Are there any multiplayer games on Facebook that involve skill and strategy (as opposed to pushing buttons or buying credits)?

Every multiplayer game I’ve seen on Facebook so far can be “won” by being the player who either pushes the most buttons or buys the most credits. Games like Mafia Wars and Farmville seem to require no skill, no strategy, and very little thinking. Rounds can be won by returning the game all day and pressing a lot of buttons and/or buying credits to obtain tools within the game. That is so lame.

Are there any multiplayer games on Facebook that involve strategy? I realize there’s word-scrabble like games, but I am looking for games involving themes like Farmville and Mafia Wars do, but with more strategy and less button pushing.