An update on the 517-move win: Tim Krabbe, item #393, http://timkr.home.xs4all.nl/chess2/diary.htm ... Including my own predictions to 10-man chess. Rules about 'general wins' in Pawnless chess can be checked out against data about extreme wins in my 'Chess Endgame Records', http://centaur.reading.ac.uk/34268/ . John Nunn gives a review of 'general win/draw' in a subset of 6-man endgames in 'Secrets of Pawnless Endgames'. Basically, we are seeing smaller and smaller advantages playing out in larger and larger spaces (x60, x59, x58 etc) ... The maxDTM win in KQPKRBN derives its length (1,097 plies, 549 winner's moves) from an underpromotion of P=N (which is not strictly an underpromotion as the Q cannot do a N-move) and a very long phase in KQNKRBN (1,006 plies, 503m). The main restriction on the number of positions is the constraint that the side-not-to-move should not be in check. The statistical sampling idea seems to be news and interesting. Guy