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Correct me if I'm wrong, but each and every possible series of coin tosses is just as likely as any other series -- regardless of the length of the series. You cannot look at a series of "random" events that have happened and declare the series impossible or unlikely.

You are correct with respect to any given series. For a fair coin "HHHHHHHHHH" is as likely as "HHTHTTTHTH". For distributions of results in the aggregate, however, the head-to-tail ratio should be about 1-to-1. (For a any roll of a pair of fair dice, they should total 7 about 1 out of every 6.) So based on the known properties of a coin, the probability of observing a series containing 10 heads (~.09%) is far less than the probability of observing a series containing 5 heads and 5 tails (~24.6%).

however, the head-to-tail ratio should be about 1-to-1.

But this is not the issue when deciding whether chance events can result in complexity. You could make a character count of a computer program and list the relative frequencies of the characters, but that would tell you nothing about the nature of the program or its operation. It is the sequence that matters.

the other thing that needs to be considered is selection. Nature, for whatever reasons, favors certain sequences. It is as if a dice player could always keep his winnings and always rule losing tosses "invalid".

the "whatever reasons" part is not arbitrary, but is the subject of study.