We have a large collection of Euro games and the kids love them. Right now they have been playing Aquadukt which involves strategy but doesn't have complicated rules. They also like the kids version of Settlers of Catan (although I suspect DD could play the adult version). DD likes the Downfall of Pompeii and thowing people into the volcano. Transamerica is another good one--not too complicated--the six year old does fine as well. Also Key Largo, Flash Point, Castle Panic, and For Sale. I bought Deadwood on clearance at Target and they love that one, but I personally find it kind of tedious.