The idea came from a book I am reading, called "Am I Making Myself Clear?" The author, Cornelia Dean, was talking about the importance of understanding statistics in understanding science.

So, lets think about it, one step at a time. On the first flip, how likely are you to get heads? Its 50/50, right? What about for the second flip? Again, it is 50/50. So it is just as likely for you to get HH as it is for HT, TH, or TT. Now, on the third flip, what are the odds for getting heads? Again, 50/50, so the odds for HHH are the same as for HTH, HTT, TTH, THH, or TTT.

You can continue on, and no matter how many times you flip the coin, each time, you have a 50/50 chance of getting heads. That means that HHHHHHHH is just as likely as HHTHTTHT or any other combination.

Why does it seem that HHHHHHHH should be less likely? Because we expect random events to look random. This has too much pattern, so it seems less likely, but the odds of getting the exact sequence HHTHTTHT or any other exact squence is the same, 1 out of 256 possible combinations.