For humans, referential disambiguation is a collaborative process involving clarification questions asked when they will meaningfully change the outcome. However, large language models (LLMs) have been shown to be biased toward premature answering, preferring definite single-turn responses over more clarification exchanges. In this paper, we study the problem of "strategic clarification" -- asking clarification questions in a reference game when their answers will narrow the set of candidate referents. We construct a controlled test environment from the SIMMC 2.1 dataset that records how many questions each ambiguous reference needs to be successfully resolved, and examine how baseline LLM behavior and common post-training methods ask clarifying questions vs. attempt to answer the referent. We also propose BACE (Belief-Aware Critic with Epistemic tracking), a lightweight action chooser method on top of a frozen LM backbone, and show that BACE more consistently chooses the optimal number of clarifying questions than methods such as GRPO and ArCHer.

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