Magnesium has attracted a growing interest for its use in various applications, primarily due to its, abundance, lightweight properties and relatively low-cost. However, one major drawback to its widespread use remains its reactivity in aqueous environments, which is poorly understood at the atomistic level. Ab initio density functional theory methods are particularly well suited to bridge this knowledge gap, but the explicit simulation of electrified water/metal interfaces is often too costly from a computational viewpoint. Here we investigate water/Mg interfaces using the computationally efficient implicit solvent model VASPsol. We show that the Mg (0001), (10-10), and (10-11) surfaces each form different electrochemical double layers due to the anisotropic smoothing of the electron density at their surfaces, following Smoluchowski rules. We highlight the dependence that the position of the diffuse cavity surrounding the interface has on the potential of zero charge and the electron double layer capacitance, and how these parameters are also affected by the addition of explicated water and adsorbed OH. Lastly, we calculate the equilibrium potential of Mg ²⁺ / Mg ⁰ in an aqueous environment as 2.46 V vs. standard hydrogen electrode in excellent agreement with experiment.