arXiv:2603.29761v1 Announce Type: new Abstract: A human-like chess engine should mimic the style, errors, and consistency of a strong human player rather than maximize playing strength. We show that training from move sequences alone forces a model to learn two capabilities: state tracking, which reconstructs the board from move history, and decision quality, which selects good moves from that reconstructed state. These impose contradictory data requirements: low-rated games provide the diversity needed for tracking, while high-rated games provide the quality signal for decision learning. Removing low-rated data degrades performance. We formalize this tension as a dual-capability bottleneck, P