The labelling of DNA oligonucleotides with signalling groups that give a unique response to duplex formation depending on the target sequence is a highly effective strategy in the design of DNA-based hybridisation sensors. A key challenge in the design of these so-called base discriminating probes (BDPs) is to understand how the local environment of the signalling group affects the sensing response. The work herein describes a comprehensive study involving a variety of photophysical techniques, NMR studies and molecular dynamics simulations, on anthracene-tagged oligonucleotide probes that can sense single base changes (point variants) in target DNA strands. A detailed analysis of the fluorescence sensing mechanism is provided, with a particular focus on rationalising the high dependence of this process on not only the linker stereochemistry but also the site of nucleobase variation within the target strand. The work highlights the various factors and techniques used to respectively underpin and rationalise the BDP approach to point variant sensing, which relies on different responses to duplex formation rather than different duplex binding strengths.