PokéBase - Pokémon Q&A
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Im playing Crystal on VC. I want to breed my shiny female pikachu for a male shiny Pichu, evolve him, and then breed him with Bill’s Eevee for a shiny Eevee. I’m a bit confused by the sources, since Eevee’s strange gender odds, and it’s just a weird mechanic. Would this idea work? If yes, what would my odds be?

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Not quite. Gen 2's breeding makes it so that Pokemon always inherit IVs from the opposite gender parent only. This means that your shiny Pikachu's IVs will only be inherited by female offspring, which for Eevee, cannot be shiny.

However! The IVs that the female Eevee offspring will inherit is still usable as a "shiny gene." So if you breed your shiny male Pikachu with a female Eevee, all female offspring from that pairing will be non-shiny, but with dormant "shiny gene" IVs. This can then be passed down to the next generation for the 1/64 chance of hatching a shiny Eevee.

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So I breed my shiny male pikachu’s daughter with him, and I’ll likely get a shiny Eevee?
You won’t be able to breed the male Pikachu’s daughter with him because Gen 2 has a check against breeding related Pokémon (based on IVs, which incidentally means no two Pokémon with the “shiny gene” can breed). Breeding the Pikachu’s daughter with any other compatible Pokémon will give you the 1/64 chance.
That's really interesting. I didn't know inbreeding wasn't allowed in Gen 2.