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Yeah it's just difficult to determine what one views as "counter-intuitive".

I guess the birthday paradox is one such example (https://en.wikipedia.org/wiki/Birthday_problem) but if you've taken a course in probability theory then it doesn't really seem counter-intuitive.

There's quite a few veridical paradoxes in probability theory

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Oh good thinking! :) Yes, that reminds me of one. The "two random choice" thing, which I think is connected to the "Pick a Door" problem, of famous Math Lady Column infamy. I'm not familiar with it if anyone can give a good, Here is the problem, here is the regular intuition, and here finally is the counter intuition that's actually correct about it.

But haha I was just thinking about math stuff at all. More like sociological, biological, systems, anything!

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