I'm not sure I'd dignify this with the word "game"; it's more something to watch hypnotically when you're bored, and let it run when you have other things to do:
Cookie Clicker
There is certainly a "strategy", though what strategy you adopt really depends on what goal you set yourself. Given enough time, there is in principle no limit to how many cookies you can produce. I guess you could set a target of making as many as possible in an hour, trying to make 1 trillion in the shortest possible time, or something like that. It could also be an incredible time-waster, if you allowed it to.