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I’m trying to breed a shiny Eevee and I just want to confirm the odds. I have two Eevees in the daycare, one Male and shiny with a different OT, and female with my OT with the shiny gene. I believe the odds are 1/64 but I just want to make sure I’m doing this right before I mass hatch eggs.

Sorry for the title. Character lengths are blocking me

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In Crystal, since there's a seven-bit mask on the IV bytes that is guaranteed to pass down verbatim, the game attempts to do something it hasn't been able to do in any later games: it has an "incest clause" that detects Pokemon that could potentially be related, even if they aren't really and just lucked into the 1/128 chance of a matching value on the bitmask that places them into the same "family".

If you leave both of those Eevees at the day care, the game will say they're "brimming with energy" and they will refuse to make any eggs, no matter how long you leave them there. The usual 1/64 odds thus go out the window; you have zero chance to get a shiny with that particular pairing.

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I DID FORGET TO UPDATE THAT yeah the female Eevee did not, in fact, have the shiny gene, and when I found one that did, I got the brimming message. I since changed it to a Female with the proper stats and a male non-shiny; does this work as intended?
IVs in Gen 2 will always be inherited by opposite-gender offspring; so the shiny male's stats will only be inherited by female Eevees, which can't be shiny. You need a shiny gene female breeding with a non-shiny gene male for it to work.