PokéBase - Pokémon Q&A
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I am breeding a female shiny raichu with a male rattata in Pokemon crystal. I have a 1/128 chance of getting a shiny, right?

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With a little bit of exploiting, you can get a shiny ditto, boosting your odds to 1/64 for all pokemon.
I’ll consider that........
How do I do it?

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If your offspring and shiny parent are opposite genders (ie. you get male Pichus), then the shiny chance is 1/64. Otherwise it's 1/8192.
Pichus are 1/2 male, so the chance of a Pichu being shiny = chance of Pichu being male * chance of male being shiny + chance of Pichu being female * chance of female being shiny
= (1/2) * (1/64) + (1/2) * (1/8192)
= (1/128) + (1/16384)
= 129/16384
This is a tiny bit more than 1/128.

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Ok. Thanks!
You're welcome I guess.
Assuming the Raichu and Rattata can make eggs at all, the Rattata's inheritable signature must be different than Raichu's, and the odds of a female Pichu getting the right combination of stats to be shiny in that case aren't 1/8192--they're exactly 0.
How do you know this? How exactly do "inheritable signatures" work in gen 2?
The inheritable signature consists of the seven IV bits that, in GSC, are always faithfully passed down from one parent or the other. All seven of those bits are included among the 13 bits that the game checks to have specific values for the shiny mask, so if the egg inherits anything other than an exact 7-out-of-7 match with that mask, there are no values that the remaining 6 bits could possibly have to make up for it.

GSC, unlike any future games, included an attempt at an "anti-incest clause" in breeding, which it can at least attempt to track by the nature of this inheritance system. If both prospective parents have the same value in all 7 of those bits, it will say the Pokemon are "brimming with energy," and refuse to allow any eggs to be created.
Is this true every time a shiny Pokemon and a regular color Pokemon breed? If yes, why does Bulbapedia say there's a 1/64 shiny chance if the offspring is the opposite gender of the shiny parent?