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It always feels like if I run away from a couple of battles in a row with wild Pokemon, then I end up having to battle wild Pokemon every few steps, whereas if I just battle them and get it over with, I might not battle another for quite a while.
Is there actually a relationship between running and more Pokemon appearing? Or is this just an example of confirmation bias on my part?
Bulbapedia has a page about tall grass that has a formula for the pokemon encounter rate. According to the algorithm, the probability is not dependent on anything but the rarity of pokemon that you can encounter in that area. So, your experience is probably just psychology as Raven said.
