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While heuristic pruning is a critical countermeasure, existing approaches lack formal safety guarantees when guided by surrogate evaluators such as Large Language Models (LLMs), which exhibit systematic biases. We formulate node expansion as a localized Best-Arm Identification (BAI) problem under bounded bias $L$ and derive a sample complexity upper bound of $\\mathcal{O}((\\Delta-4L)^{-2})$, identifying $\\Delta > 4L$ as the regime where safe elimination is feasible. We further establish an information-theoretic lower bound of $\\Omega((\\Delta-2L)^{-2})$ that characterizes the structural limits of biased exploration. Motivated by these results, we propose PAC-MCTS, a bias-aware pruning framework that dynamically adapts confidence bounds during search. 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