Combinatorial Game Theory, as an academic discipline, is still in its infancy. Many analyses of individual games have appeared in print, starting in 1902 with C. L. Bouton's analysis of the game of Nim. (For exact references to the works mentioned here, please see A. Praenkel's bibliography on pages 493-537 of this volume.) It is was not until the 1930's that a consistent theory for impartial games was developed, independently, by R. Sprague and P. M. Grundy, later to be expanded and expounded upon by R. K. Guy and C. A. B. Smith. (Guy is still going strong, as evidenced by his energy at this Workshop.) J. H. Conway then developed the theory of partizan games, which represented a major advance. Based on this theory, D. Knuth wrote his modern moral tale, Surreal Numbers. The collaboration of E. R. Berlekamp, J. H. Conway and R. K. Guy gave us Winning Ways, which “set to music”, or at least to “rhyme”, the theory so far. In the process, many more games were discovered and analyzed: but more were discovered than solved!

This Workshop, held from 11 to 21 July 1994, gave evidence of the growing interest in combinatorial games on the part of experts from many fields: mathematicians, computer scientists, researchers in artificial intelligence, economists, and other social scientists. Players, some of whom make their living from games, also attended. Visitors such as D. Knuth and H. Wilf dropped in for a few hours or days and gave impromptu lectures. There was much cross-fertilization of ideas, as could be expected from a meeting of people from such varied backgrounds.