Quantum-mechanical studies have predicted, and experimental studies on SrCu2O3 have confirmed, that the propagation of bound pairs on even-chain copper oxide ladders is possible, but not on ladders with an odd number of legs. To study whether this quantum-mechanical lattice parity effect has a classical analog, and to document the consequences of assuming different coupling scenarios between the ladder and adjacent sublattices, we develop a classical Markovian lattice-statistical model to monitor the efficiency of migration on a composite lattice. Regions of parameter space where significant departures from results obtained via a symmetrical random walk are identified. (C) 2011 Elsevier B.V. All rights reserved.