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Complex multi-hop question answering requires large language models (LLMs) not only to retrieve external knowledge but also to reason over the retrieved information in order to arrive at the final solution. This involves two key challenges: (i) how to effectively explore the solution space and generate more potentially correct solution candidates, and (ii) how to select the optimal solution from multiple solution candidates, both of which require a training-free approach without introducing a more powerful teacher model. To address these challenges, we propose Retrieval-Augmented Monte Carlo Tree Self-Play with Reasoning Consistency (RASPberry), which introduces a more flexible action-level sampling granularity compared to existing methods, leverages Monte Carlo Tree Search for efficient solution space exploration, and utilizes an enhanced version of reasoning consistency to guide the selection of the optimal solution. Experimental results demonstrate that our proposed RASPberry effectively tackles the two challenges outlined above, achieving more efficient RAG inference-time scaling. Our code is available at https://github.com/BaixuanLi/RASPberry.