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Obvious clickbait: individual videos do not need to reach 10,000 views; only a channel itself needs to hit 10,000 or more lifetime views.

Clickbait will always be clickbait. Hopefully the OP realizes the wrong in his ways and edits the title.

I thought the value of 1000 views was a fraction of a cent. Surely they aren't going to send a check for less than a dollar?

There's a payment threshold of $100 before you can cash out. This is an adsense thing and applies for the Google website adverts too.

I've searched and found that 1000 views seems to range anywhere between $0.80 to $8. It must be part of some mystery YouTube algorithm.