"Open and shut cases" refers to a situation where the solution or outcome is straightforward and obvious. However, there are several antonyms to this phrase that describe situations where there is ambiguity, complexity, or uncertainty. For instance, a "complicated case," "muddled case," "ambiguous case," or "difficult case" are antonyms to "open and shut cases." Other antonyms include "unsolved case," "cold case," and "impending case." These phrases depict situations where the outcome is uncertain, the evidence is scarce, and the solution may require more time and effort. In such cases, investigation, analysis, and critical thinking are highly essential to uncover the truth or resolution.