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christopherj comments on Yes, Virginia, You Can Be 99.99% (Or More!) Certain That 53 Is Prime - Less Wrong
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Getting 200 heads only in coinflipping is just as likely as any other result. However, it is of incredibly low entropy -- you should not expect to see a pattern of that sort (less bits to describe than listing the results). It's also impossibly unlikely as a result from a fair coin, compared to as a result of fraud or an unfair coin.