[WildTurkey]

Assuming randomness, what is the probability of obtaining the following sequence?

HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH HTHTH

[bvw]

The "assuming randomness" -- by which you must mean that the coin and toss are designed so that neither face is more likely -- that is the sticker. Whyever would you do that?

Never play three-card monte against one of those park card-sharks. Why? Same reason. The outcome of the game is designed, even though the shark will make every effort to make it appear to fit your "random" assumption.