Martial arts expertise presents a paradox: elite fighters make optimal decisions in 100-200 milliseconds—faster than conscious deliberation allows—yet their performance degrades when instructed to attend to specific cues. This paper resolves the paradox using ACAT. Expert fighters have compressed thousands of sparring rounds into R(D)-optimal gists: minimal representations that preserve all decision-relevant structure while discarding all surface features. The instruction to 'watch the right hand' forces a reversion from gist extraction to verbatim processing, which is both slower and less information-rich. Combat sports are identified as Earth's fastest-feedback compression training environment (0.1-second feedback loops), structurally isomorphic to comedy (where the output is laughter rather than a punch). Five predictions are provided.