The aim of the paper was to discuss the accuracy of the multiple indexes used for random sequences generation results calculation. In the first part of the paper the models explaining deviations from randomness were presented. The key role of the structural limitations interpretation was suggested. Secondly, the multiple indexes of the deviation from randomness used in random sequence generation task studies were presented. The authors concluded that too many indexes are used in the studies of deviation from randomness. In order to avoid such problems two indexes were proposed: entropy and correlation function. The last part of the paper presents the preliminary version of the mathematical of random sequences generation in which the limited capacity of the short-term memory assumption was introduce.