The use of DNA strands as nanowires or electrochemical biosensors requires a deep understanding of charge transfer processes along the strand, as well as of the redox properties. These properties are computationally assessed in detail throughout this study. By applying molecular dynamics and hybrid QM/continuum and QM/QM/continuum schemes, the vertical ionization energies, adiabatic ionization energies, vertical attachment energies, one-electron oxidation potentials, and delocalization of the hole generated upon oxidation have been determined for nucleobases in their free form and as part of a pure single-stranded DNA. We show that the reducer ability of the isolated nucleobases is explained by the intramolecular delocalization of the positively charged hole, while the enhancement of the reducer character when going from aqueous solution to the strand correlates very well with the intermolecular hole delocalization. Our simulations suggest that the redox properties of DNA strands can be tuned by playing with the balance between intramolecular and intermolecular charge delocalization.