Anyway, one professor provided me many helpful suggestions and introductions, and permited me to cite his papers in my essay. He has also promised me to be his research assistant if I am enrolled in the program. He will even correct my essay. I think that is the benefits of introducing yourself to professors beforehand. It, although does not guarantee, actually enhances your possibility of being accepted. However, to be honest, the chance of meeting such a warm professor is rather low.
Yes, it really depends on luck. Even a dean that promised to guide me said that she could not interfere with the committee. I think that the goal should actually be to get the first-hand information and to know what professors really expect from applicants.