For the mathematically minded

[jason_t]

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Wow what a wonderful contribution.

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I assume that's sarcastic, although it's hard to tell in message postings. I apologize if I'm wrong.

It is an important contribution. Of all the coins in the history of the world that have been flipped 21 times heads in a row, I'll bet none of them were fair. When you see a highly unusual event, it's very likely that the assumptions underlying the computation were wrong. If a coin flips 21 heads in a row, bet on heads next flip.

As a theoretical calculation, 0.5^21 is correct. But it's important to state the assumption.

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When people talk about probability problems involving coins they always mean fair coins unless they specify otherwise. It's not close.