I do play a few "games" on mobile, but they tend to be puzzle/trivia games, since that's really the only thing that works for it IMO. They don't require precise controls, and touch screen only seems to be fine with those kinds of games. Waiting for "energy" to keep playing tends to be much more bearable for the trivia games, and some of the puzzle ones don't put that kind of restriction. Ads are always a problem, though. It's understandable why they do it (revenue), so I don't really complain about that.
If you want to approach the more "hardcore" side, I would say it's very unlikely you'll be able to pull it off. There are too many obstacles like the ones people mentioned here already. Plus, some "hardcore" gamers generally just don't game on mobile no matter what.
