Quarto!

Quarto! has a 4x4 board and 16 pieces. Each piece has four dichotomous attributes: color, height, shape and consistency. So each piece is either black or white, tall or short, square or round, and hollow or solid. The object is to place the fourth piece in a row where all four pieces have at least one attribute in common. The twist is your opponent gets to choose the piece you place on the board every turn. - BoardGameGeek