A Computational Toolkit for Designing and Analysing Repeated Binary Choice Experiments

Adaptive human behaviour depends on the ability to detect regularities and probabilistic structures within a noisy environment. Repeated binary choice tasks, in which individuals predict one of two possible options, have long served as a fundamental tool for investigating learning, reward processing, and decision-making under uncertainty. However, traditional analyses of these tasks often rely on coarse measures such as accuracy or mean responses, overlooking the temporal information contained in behavioural sequences. This paper introduces a mathematical and computational framework to improve the analysis of binary choice data. First, we employ higher-order Markov chains to generate sequences with controlled probabilistic dependencies, allowing for a more subtle examination of how participants extract information and learn temporal structures. Presenting analytical methods derived from time series analysis (autocorrelation, cross---correlation, shifting probabilities and Markov reconstruction) to extract structural information from simulated data of prototypical behaviours, we demonstrate how these methods can identify distinct decisional patterns that remain hidden when using conventional approaches. Finally, we validate the proposed toolkit by applying it to empirical datasets. By revealing subtle but meaningful features of sequential decision-making, this framework enhances the interpretive power of probabilistic learning experiments. It provides researchers with tools to more accurately describe behavioural dynamics and deepens our understanding of the cognitive processes governing adaptive decisions in both healthy and clinical populations.