An interesting social game would be a trading card game, probably similar to Magic the Gathering. The system would be like texas holdem poker, where a room is created and has limits of how many people that could join. The game would be a royal rumble if the total number of people is more than 2, each player trying to kill one another.
The game will have ranks, and will provide the top 5 winning player with money. The money could be used to buy more cards, or a pack of random cards, that has either good or bad cards depending on our luck. We could also trade with other players, either trading by cards, or by selling them to other players.
I think this game would work great on facebook.
