@article{TEXTUAL,
      recid = {5436},
      author = {Rao, Kariyushi and Hastie, Reid},
      title = {Predicting Outcomes in a Sequence of Binary Events: Belief  Updating and Gambler's Fallacy Reasoning},
      journal = {Cognitive Science},
      address = {2023-01-21},
      number = {TEXTUAL},
      abstract = {Beliefs like the Gambler's Fallacy and the Hot Hand have  interested cognitive scientists, economists, and  philosophers for centuries. We propose that these judgment  patterns arise from the observer's mental models of the  sequence-generating mechanism, moderated by the strength of  belief in an a priori base rate. In six behavioral  experiments, participants observed one of three mechanisms  generating sequences of eight binary events: a random  mechanical device, an intentional goal-directed actor, and  a financial market. We systematically manipulated  participants’ beliefs about the base rate probabilities at  which different outcomes were generated by each mechanism.  Participants judged 18 sequences of outcomes produced by a  mechanism with either an unknown base rate, a specified  distribution of three equiprobable base rates, or a  precise, fixed base rate. Six target sequences ended in  streaks of between two and seven identical outcomes. The  most common predictions for subsequent events were best  described as pragmatic belief updating, expressed as an  increasingly strong expectation that a streak of identical  signals would repeat as the length of that streak  increased. The exception to this pattern was for sequences  generated by a random mechanical device with a fixed base  rate of .50. Under this specific condition, participants  exhibited a bias toward reversal of streaks, and this bias  was larger when participants were asked to make a  dichotomous choice versus a numerical probability rating.  We review alternate accounts for the anomalous judgments of  sequences and conclude with our favored interpretation that  is based on Rabin's version of Tversky & Kahneman's Law of  Small Numbers.},
      url = {http://knowledge.uchicago.edu/record/5436},
}