Proficient multilingual speakers often intentionally switch languages in the middle of a conversation. Similarly, recent reasoning-focused bilingual large language models (LLMs) with strong capabilities in both languages exhibit **language mixing**—alternating languages within their chain of thought. Discouraging this behavior in DeepSeek-R1 was found to degrade accuracy, suggesting that language mixing may benefit reasoning. In this work, we study language switching in Chinese-English bilingual reasoning models. We identify reinforcement learning with verifiable rewards (RLVR) as the critical training stage that leads to language mixing. We show that language mixing can enhance reasoning: enforcing monolingual decoding reduces accuracy by 5.6 percentage points on MATH500. Additionally, a lightweight probe can be trained to predict whether a potential language switch would benefit or harm reasoning, and when used to guide decoding, increases accuracy by 2.92 percentage points. Our findings suggest that language mixing is not merely a byproduct of multilingual training, but is a *strategic reasoning behavior*.