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I’m doing that battle method with Rookidee for a shiny and I am close to 500 battles, and I am wondering what the chances are after 500 with the shiny charm

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Once you reach a total of 500 battles for a Pokémon, the odds (with the shiny charm) are 1/512, just like the Masuda Method.

However, (and this is a big one lol), the method only works 3% of the time. This was likely a glitch that Game Freak is not fixing, but it is not confirmed.

So, overall, Rookidee has a shiny chance of 1/512 3% of the time, and a 97% percent chance of having the regular shiny charm odds, being 1/1365

I Hope I Helped! (Good Luck on the hunt)

Source: Prior Knowledge & This

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Grr darned gamefreak. Well, thanks
It's weird that the 3% chance has been known almost since Day 1, but GameFreak hasn't done anything about it.  Well anyway, I'm glad to help :)
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With Shiny Charm: 1 in 455.1111

Without Shiny Charm: 1 in 585.1249

Source

Hope I helped!

Bear in mind these chances only have a small chance of taking effect, they are not guaranteed. You're much better off with the Masuda Method.

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Oh, yeah some sources said 1/455 while others said 1/512.  I went back and forth a few times, but chose 1/512 because I got those odds from Bulbapedia and Serebii specifically.
Yeah, bulbapedia is likely more reliable than my source.
Thanks to you as well, I think I will keep going with this cuz I have made it this far and I can’t stand eggs
Ok, good luck with your hunt!