Near me there was a little chess tournament today, which brought up some interesting experimental design questions. I know nothing of Experimental Design, but here's the kind of thing: There were 8 players altogether, and only time enough for 4 sessions (during each of which, 4 pairs are matched up to complete one game per pair). Without defining the question formally: Suppose we want to invent a schedule of matchups for this situation so that after all 4 sessions (and 16 games in all) *the maximum information about player's strengths* can be extracted from the results. It seems intuitively clear that you want to avoid the node-edge graph of who has played whom is, by the end, in just one piece. But what else might be important? Note: To simplify the problem, assume that the entire schedule of play is determined in advance, and is independent of any outcomes. E.g., for today's situation (4 sessions, 8 players) one could label each vertex of a regular octagon with the players' names and use each of the 4 families of parallel lines between pairs of vertices as the matchup schedule for one of the 4 sessions. Is that optimal? And of course, what about other numbers than 8 and 4 ? —Dan