If you are a casual/amateur chess player, then the Chess app from AI Factory is for you.
This mobile app, available on Android and iOS, allows you to play chess either with the software or another human player.
The chess engine is pretty strong, and you can adjust its strength at levels 1 to 12 (which correspond roughly to Elo ratings 700 to 2100). There is an excellent 'Tutor' that can suggest and analyse each move.
The user interface is very intuitive and graphics are top-notch. After a game, you can record it, replay it, save it, or share it online. In short, this app offers all you can expect from a free mobile game, and much more.
After installing it last week, I have played 15 games so far across various levels, with 9 wins and 6 losses. Interestingly, no draws so far.