[Doctor Stochastic]

But in a single string, what is the probablity of getting a HH before a TT or a HT or a TH? (It's been answered on one of these threads already; no fair peeking.)

[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."