On New Years, I told my daughter that she was probably old enough to play "Daddy's Games." Needless to say, she beemed with pride. We've mainly been playing Settlers of Catan (with Jacqui); she wins often. It's a forgiving game, given the dice and that Jacqui and I will rob each other rather than Rebecca, unless she's in the lead.
I've also introduce Ticket to Ride, which she wants to play again. I don't think she has a realistic chance to win (without deliberately throwing the game), so I'm pushing Settlers for now.