The Battle for Polytopia is a good game. Basically, they took Civilization and condensed it from several hours to a few minutes. You've got a number of tribes that you can choose from, and a very finite number of turns to totally take over the small maps. There are no culture, religion, or science victories here. The only thing that matters is total domination. If you can't do that you better have the best score when the timer runs out. The makers of this game had a theme and stuck to it faithfully.
Beyond that, Polytopia is a beautiful game. The art style is minimalist, simple angles and planes, but rich in color and motion. The art perfectly fits the sparse gameplay.
Theoretically you can keep playing this game just about forever; the mechanics are simple but engaging. The different tribes have just enough variation between them to keep the gameplay feeling fresh while allowing you to learn the various systems and get good at them, whichever tribe you're playing.
And if you get bored with fighting the AI you can start fights online with your friends, but not strangers. This seems like a very clever design decision they made when creating the game.
I've had Polytopia on my phone for about five months or so, and I've really enjoyed my time with it.