When does the game determine whether the Pokemon will be Shiny or not?

Question

Right when the Pokemon is encountered? Is it the same for roaming Legendaries?

Comments

Notice how the question says 'when'.

Answer 1

A Pokemon's chance of being Shiny is determined as part of it's personality values, which means this gives your answer:

>A Pokémon's personality value is an unsigned 32-bit integer that is created when the Pokémon is first encountered; it is set as soon as the Pokémon appears in the wild, the Pokémon's Egg is received from the Day Care man or another NPC, or the Pokémon itself is received from an NPC.

http://bulbapedia.bulbagarden.net/wiki/Personality_value
So yeah, as soon as the Pokemon is encountered.
This is no different for roaming legendaries.

Comments

Ok, the clear explanation I was looking for. Thanks Fizz :D

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No worries. :)

Answer 2

From my experience, it is random.

Here is the link, please read the box at the top. It will probably answer this question better than I can.
http://pokemondb.net/pokedex/shiny

Answer 3

Whether a Pokémon is Shiny or not depends on the values of the Trainer ID number, secret ID number, and personality value.
-Bulbapedia

They are determined by their personality value, which are binary, making it 1/2^13
Personality value also determines Pokemons nature, burmys evolution, spindas dots, unowns letter, ability, and gender

Source with more info: http://bulbapedia.bulbagarden.net/wiki/Personality_value