An Ising model exhibits zero-energy antiphase boundaries (APBs) and frustration on close-packed face-centered cubic (fcc) and triangular lattices. The frustration results in degenerate structures and chains of long-period superstructures forming a quasicontinuous ground-state “hull” in the formation energy versus composition (c) diagram. In alloys, a nonzero but small APB energy yields a c-dependent reduction in this degeneracy that affects the phase diagram topology and range of the two-phase coexistence. Using density functional theory combined with cluster expansions (CEs), we study Ag-Au alloys as a prototype and find the effective cluster interactions (dominated by nearest-neighbor pairs), predict energetics of millions of structures, and construct the temperature versus c phase diagrams. We then compare the CE interactions for Ag-Au with those calculated directly from a supercell approach, and visualize the electronic origins of pair and multibody interactions, highlighting the physical nature of the chemical interactions implicit in the CE methods. We discuss generality of the results for close-packed alloys.