The ability to accurately predict the arrangements of constituent atoms in a surface alloy is indispensable to explaining and predicting the performance of bimetallic model catalysts. We have developed a scheme to predict the equilibrium arrangement of atoms in surface alloys at finite temperatures. Our scheme is based on the Ising model, and is capable of reproducing DFT-predicted total energies to within no more than a few meV per surface atom. We will present our scheme in detail, as well as what we have learned about the effects of temperature, composition, surface facet, and particle identity on the arrangement of surface atoms for various gold-based binary alloys including gold-palladium and gold-platinum. We will also discuss how the atomic arrangements affect the reactivity of gold-based alloy surfaces particularly towards oxidation of hydrogen and carbon monoxide.