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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 :)