Formation energies of a number of hcp-based Ag-Al structures are obtained from ab initio electronic-structure calculations and used within a cluster expansion approach to construct an effective alloy Hamiltonian. Formation energies are found to be inherently asymmetric versus composition, providing an incipient tendency for precipitation in Al-rich alloy. Both ground-state search and Monte Carlo simulations based on the cluster expansion are used to determine the metastable hcp Ag-Al phase diagram. A new equilibrium hcp AgAl ground state is predicted and zero-energy domain boundary defects are found. From thermodynamic results, we discuss the precipitate structure and composition in Al-rich Al-Ag alloys and explain recent microscopy data.