Waiting time distributions reveal natural “period” of humans in random number generation tasks

Abstract

Humans introduce a bias in random number generation (RNG) tasks, making a completely random human-generated sequence impossible without post-processing. Instead of an exponential distribution characteristic of random events, human generated sequences show a universal trend of having a mode at seven, termed the “period” T of human RNG. Two post-processing procedures that are based on T are shown to be successful at producing completely random sequences that follow exponential waiting times: (1) stitching seven independently-generated sequences by different individuals; and (2) shuffling the raw sequence by taking every seventh digit at a time.