A simple probability problem

This is not a math blog, so here is a hint and a word to learn: The answer is counterintuitive!
To see the detailed explanation, go to peetm's blog.

Suppose you toss a coin lots of times. On average, which sequence is likely to appear first:
HTT or HTH (where H=heads and T=tails).

(a) hit HTT in less tosses than HTH;
(b) hit HTH in less tosses than HTT;
(c) find that the number of tosses is the same?