I've built a Facebook game that makes use of rounds where you can only make a single move in a round. You then need to wait until the round ends to see the result (which can take up to 24 hours).
So far, it seems that a significant fraction of users keeps coming back to see the result -- and while they are visiting, make another move.
This seems like a better way to go than instant feedback if you would like a significant fraction of users to play the game every day. Of course, there should be a good reason for the wait -- and in my game, there is.
BTW, I actually have several games in progress so you may be able to make multiple moves in a single visit. This allows players to have more to do per visit.
