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.