Cyclic zugzwangs (John as reporter, July 2023)

A cyclic zugzwang is a position from which the side to move can win, but in at least one line only by returning to the same position with the other side to move.

Shortly before his death in May 2021, Guy Haworth told me that a team consisting of Galen Huntington, Árpád Rusz, and himself had been investigating the occurrence of cyclic zugzwangs in positions with small numbers of men, and had found that there were 3 with four men and 1,132 with five. A paper describing their results was ready for publication, but the journal to which it was intended to be sent required it to be submitted in a different format, and following Guy's death it was not found practical to do this. We have therefore offered to post it here.

Three files have been posted: the paper itself as a PDF, a PGN file containing the positions with the relevant lines of play, and a PDF describing the PGN file.

Please note that the authors reserve all rights in this matter (contact Galen or Árpád).