Surprisingly, my teenage daughter wanted to play a game with me. She suggested Othello, but when we opened the box... the horror: the board and pieces were gone! We were too lazy to go look for them and so we agreed on another game, Blokus.
In the two-player variant, each player takes turns in putting pieces of two alternating colours on the board, and in the end the separate scores of those colours are added. The game feels slightly different, because friendly colours won't get in each other's way. However, as in the 4-player game, the board gets really crowded, you start using the smaller pieces to fill up those nooks and crannies in enemy territory, and sometimes you even have to block your own friendly colour to control the overall damage, i.e. to minimize the overall size of unplaced pieces. It hurts... The end score was as close as it gets: -22 for my daughter, -21 for me. Whether with 4 or 2 players, Blokus is a great, unforgiving, tense and yet well-paced abstract game.