My grandfather is psychic. For instance, I was sitting on his couch ostensibly watching TV. I was really thinking about religion, and how mine was different from my grandfathers...how I could respect his views, but he couldn't respect mine.
He sat up and said my name in that way he only does when he's really angry. "I don't care what you do in your house, in your own time, but here..." and he proceeded to lecture me on religion.
That is, until I thought "And what does your religion say about spying on people's minds?" at which point he abruptly said, "Now you go on back to watching your show."
LOL. That's grandpa for you. He does that sort of thing with amazing frequency. He also tells all the women in the family when they're going to have a baby, and what gender it'll be. My mother knew she was pregnant when grandpa called and said, "You're going to have a blue-eyed, blonde-haired boy." She did. Brother's hair darkened as he aged--it was brown by about age ten--but he definitely was a blue-eyed blonde haired boy, despite both our parents having dark hair.
I read the tarot. I don't do it often...I really use it almost like a party trick, now. I go back and forth about how much I really believe in it. But the thing is, I've done some very in-depth, spot-on readings. I never ask a person their question; instead, I do the reading and see what question it seems to be answering. I tell the questioner what each card means in its position, then put all those bits together in a way that makes sense, then say, "So this is your answer. I'm assuming your question was ______?"
I'm pretty sure I'm not just reading the person, because, like I said, I start by giving a card-by-card breakdown. I'm not making any conscious attempt to read the questioner, and I don't know their question. I try to be as specific as possible, and very rarely ask any questions during the reading. (No "is it about a man?" sort of questions.)
I have a hard time doing readings for myself--too close to the material, I guess. But when I was learning the tarot, I'd write all my readings down. I found that even if I screwed up the interpretation at the time, in hindsight, I could see exactly what the cards were saying.
My readings can occasionally be incredibly specific, and I've never been wrong on a reading I did for someone else (although I have had readings where the cards pretty much refused to answer the question asked--and that's what I told the questioner. "The cards say, 'I'm not telling'."

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And yet, I'm something less than a firm believer, even so.