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jimmy comments on Halloween thread - rationalist's horrors. - Less Wrong Discussion
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2^-60 and 2^-120 are both zero, so if it happened as you say, you were clearly reading them. It's not that surprising, since we pick up on a lot of subtle stuff that we can't consciously pinpoint.
I was playing a similar card game once, however no one could see the cards in advance and I still guessed wrong 18 times in a row (~4 in a million)
I's certainly expect at least some face-reading on my part...but as solipsist pointed out, even at 90% accuracy getting every card right is pretty unlikely. It starts entering the realm of not-spooky but still improbable if you do 95%^60, but I don't regularly experience that level of certainty in daily life...so why did it happen then? (And I did feel unusual levels of certainty on that day - those "vibes" I described were pretty unmistakable)
Although, this is pretty much the only really "weird" experience I've ever had. I suppose at least a few miraculously unlikely yet salient things must occur during most people''s lifetimes.
Still, this experience has definitely upped my respect for the notion that one might gain certain cognitive abilities by putting one's mind in a certain mental state.