Many errors in probabilistic judgment have been attributed to people's inability to think in statistical terms when faced with information about a single case. Prior theoretical analyses and empirical results imply that the errors associated with case-specific reasoning may be reduced when people make frequentistic predictions about a set of cases. In studies of three previously identified cognitive biases, we find that frequency-based predictions are different from—but no better than—case-specific judgments of probability. First, in studies of the "planning fallacy," we compare the accuracy of aggregate frequency and case-specific probability judgments in predictions of students' real-life projects. When aggregate and single-case predictions are collected from different respondents, there is little difference between the two: Both are overly optimistic and show little predictive validity. However, in within-subject comparisons, the aggregate judgments are significantly more conservative than the single-case predictions, though still optimistically biased. Results from studies of overconfidence in general knowledge and base rate neglect in categorical prediction underline a general conclusion. Frequentistic predictions made for sets of events are no more statistically sophisticated, nor more accurate, than predictions made for individual events using subjective probability.