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I was wondering if you were guaranteed a shiny after meeting 4096 of a certain species in the wild. There was a similar question but that was for soft resetting and (just to clarify) I'm asking if encountering 4096 wild Pokemon would give you a shiny. Also this is for Generation 8.

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Absolutely not. The odds are completely random; the game does not promise you a shiny after a certain amount of encounters. You could do a billion of the same Pokémon and never find a shiny, just as you could find a shiny your first encounter.

Think of it this way, you have a dice that has ~4000 sides, and one is painted pink, the others are all white. If you can land on the pink one, that’s the shiny. It’s still very unlikely after 4000+ roles.

Source: I shiny hunt

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dang sniped I was gonna answer
Ok, thank you for the clarification!
TY's answer is as good as always, but I just want to add something.  Each encounter is an independent event, or an event's outcome that has no impact of the odds of future events outcomes.  So, each encounter has a 1/4096 of being a shiny because each encounter is an independent event.  This is like a dice roll as TY described.

What you are thinking of is called an in Dependent event.  This is where the outcome of an event HAS an impact on future events.  Think of it this way, I have 8 beans in a jar, 4 blue and 4 red.  The odds of pulling out a blue one is 1/2.  Let's say I pull a blue one out of the jar and set it aside.  Now there are 3 blue and 4 red.  Now, there is a 3/7 chance to pull a blue bean.
Hopefully this clarifies this for you.
Thanks for building on the answer. I really appreciate it!