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A stochastic revelation on the deterministic morphological change of 3x+1

From the probabilistic perspective, we present an analysis on potential incurred chances of division by “2” without reminder during a single process of the conjuncture of “3x + 1” in different sections of the binary expression of an input number. We revealed the difference of the tail section and the other parts for a large input number. Based on the ratio of the difference of the change of different sections of the expression with randomly assigned values in a single process, we identified the decreasing tendency of the input number.