Frozen Synapse is one of the more innovative turn based strategy titles to come along in recent years. It's a good example of the player dictating their own level of involvement. You have a collection of units that you can assign a string of iterative orders to, and you can test out how these orders will play before confirming. Even more down the rabbit hole, you can assign the visable enemy units orders based on how you think they might react to your movements, or what your foe might be doing on their turn.
The level of involvement is insane, is wrapped up in a really cool aesthetic. It will be available on iPad on May 16th. It will be interesting to see if the game loses anything in its transition to a touch interface. In the meantime, here's the launch trailer for the PC version so you can see what i'm talking about.