[PatrickHenry]

To summarize the obvious, in a series of coin tosses:

(1) the chance of getting one completely specific string involves a factorial computation;
(2) the chance of getting any string at all is 100%; and
(3) at any step along the way, the odds of getting H or T is 50%.

And, to stroke myself one more time, misunderstanding item (3) to involve item (1) above involves my "fallacy of incorporating the continuum."

[PatrickHenry]

And if I've goofed it up, I welcome and acknowledge all corrections.

[Doctor Stochastic]

People often make the mistake of using "crossstream" (inferences from a population of sequencess of a given length, sometimes called "weak") computations to model "downstream" (inferences along a given sequence, sometimes called "strong") computations. Coin tossing (and similar models) are not intuitive at all. For example, in a single game of heads and tails, it is most likely that either H or T is "ahead" most of the time. Crossings are rare.