Interaction between real-world environments and embodied autonomous cognitive agents within-and-of those environments is channeled by the overwhelming ‘riverbank’ influences of culture and path-dependent historical trajectory, often intertwined with the burdens of fog, friction, and deadly adversarial intent. These and related factors sculpt conflict at all scales and levels of organization. Using the asymptotic limit theorems of information and control theories, this work formally argues that autonomous intelligence—always and inevitably embodied—must suffer significantly increased probability of failure under such foundational ambiguity, the so-called ‘wickedly hard’ multiple-option/multiple-intent strategic problems not amenable to straightforward, if often exceedingly difficult, tactical and operational engineering solutions. Problems at the strategic level thus enter realms of subtlety parallel to those that confound the understanding and representation of individual human consciousness, albeit on a differing time scale. In particular, we develop probability models of cognitive dynamics on wickedly hard problems that can be converted to statistical tools for their empirical study and limited control.