What is a better strategy in terms of monetizing online, opening a single website and focusing on it completely or working on multiple websites with the idea that one of them will at least work?
One of them will atleast work is a statement of shooting in the dark and so not sure if you should be doing it. Focus on building quality and if that can be achieved on multiple sites fine, else one is a good choice.
Both the choices are good at their place but in my opinion using multiple sites is more profitable than the single one. When the marketer comes in contact with huge number of people, the product's marketing is doubled. A single site will not help you to connect with that many people as multiple sites will help. But it will only be fruitful only if you are active on each and every site, otherwise you will lose your popularity.