When a rhythm makes an event predictable, that event is perceived faster, and typically more accurately. However, the experiments showing this used simple tasks, and most manipulated temporal expectancy by using periodic or aperiodic precursors unrelated to stimulus and task. Three experiments tested the generality of these observations in a complex task in which rhythm was intrinsic to, rather than a precursor of, the information needed to respond: listeners averaged the laterality of a stream of noise bursts. We varied presentation rate, degree of periodicity, and average lateralisation. Decisions following a probe tone were fastest after periodic stimuli, and slowest after the most aperiodic stimuli. Without a probe tone, listeners responded sooner during periodic sequences, thus hearing less information. Periodicity did not benefit accuracy overall. This gain in speed but not accuracy for less information is not reported for simpler tasks. Neural entrainment supplemented by cognitive factors provide a tentative explanation. When the task is inherently complex and demands high attention over long durations, both expected-periodic and unexpected-aperiodic stimuli can increase response amplitude, enhancing stimulus representation, but periodicity increases confidence to respond early. Drift diffusion modelling supports this proposal: aperiodicity modulated the decision threshold, but not the drift rate or non-decision time. Together, these new data and the literature point towards task-dependent effects of temporal expectation on decision-making, showing interactions between rhythmic variance, task complexity, and sources of expectation about stimuli. We suggest the implications are worth exploring to extend understanding of rhythmicity on decision-making to everyday situations.