If you hear "Yes", then the one you asked is the cursed one. If you hear "No", then the one you didn't ask is the cursed one.
Original answer (invalidated by an edit to the question after this was written):
The worst case has the potential to reach any positive, finite number. I will demonstrate this with a counter-example using the 11-question strategy.
Let's label the guards:
T always tells the truth.
F always lies.
Y always says yes.
N always says no.
R gives a random answer.
Since the worst possible case is ...
The existing answer from Deusovi is good, but it can also be solved in a way that will, one third of the time, only need 2 questions, and the rest of the time still be solved with a third question. I'm not saying that's better, but it might be interesting anyway...
Please excuse my formatting troubles, it's my first answer on here.