PokéBase - Pokémon Q&A
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considering glitches, I believe I heard it gets below 1/16000 in some situations in early gens but I don't recall where I heard that.

thx frog for making me curious
Frogadier

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In Generation 4, if none of the values forced by Cute Charm force a shiny, then the shiny odds with it equipped are 1/24576. This is because a shiny is only possible if Cute Charm fails.
I don't know if the odds get any lower than this beyond unintentional shiny locks, such as wild encounters in Gen I
hey, now I'M curious. +1

Also I love how I jokingly asked not to be called "froggy" on my "about me" one time, which I figure nobody ever reads, and all of a sudden nobody ever called me froggy again, and they did call me what I recommended: "frog" and "fraug". Frog IS still way better though.
All of the unown forms have different shiny odds in gen3 due to them being attached to personality value back then. This means that wich forms have wich odds changes per save file. The chance per form can either be higher or lower than normal but I can't find the exact odds
It might be possible to get a lower shiny chance by breeding in gen 2.
I just tried reading a few Bulbapedia articles, and it seems like the shiny chance for breeding in gen 2 is always either zero or 1/64.
Does this only count shinies obtainable by the player, or any shiny at all? If the latter, the answer is an opponent's shiny Pokemon in the Diamond and Pearl Battle Tower at 1/204,800.
Let’s say for both; I didn’t think of it prior to your comment. But I’d love to know for catchables, too

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The absolute lowest shiny chance across the franchise comes from Diamond and Pearl's Battle Tower. Due to a small coding error (the anti-shiny check is performed using "and" instead of "or"), opponents' Pokémon have a 1/204,800 chance of being shiny. This was fixed in the other Generation IV games, but it can still be seen if a Diamond or Pearl player hosts a Multi Battle.

The Accidental Shiny Pokémon of Gen 4's Battle Frontier (YouTube)

The rarest catchable shiny Pokémon come from Generation IV's Cute Charm glitch. If none of the 25 personality values forced by Cute Charm would result in a shiny Pokémon, the shiny odds are 1/24,576. I am underqualified to talk about the intricacies of this glitch; refer to Smogon's page for a comprehensive explanation.

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