Frontier black-box Large Language Model (LLM) agents are proficient at long-horizon reasoning and precise action generation. However, when it comes to a specific agentic task, they have no internalized knowledge of how that particular environment unfolds. A world model offers a natural remedy, providing the agent with environment specific knowledge by foreseeing how the environment will respond to the action it is about to take. Prior world models for LLM agents mainly predict next observations at each step, which is costly and often uninformative because individual observations provide limited task-relevant guidance and not every step requires call for foresight. This raises a key question: what a world model should predict and when should it be invoked for agentic tasks? Our pilot study suggests that world model guidance is most useful when it anticipates pitfalls within a bounded multi-step future. Motivated by this, we introduce Pitfall Anticipation World Model (PAWM), which selectively intervenes when a potential pitfall arises and predicts the impending failure to steer the agent away from it. PAWM is trained in two stages: Supervised Fine-Tuning (SFT) on synthetic data labeled with agent pitfalls, followed by GRPO co-training with a black-box LLM to further optimize it in the target environment. PAWM improves Claude Sonnet 4.5 performance by 24.3% on ScienceWorld and 7.7% on WebArena-Lite, outperforming a range of baselines. These results demonstrate that PAWM provides an effective form of world model guidance for black-box LLM agents.