[bvw]

Algebraically substitute "HT" for "HH", since the faces are by design equally likely to occur. Use last result.

[WildTurkey]

I think that means you agree that any sequence is as likely to occur as any other sequence, even the sequence I just tossed had that same probability, right?

[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.)