There’s a classic [0] scam: send 2^12 letters to 2^12 random people. Half say that some stock will go up next week and the other half say it’ll go down. 2^11 of them will be correct [1]. Send those people similar letters the next week, half with one prediction and half with the opposite. Repeat until you have, say, 2^4 people who have seen 8 consecutive correct predictions. Now offer them more predictions at $500 a pop based on your track record.

It is, of course, quite possible to fool yourself based on this fallacy.

[0] no citation — it’s folklore as far as I know.

[1] I’m ignoring issues like the stock simply not moving.