[math-fun] New methods in combinatorial game theory

For people interested in such things, the paper linked below solves some previously unsolved problems for the game of Chomp. For example, it proves that the 3 by n game always has a unique first move. The interest, however, is not so much in the specific results as in the innovative methodology which uses the "renormalization" technique (a la Feigenbaum), -totally different from anything I've seen applied to combinatorial games. For Chomp-savvy people, the paper gives precise estimates for the limit size of the first moves ("bites") and shows that the relative frequency of one-row to two-row initial bites is sqrt(2)-1 to 2-sqrt(2). There are intriguing illustrations. ftp://ftp.orie.cornell.edu/pub/techreps/TR1422.pdf David