PokéBase - Pokémon Q&A
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I’m in New Mauville and wanted to do a silly challenge so I started soft resetting the Voltorbe in the pokeball at the entrance of New Mauville. Is it possible? I’m currently at 3257 resets and getting tired lol.

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Are these the Voltorb you were talking about? I assume you already know how shiny hunting works? Anyway, you have a chance of getting a shiny every 1/4,096 soft-resets, so a shiny should appear after 4,096 soft-resets, unless its Shiny Locked. I think you can get the Voltorb in the Pokéball as a shiny.

Note: Any Pokémon can be shiny, unless its Shiny Locked.

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A shiny Pokemon is never guaranteed to appear after 4000 soft resets (unless it's guaranteed to always be shiny). 1/4096 chance only means that, if you soft reset a lot of times, then the number of shinies would be close to 1/4096 to the number of times you soft reset.
sumwun is right. Based on my experience, I think a good way to clarify it is that that number is not saying every 4,096th Pokemon you encounter will be shiny -- that is just the rough chances of it happening for when you encounter it. In other words, that's the standard chance for you getting a shiny in an individual encounter, not in a grand total. 1/4,096 is the same as 0.0244140625% (so less than a 1% chance of a Pokemon being shiny when you encounter it).
@sumwun and FlappersFlappers, Oh, okay.