Effective debugging is a crucial aspect of software development, demanding problem-solving skills, expertise, and appropriate tools. Although previous research has studied expert developers' debugging strategies, the specific factors influencing strategy choice in complex scenarios remain underexplored. To investigate these contextual factors, we conducted two studies. First, we surveyed 35 developers to identify experiences with challenging debugging problems and contextual complexities. Second, we held semi-structured interviews with 16 experienced developers to gain deeper insight into strategic reasoning for complex debugging tasks. Insights from both groups enriched our understanding of debugging strategies at different expertise levels. We found that contextual factors interact in complex ways, and combinations of factors influence strategy choice, evolving throughout the debugging process. Hypothesis making is the baseline for debugging, with experience and code familiarity crucial for strategy selection. Our results show a gap between learning and effectively practicing strategies in challenging contexts, highlighting the need for carefully designed debugging tools and educational frameworks that align with problem contexts.