Note that some/many of the western chain hotels often offer deals like buy two nights, get one free. IME to find these rates, you need to just experiment with the codes your chain uses for such offers. They tend NOT to appear in the online booking engine, even when you check the box for promos and offers, nor are they listed in the hotel's website under "offers." Sometimes AmEx PTS/CTS has these rates, often as a FHR rate, but sometimes agents find them as AmEx corporate or select rates. YMMV.