# When a Verified World Model Still Loses: Play-Adequacy vs Prediction-Accuracy in LLM-Synthesized Code World Models

arXiv: https://arxiv.org/abs/2607.14169 · HTML: https://mlsanity.com/paper/2607.14169/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in World models for language agents, one of 11 directions in World models.
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Placed in

- World models / [World models for language agents](https://mlsanity.com/wm/world-models-for-language-agents/)

## Builds on (most cited first, 2 of 2)

- [Objective Mismatch in Model-based Reinforcement Learning](https://mlsanity.com/paper/2002.04523/) (2020)
- [Solving Large Imperfect Information Games Using CFR+](https://mlsanity.com/paper/1407.5042/) (2014)

## Built on by (most cited first, 3 of 3)

- [An Omitted Mode Is a Rare Rule: The Sampling-Verification Danger Law in Continuous Code World Models](https://mlsanity.com/paper/2608.17956/) (2026)
- [An Enclosed Mode Is a Gauge Choice: Topology Relative to Reach in Certified Code World Models](https://mlsanity.com/paper/2608.28541/) (2026)
- [Kepler: Auditable World Models for ARC-AGI-3](https://mlsanity.com/paper/2610.00834/) (2026)

## Abstract (arXiv)

Large language models can synthesize a game's rules as executable code - a Code World Model (CWM) - which a classical planner then searches over. Such models are typically accepted when they reach high transition accuracy on sampled trajectories. We argue this is the wrong notion of adequacy for planning. We show four things. (1) An LLM-synthesized CWM can pass a sampling gate at 100% transition accuracy and be ≥ 98% state-accurate on the planner's own search distribution, yet lose systematically at play, because the <1% it gets wrong is exactly the pivotal dynamics; the play cost of the omitted rule is 0.091 (seed-clustered 95% CI [0.065,0.117], n=4800). We call this the verified-vs-correct gap, and confirm it end-to-end through the synthesis pipeline. (2) The harm follows a quantitative law, danger=playcost×(1-rarity)N, whose (1-rarity)N gate-miss factor is proven exact and whose play cost is empirically bounded. (3) The failure is not repaired by more data: LLM synthesis behaves as rule translation, not rule inference, and did not infer the omitted rule across models (GPT-5.x) and data regimes (including DAgger and targeted examples). (4) The same mechanism recurs on the belief-inference function of imperfect-information CWMs: we prove a coverage bound (a size-N gate is identifying when Ngtrsim b^dmax), explaining why shallow games such as Kuhn poker show no gap, and hand-construct Beacon, a verified-but-wrong inference function that passes the gate yet loses every game. These results suggest adequacy for planning-oriented world models should be measured on the search distribution or by play directly, not by prediction accuracy on sampled transitions.