Occurrence and nonoccurrence of random sequences: comment on Hahn and Warren (2009)

On the basis of the statistical concept of waiting time and on computer simulations of the "probabilities of nonoccurrence" (p. 457) for random sequences, Hahn and Warren (2009) proposed that given people's experience of a finite data stream from the environment, the gambler's fallacy is not as gross an error as it might seem. We deal with two critical issues in Hahn and Warren's argument, a possible ambiguity in distinguishing the events of occurrence and nonoccurrence, and an incomplete consideration of the context in which the statistics of waiting time are defined. Our analyses show that the statistics of waiting time and the probabilities of nonoccurrence, once correctly interpreted, do not vindicate the error in the gambler's fallacy.