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The learning of first object names is deemed a hard problem due to the uncertainty inherent in mapping a heard name to the intended referent in a cluttered and variable world. However, human infants readily solve this problem. Despite considerable theoretical discussion, relatively little is known about the uncertainty infants face in the real world. We used head-mounted eye tracking during parent–infant toy play and quantified the uncertainty by measuring the distribution of infant attention to the potential referents when a parent named both familiar and unfamiliar toy objects. The results show that infant gaze upon hearing an object name is often directed to a single referent which is equally likely to be a wrong competitor or the intended target. This bimodal gaze distribution clarifies and redefines the uncertainty problem and constrains possible solutions.