When Fabio Caruana won the Wijk aan Zee chess tournament in 2020, suggestion was that he was helped by his Norwegian rival, Magnus Carlsen. The schedule used for the 14-player round robin tournament was such, that Caruana would face opponents in the round after they played Magnus – thus, picking up exhausted left-overs and presumably winning with more ease. The presence of this type of advantage in scheduling is measured in a so-called the Carry-Over Effect, and it was particularly high for this chess tournament. Ideally, the COE of a schedule is minimum, whereas in this case it was in fact maximum.
It is not easy at all to find schedules on sets of players that have minimum COE – for only a handful of instances optimal values are known. In this talk, we discuss ways of efficiently looking for ‘perfect’ schedules on any number of N players.