PokéBase - Pokémon Q&A
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I play Pokémon emerald a lot and I have never encountered a shiny pokémon before so where and how do you get one???
The same for brilliant diamond.

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Wait emerald is a totally different game than brilliant diamond you should ask two different questions
The odds are 1/8192 in emerald and 1/4096 at base in BDSP. You have to get lucky unless you plan on hunting them
There are several ways to raise your shiny chance in BDSP, like Masuda method, Poke radar, Grand Underground, and outbreaks. In Emerald, the only way to get it higher than 1/8192 is by abusing the RNG, which you can read about here: https://www.smogon.com/ingame/rng/emerald_rng_intro

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There are several ways to raise the shiny chance in BDSP.

Masuda method

The Masuda method, also known as Masuda's method, is a fan-made term for the increased chance of Shiny Pokémon being produced when breeding Pokémon with different languages of origin.
While the standard encounter rate for a Shiny Pokémon (either in the wild or by breeding) is 1/8192 from Generation II to Generation V and 1/4096 in Generation VI onwards, the Masuda method multiplies this rate by 5 (to 5/8192 or about 1/1638) in Generation IV, by 6 (to 6/8192 or about 1/1365) in Generation V, and by 6 (to 6/4096, or 1/683) from Generation VI onwards.

Poke radar

all games feature a very rare and distinct type of shaking grass that glows white twice (hereafter referred to as a "Shiny patch"); such a grass patch will always contain a Shiny Pokémon.
As the chain length increases, the probability of finding a Shiny patch also increases, up to a certain maximum. After reaching this maximum, the player no longer needs to attempt to increase the chain, and can simply recharge and reset the Radar over and over until a Shiny patch appears.

Shiny charm (obtained from Valor Lakefront after completing the national Pokedex, raises the shiny chance when breeding)

Grand Underground

Diglett and Dugtrio will occasionally pop out and leave pink sparkles that give 1 and 3 points respectively, and accumulating 40 of these points causes "something good to happen". This results in a variety of special effects lasting for a period of 4 minutes, which begins and ends when a whistle is heard:
The odds to encounter a Shiny Pokémon in Hideaways is raised from 1/4096 to 1/2048.
All Stone Boxes found while digging will be Gorgeous Stone Boxes.
The progress gauge and bonus period is shared between all players connected to the same instance of the Grand Underground. If all connected players leave the Grand Underground, this gauge resets to zero.

source
Emerald wasn't intentionally designed to have any shiny hunting methods, so the only way to raise the shiny chance is by abusing the RNG.
source and more information on RNG abuse

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Correction, Mass Outbreaks in BDSP don't influence the shiny odds. A more appropriate/familiar term to describe them in BDSP is Swarms. The key difference is that there's a visual cue in the overworld whenever swarms are present in the grass of an area, but they function the same as in DPPt otherwise.
Do they affect shiny chances only in Legends Arceus?
Mass Outbreaks increase shiny chances in PLA and S/V as of currently.
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Every time you encounter a Pokémon there is a 1 in 8192 chance that it will be shiny. It is purely just luck based and you will just have to encounter loads of Pokémon hoping one will be shiny. As for brilliant diamond the odds of finding a shiny are one in 4096 so it is a lot easier
I don’t play either of these games so I don’t jnow a lot about the shiny methods but I know that
Source: I shiny hunt practically every day (in other games)

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