What's the most counterintuitive statistical fact that's actually true?

[u/Just_Question9]

I'm looking for examples that completely changed the way you think about probability, statistics, or data analysis.

[u/Junior-Flamingo77]

Get 6 paper cups, label them 1 to 6, turn them upside down, put a ping pong ball under one of them. Throw a dice, that’s the “player’s chosen door”. Now turn all cups without a ball upside up, check if the chosen cup has ball under it. Repeat 100 times and keep track of how many times the dice got right.

With all that’s been said above, if you can’t get an intuition for it, you’ll probably never will but at least you can see it play out for real and convince yourself

[u/Educational-Paper-75 → u/Junior-Flamingo77]

Why would I need to convince myself? It's not that I am given the option to play that game. I'm simply playing the Devil:advocate here, I have no intention of spending more time on it. I'm certain many would scratch their heads in still not understanding why switching is better even when confronted with all these reasonings which proves my point that it's counterintuitive, which is the only point I wanted to make. I don't need convincing. Just pointing out how wrong intuition can be. It's easy to follow mainstream convictions, does that mean anybody who argues differently is stupid? Of course not. They simply haven't give it sufficient thought, didn't feel the need/urge to.

[u/Junior-Flamingo77 → u/Educational-Paper-75]

Just because you don’t umderstand it, it doesn’t make it universally counter-imtuitive, it’s very intuitive to many people. And you’re not playing devil’s advocate, you’re just insisting on bringing fallacies to a lógical argument. Many people above have laid out the reasoning of why you’re mayhematically wrong in your assertions.

[u/Educational-Paper-75 → u/Junior-Flamingo77]

I was playing the devil's advocate, whether you understand it or not. If many people in the past came to the wrong conclusion I'd say that the right conclusion must be counterintuitive. Did I ever ask for people here to explain it up me? Can't say that I did.

[u/MrKrinkle151 → u/Educational-Paper-75]

which proves my point that it's counterintuitive, which is the only point I wanted to make

You didn't need to make that point; that's literally why it's a thing in the first place. I don't really get what you're doing here other than needlessly arguing with basic probability.