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We propose that these judgment patterns arise from the observer's mental models of the sequence\u2010generating 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\u2010directed actor, and a financial market. We systematically manipulated participants\u2019 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 &amp; Kahneman's Law of Small Numbers.<\/jats:p>","DOI":"10.1111\/cogs.13211","type":"journal-article","created":{"date-parts":[[2023,1,21]],"date-time":"2023-01-21T08:18:52Z","timestamp":1674289132000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler's Fallacy Reasoning"],"prefix":"10.1111","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5027-8233","authenticated-orcid":false,"given":"Kariyushi","family":"Rao","sequence":"first","affiliation":[{"name":"Department of Behavioral Science The University of Chicago Booth School of Business Chicago United\u00a0States"},{"name":"Behavioural Science Group Warwick Business School, University of Warwick Coventry United Kingdom"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Reid","family":"Hastie","sequence":"additional","affiliation":[{"name":"Department of Behavioral Science The University of Chicago Booth School of Business Chicago United\u00a0States"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2023,1,21]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/13546780600717244"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cogsys.2004.09.002"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0732-3123(99)00018-8"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0049023"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1006\/obhd.1995.1099"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1090.1059"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/1612197X.2013.773661"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/bdm.3960020403"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.3758\/BF03206327"},{"key":"e_1_2_11_11_1","volume-title":"Hedge fund flows and performance streaks: How investors weigh information (No. ESMT\u201015\u201001)","author":"Baquero G.","year":"2015"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.psychsport.2006.03.001"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(91)90029-I"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-405X(98)00027-0"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/bdm.676"},{"key":"e_1_2_11_16_1","first-page":"1","volume-title":"Research on teaching and learning probability","author":"Batanero C.","year":"2016"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1002\/bdm.596"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-405X(02)00147-2"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0022372"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-1465-0_9"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0749-5978(03)00064-5"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jesp.2018.03.006"},{"issue":"441","key":"e_1_2_11_23_1","first-page":"359","article-title":"Irrational analysts\u2019 expectations as a cause of excess volatility in stock prices","volume":"107","author":"Bulkley G.","year":"1997","journal-title":"Royal Economic Society"},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cogpsych.2003.07.003"},{"key":"e_1_2_11_25_1","unstructured":"Burns B. 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