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Elo comments on What's wrong with this picture? - Less Wrong
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For any n coin flips p(sequence) = 1/2^n right?
for 100 coin flips, p(sequence) as a result is 1/2^100 = 7.8886091e-31
you have observed an event that could have gone 2^100 different ways, and found one version of the result. just because you have done something with a specific probability doesn't mean it's a low probability.
The probability of getting a sequence is (pretty much) 1 (given that flipping 100 coins in a thought experiment is pretty safe)
The probability of getting that sequence again is quite low.
The probability of all heads is the same as the probability of any other sequence of flips. You'd feel somewhat differently about flipping heads one hundred times in a row than most other distributions, however, even though it's just as likely as any other distribution of flips.