Bayesian mathematics provides a tool for combining 14C dating results on findings from an archaeological context with independent archaeological information such as the chronological order, which may be inferred from stratigraphy. The goal is to arrive at both a more precise and a more accurate date. However, by means of simulated measurements we will show that specific assumptions about prior probabilities - implemented in calibration programs and hidden to the user - may create artifacts. This may result in dates with higher precision but lower accuracy, which are no longer in agreement with the true ages of the findings.