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Collecting ground-truth rewards or human demonstrations for multi-step reasoning tasks is often prohibitively expensive, especially in interactive domains such as web tasks. We introduce Self-Taught Lookahead (STL), a reward-free framework that improves language model–based value functions by reasoning explicitly about state transitions. STL can be viewed as a chain-of-thought analogue of the value iteration algorithm: instead of regressing directly on numeric values, a value LLM is trained to simulate a step of lookahead in natural language—predicting the next action, resulting state, and rationale for its value. This process refines value estimates without any labeled data. The self-supervised procedure yields more accurate state-value predictions, which in turn enable lightweight search algorithms to expand fewer states while maintaining strong performance. Empirically, STL-trained value models built on moderately sized (8B-parameter) open-weight LLMs boost web agent success rates by over 39%, achieving performance comparable to proprietary models. STL also generalizes to multi-hop question answering and math puzzles. Overall, STL enables small open-source models to guide efficient search, reducing inference costs by integrating explicit reasoning with value learning.