The 'certainty effect' is a notable violation of expected utility theory by decision makers. It shows that people's tendency to select the safer of two prospects increases when this prospect provides a good outcome with certainty (for example, people prefer a monetary gain of 3 with certainty over 4 with a probability of 0.8, but do not prefer 3 with a probability of 0.25 over 4 with a probability of 0.2). Subsequent work on experience-based decision making in rats extended the certainty effect to other animals, suggesting its generality across different species and different decision-making mechanisms. However, an attempt to replicate this study with human subjects showed a surprising 'reversed certainty effect', namely, the tendency to prefer the safer option decreases when this prospect is associated with certainty (and people now prefer 4 with a probability of 0.8 over 3 with certainty). Here we show that these conflicting results can be explained by perceptual noise and that the certainty effect can be restored experimentally by reducing perceptual accuracy. Using complementary experiments in humans and honeybees (Apis mellifera), we show that by manipulating perceptual accuracy in experience-based tasks, both the certainty and the reversed certainty effects can be exhibited by humans and other animals: the certainty effect emerges when it is difficult to discriminate between the different rewards, whereas the reversed certainty effect emerges when discrimination is easy. Our results fit a simple process-based model of matching behaviour, capable of explaining the certainty effect in humans and other animals that make repeated decisions based on experience. This mechanism should probably be distinguished from those involved in the original certainty effect that was exhibited by human subjects in single description-based problems.