Statistical analysis of the results of real dice rolls using the object detection model in the context of the Central Limit Theorem

The study conducted an analysis of the convergence of the distribution of sums of real dice-roll results toward the normal distribution in the context of the Central Limit Theorem. The data were obtained from video recordings, and the roll results were identified using the YOLOv8 object detection model. The influence of the original distribution and detection errors on the rate of convergence was examined. A dedicated fitting metric, S_n,k, based on the least squares method, was employed. The results confirmed convergence to the normal distribution even for small number of samples, achieving a repeatable and stable level of the S_n,k metric. The study also demonstrated the robustness of the process to minor data perturbations.