The attacker is in your head. By this I mean that the attacker knows you and knows your password generation strategies. If you systematically use passwords beginning with a 'Z', then he will start his search with such passwords. (Especially since you have described this very method on a publicly readable Web site.)
You might have an edge if you choose your passwords differently from everybody else; but attackers adapt, and adapt fast. Choosing 'ZZZZZZZZZZ' as password is strong only as long as attackers try potential passwords in alphabetical order; and attackers have already stopped doing that. They first try passwords with "structure", such as ten repetitions of the same letter, because that's a kind of passwords that human users choose (then they continue with derivations from common words and names).
It is hard to outsmart attackers; it is especially hard to know how much you outsmarted attackers, because smartness is not something that is readily quantified and measured. The normal stance is to assume that the attackers knows everything about your password generation process, save the random choices within that process; this is the only way you can reliably estimate the strength of your password.
Regardless of how you choose your password, an attacker who is intent on trying all possible letter combinations can always generate these combinations in a random order, which guarantees him the theoretical average success rate of N/2 (if there are N possible passwords, he will try on average half of them before hitting the right one). There is no password generation method which can be used to prevent that.