Ligand-binding epitopes of proteins can mutate rapidly, as shown by viral mutations that lead to escape from neutralizing antibodies. We have undertaken to recreate in vitro the evolutionary competition between viral mutations that allow escape from antibody binding and host mutations that generate new neutralizing antibodies to the mutated viral antigen. To examine this vital race, we describe a phage-based method that allows rapid analysis of molecules that perturb the binding of proteins to their ligands. Because the system can amplify by replication, single-molecule sensitivity can be achieved. When combinatorial protein or small-molecule libraries are studied, large numbers of binding events can be analyzed simultaneously. Such libraries may be used in a sequential phage escape format, where cycles of phage binding and release of mutants are driven by antibodies or small molecules and the difficulty of escape increases at each cycle. Ultimately, the sequencing of the viral mutants allows annotation of the allowed trajectory of escape. Likewise, sequencing of the antibody perturbants charts the chemistry of the immune system response to the viral challenge. We have termed such analysis of competing mutations a "checkmate analysis." When viral systems are studied, a checkmate analysis allows experimental evaluation of the evolutionary contest between viruses and the immune system and may predict which antibodies and small-molecule ligands should be generated in anticipation of viral mutations before these mutations create viral epidemics.