The canonical method is widely used to build single round robin schedules for sports competitions. Certain properties of the canonical method may entrap local search procedures. In this paper, we study the connectivity of one of the most used neighborhood structures in local search heuristics for single round robin scheduling and characterize the conditions in which this entrapment happens. This characterization brings to light a relation between the connectivity of the analyzed neighborhood and the riffle shuffle, a method of shuffling playing cards. (C) 2016 Elsevier B.V. All rights reserved.