Downloaded Carcassonne a few weeks ago on the iPad - the game of the year in 2001 consisting of tiles and wooden 'followers'. Like all the best games, deceptively simple yet very rich in game play strategies. In fact, I hadn't realised just how rich it was until playing the in built AI players. Initially, losing frequently to the 'Easy' players I eventually learned the strategies to overcome them and managed to get my level to at least on par with the strong players, without really understanding the subtle changes I'd made to my game play.
Haven't tried my new found powers on any humans yet, though I'm pretty sure I'm a better player now than a month ago.
The app also lets you play against human opponents or a mix of AI and human, and has a very nice 'solo' game too with completely different rules which is addictive. Highly recommended all round.