendary pokemon with the nature and IVs i want, I was wondering the best way to go a bout it. Are the nature and IVs set in stone before you even meet the pokemon like whenever you make a new game, or are they completely randomly generated every time you start an encounter? I'm thinking pokemon like Suicune you have to interact with in HG SS may change every time you start the encounter. If this is true is the best way to just save, use a master ball, check it, then rinse and repeat until i get a good one? How does it all work? And what about Latias and Latios? What I am mainly wondering about is stationary ones like heatran and regigigas.

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The first time you ecounter a roaming pokemon, its nature, IVs and Hidden Power are set. If you save after the first ecounter, these stats will stay the same as the first time you found it.

In other words No matter how many times you ecounter a roaming pokemon, its nature, IVs, and Hidden Pwer type are set and they cannot be changed unless you turn off without saving, and find the pokemon again.

Also, If the first ecounter was shiny, Its future ecounters will also be shiny (remeber, this is VERY rare; roughly 1 in 8,192% chane)

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Hahaha, Shiny chance is 1/8192.
The percent chance is 0.000122070312%.