Royal Chess

The simple rule or playing a card to have the right to move a piece is surprisingly interesting. There is obviously luck in when you draw the cards you need, but also a lot of calculated risk taking and inference about the opposing hand. It's cute, and the distributions of cards is well designed to ensure the game ends (e.g. there is only one king card!).

It's also a cute way to provide a handicap against children who are learning -- you play royal chess, they play regular chess.