Get cheaper rate at last minute booking

I am searching for some traveling information again. I am looking for my trip to Hong Kong and keep looking for hotel and other traveling information since last two months. I was planning to book hotel room last month but was delay the booking now. I saw few hotel website, most of them offer cheaper hotel rate for current month or within the 3 months before traveling date. If you book early then 3 months, then you probably will get the higher hotel rate. So, no point to book those expensive hotel room since I have so many hotels selection there. I better book at last minutes lor.