Abstract
<title>Abstract</title> <p> The Theory of Subjective Entropy formalises apparent randomness as a property not of the source alone, but of the relation between a sequence and the internal model of the agent that perceives it. We treat cognition as compression of information and operationalise the concept of <italic>subjective entropy</italic> using the Context-Tree Weighting (CTW) algorithm, yielding a model-relative code length (or algorithmic complexity) for finite binary sequences. Consequently, we define sub-entropic (compressible) and super-entropic (incompressible) structure relative to a compression threshold, which partitions the sequence into a set of <italic>entropic regions</italic> .Across two online experiments, participants predicted the next symbol in randomly generated binary sequences while receiving feedback. Sequences were generated to have near-maximal Shannon entropy while varying in subjective entropy, allowing classical and model-relative accounts of predictability to be dissociated. Trial-level analyses showed that higher CTW complexity predicted lower probability of a correct response, and control models showed that this effect was not reducible to symbol frequency-tracking alone. Region-level analyses indicated that greater compressibility predicted higher accuracy in sub-entropic regions specifically and that deeper structure becomes increasingly behaviourally relevant when sustained over longer spans of trials.These findings support the central claim that even globally random sequences may contain locally compressible structure that is <italic>not</italic> subjectively random to the observer’s internal model. Ultimately, this framework is intended not merely as an account of sequence prediction, but as a universal formal language for quantifying randomness and information processing in cognitive systems. </p>