According to the Accumulation of Evidence (AE) framework, reliable perceptual decisions are forged by integrating the evidence provided by each sensory sample independently of other samples. However, that framework, grounded on the mathematical formulation of the Sequential Ratio Probability Test (SPRT), does not consider that sensory samples can be conditionally dependent (i.e. partially redundant). Partial redundancies are ubiquitous in naturalistic environments. In such case, the normative framework is what we call the Accumulation of Unpredicted Evidence (AUE). In AUE, the current belief is updated with the part of the stimulus evidence not predicted by previous samples (unpredicted evidence) and not the raw stimulus evidence. We tested the AUE model in an auditory accumulation reaction-time task in humans where we introduced sequential correlations between pairs of successive tones within each stimulus sequence. The AE model predicts that first and second tones in a pair (unpredictable and predictable tones, UT and PT) should have equal impact on perception. By contrast, in AUE, PTs impact on current belief is smaller, because part of PT evidence can be predicted from the previous tone. Participants reaction time distributions revealed that the decision threshold was more frequently reached after an UT rather than PT presentation, in agreement with AUE. Moreover, a late central positivity EEG signal, previously associated with evidence integration, showed a much stronger response to evidence in UTs than in PTs, a clear indication that the brain accumulates Unpredicted Evidence. On the other hand, an earlier component corresponding to the Mismatch Negativity (MMN) encoded the sensory surprise associated with each tone, irrespective of its behavioral relevance. Overall, participants’ behaviour and neural activations confirm that human perception relies on the accumulation of unpredicted evidence, where predictive processes interact with classical temporal integration. This shows that the brain tracks complex statistical regularities to guide behavior.