I wonder if you could do most of this cryptographically. If you did, you could make a client that could do all of this peer-to-peer. I think you would just need the following to make a wide range of games (many popular ones, perhaps most?):

1. Client can produce a signature that it drew the k'th card from the deck for any k.

2. Client can produce a signature that the k'th card is X if it drew the k'th card.

3. Client can produce a signature that card X came from any arbitrary set of card indices containing k if it drew the k'th card. (This is the hardest one.) If it's easier, you could get most of this even restricting it to sets of cards that the client has drawn.

With just that, I bet you could make a protocol for most card games where no one can cheat, where the central server's role is only to give out information about k'th card one and only one time. Certainly it's enough for blackjack, most forms of poker, hearts, and go fish. Anyone have a game that would be difficult? Maybe one where hidden cards get passed from player to player.