You seem to be suggesting that if I actually flipped a coin 200 times, the actual result would be just as extraordinary as the hypothetical result H^200, having an equal prior probability.

I agree that I seemed to suggest that; I indeed disagree that some arbitrary (expected to come with attached justifications, but those justifications are not present) sequence would be just as "extraordinary". This is where simplicity comes in -- the only reason a sequence of 200 bits would be interesting to humans would be if it were simple -- if it had some special property that allowed us to describe it without listing out the results of all 200 flips. Most sequences of 200 flips won't have this property, which makes the sequences that do extraordinary. So I'd consider T^200, (HT)^100, and (TH)^100 extraordinary sequences, but not 001001011101111001101011001111100101001110001011101000100011100 000111000101110001011100011010101001000011011001011011010110101 011100011000000101011001000100011000010100001100110000110010101 01111001000. However, if I were to take out a coin and flip it now, and get those results, I could say "that sequence I posted on Less Wrong", and thus it would be extraordinary.

So I agree that extraordinariness has nothing to do with the prior probability of a particular sequence of flips, but rather the fact that such a sequence of flips belongs to a privileged reference class (sequences of flips you can easily describe without listing all 200 flips), and getting a sequence from that reference class is an event with a low prior probability. The combination of being in that particular reference class and the fact that such an event (being in that reference class, not the individual sequence itself) is unlikely together might provide a sense of extraordinariness.