Just a quick defense... When I first began with making invitations for backgammon players with a higher BKR than myself (I was at close to 2100) I did so to try to find out if these higher ranked players were really that good, and to find out how I stacked up against the best. (I did this early on playing reversi also, playing the sites top reated players) My bKR went down to almost 1900, really fsat, and has since climbed back to around 1060 or so. So there has been no real advantage, since I went from about 1500 to almost 2100 playing mostly those rated around me or lower. Plus, under your theory, those higher ranked players are not really better, but just luckier or they only play other high ranking players as not to risk losing to lower ranked players who get lucky. I personally think that if I wanted to build my bkr, I would pull out the can of whoop ass on a lot of low ranked players, and it wouldnt take long to get my ranking right up there. maybe I will try out that theory :)