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I was looking at one of my hacked Mews, which was Shiny with the Timid nature and perfect IVs, and I got thinking. Since you can transfer Mew from Gen 1 if you glitch one into the game and have a certain OT and ID, and it can be Shiny, I started to wonder if it was possible to get that combo of Shininess, nature, and IVs by the Mew glitch (which I consider legitimate). So let's say I got the OT and ID number that allowed me to transfer a Mew over and encountered that level 1 Mew. Would it be possible for it to be Shiny and Timid-natured with perfect IVs when I caught it and transferred it over to a newer game? And if so, what are the odds of it occurring?

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I believe that the only way to get a Shiny Mew that is legal is in Emerald with the event Old Sea Map.
Jhnfui, you can get one via Mew glitch in Gen 1. I consider it legitimate, and it can be Shiny... although I dunno if that counts as 'legal'.
Yeah, I remembered that glitch, but it is up to you if you feel it as "legal".  And the Old Sea Map event ended a while back, so....
A Pokémon with gen 2 shiny ivs can’t be perfect, but it can be transferred to gen 7-8 (with quite a bit of hassle) and be hyper trained. If you transferred it to gen 3+, it could theoretically become shiny with perfect natural IVs. Natures are random. So, yeah, I think that could be possible. Highly unlikely tho

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Yes, yes you can! You just gotta get ABSOLUTELY EXTREMELY AMAZINGLY SUPER INCONCEIVABLY lucky.

To show you what I mean (thank you sumwun), there are 25 natures, and a 1 in 25 chance to get a Timid one.

1/25

Then, there’s a 1 in 8192 chance for it to be shiny, which is why I don’t shiny hunt.

1/25 x 1/8192 = 1/204800

Then there’s a 1 in 31 chance (I’m assuming) that you get a perfect IV. And you want 6 of them.

1/204800 x 1/887503681 = a grand total of 1 in 1.8176075e+14.
Are you SURE this is worth it?

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The question asks for the exact chances. "ABSOLUTELY EXTREMELY AMAZINGLY SUPER INCONCEIVABLY lucky" does not answer that.
Oh ok I’ll edit
The shiny chance is 1/4096 in gen 6.
Thank you! :3
Yes, but this is in Gen I