Modern warfare is characterized by an environment of complex, multidomain operations deployed against an adversary who, likewise, responds with a complex array of tactics. Although the challenges of operating in this environment have long been recognized, the complexities of this environment have rarely been framed or studied in a structured way. In this report, the authors assess mathematical strategies for quantifying complexity in wartime environments. After comparing approaches based in linear algebra with Monte Carlo simulation strategies, they were able to provide a general road map that defined the advantages and limitations of each. These methods are demonstrated in two operational vignettes: one examining a simplified suppression of enemy air defenses scenario and a second examining the Cuban Missile Crisis.