Strategery is a highly-rated iPad and iPhone game that's based on capturing territory on a randomly-generated map. While I admire the game for its minimalist approach to world-domination, I found the game to be lacking in several major areas. The rules are straightforward: Declare war on a territory, roll dice for each marker, and whoever has more markers standing wins and gets the enemy territory. Keep playing until one person holds the whole board. The full version of the game offers online play which works well (small gripe: the game requires you to set up a separate username and password before you can play online. Too bad it can't just link seamlessly through iOS Game Center as so many other games doo).
I found one difficulty in this game to be the larger maps - games with so much random territory can too easily devolve into a never-ending back-and-forth between two players as the same territories are won, lost, and re-won over and over. Honestly, I've abandoned many of the games I started for this very reason. But more importantly, this game simply lacks...personality. Anyone who has played Quarrel has already experienced nearly identical territory-conquering rules, but with tons more fun, music, and the whole spelling combat to boot! Because of this, Strategery feels so much less than it could be. Luckily, Strategery Lite is a free download. Although it lacks the online component, it's best to give the free version a try before you invest $1.99 for the full version.