Large language models sometimes produce confident, plausible falsehoods (‘hallucinations’), limiting their reliability1,2. Previous work has offered numerous explanations and effective mitigations such as retrieval and tool use3, consistency-based self-verification4 and reinforcement learning from human feedback5. Nonetheless, the problem persists even in state-of-the-art language models6,7. Here we show how next-word prediction and accuracy-based evaluations inadvertently reward unwarranted guessing. Initially, next-word pretraining creates statistical pressure towards hallucination even with idealized error-free data: using learning theory8,9, we show that facts lacking repeated support in training data (such as one-off details) yield unavoidable errors, whereas recurring regularities (such as grammar) do not. Subsequent training stages aim to correct such errors. However, dominant headline metrics such as accuracy systematically reward guessing over admitting uncertainty. To align incentives, we suggest two additions to the classic approach of adding error penalties to evaluations to control abstention10,11. First, we propose ‘open rubric’ evaluations that explicitly state how errors are penalized (if at all), which test whether a model modulates its abstentions to stated stakes while optimizing accuracy. Second, as hallucination-specific benchmarks rarely make leaderboards12, we suggest using open-rubric variants of existing evaluations, to reverse their guessing incentives. Reframing hallucination as an incentive problem opens a practical path towards more reliable language models.