As one of the main components of sea salt aerosols, sodium chloride is involved in numerous atmospheric processes. Gas-phase clusters are ideal models to study fundamental physical and chemical properties of sodium chloride, which are significantly affected by the cluster size. Of particular interest are magic cluster sizes, which exhibit high intensities in mass spectra. In order to understand the origin of these magic cluster sizes, quantum chemical calculations at the CCSD(T)//DFT level are performed, yielding structures and binding energies of neutral (NaCl)x, anionic (NaCl)xCl- and cationic (NaCl)xNa+ clusters up to x = 8. Our calculations show that the clusters can easily isomerize, enabling dissociation into the lowest-energy isomers of the fragments. Energetics can explain the special stability of (NaCl)4Cl-, but (NaCl)4Na+ actually offers low-lying dissociation channels, despite being a magic cluster size. Collision-induced dissociation experiments reveal that the loss of neutral clusters (NaCl)x, x = 2, 4, is in most cases more favorable than the loss of NaCl or the atomic ion, i.e. sodium chloride clusters actually fragment via the cleavage of the entire cluster, not by evaporating small cluster building blocks. This is rationalized by the calculated high stability of even-numbered neutral clusters (NaCl)x, especially x = 2, 4. Analysis of the density of states and rate constants calculated with a modified Rice-Ramsperger-Kassel-Marcus (RRKM) equation called AWATAR - considering all energetically accessible isomers of reactants and fragments - shows that entropic effects are responsible for the magic cluster character of (NaCl)4Na+. In particular, low-lying vibrational modes provide a high density of states of the near-planar cluster. Together with the small contribution of an atomic ion to the sum of states in a loose transition state for dissociation, this leads to a very small unimolecular rate constant for dissociation into (NaCl)4 and Na+, which is the lowest energy fragmentation pathway. Thus, entropic effects may override energetics for certain magic cluster sizes.