if you like strategy games, i STRONGLY recommend Frozen Synapse.
this is a very well balanced game, you can spend as much time as you want planning your tactics and you never feel cheated.
skip to 5:40 if you want to see gameplay.
Battlefield Bad Company 2, yes i know you said you get too competitive, but on this game K/D ratio does not mean as much, you can get a 0/20 and still be the top scorer. you can find it dirt cheap and its lots fo fun.
if you would like a game to chill out, with other people, Minecraft is excellent.
i would also recommend mass effect 2, its only singleplayer, but its lots of fun.