Gambler’s fallacy, hot hand belief, and the time of patterns
The gambler’s fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2010-04-01
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| Series: | Judgment and Decision Making |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S193029750000098X/type/journal_article |
| _version_ | 1827831056976314368 |
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| author | Yanlong Sun Hongbin Wang |
| author_facet | Yanlong Sun Hongbin Wang |
| author_sort | Yanlong Sun |
| collection | DOAJ |
| description | The gambler’s fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition, two different statistics (mean time and waiting time) can arise from the same independent Bernoulli trials. When the coin is fair, the mean time is equal for all patterns of the same length but the waiting time is the longest for streak patterns. When the coin is biased, both mean time and waiting time change more rapidly with the probability of heads for a streak pattern than for a non-streak pattern. These facts might provide a new insight for understanding why people view streak patterns as rare and remarkable. The statistics of waiting time may not justify the prediction by the gambler’s fallacy, but paying attention to streaks in the hot hand belief appears to be meaningful in detecting the changes in the underlying process. |
| first_indexed | 2024-03-12T04:39:00Z |
| format | Article |
| id | doaj.art-4f11bfc206d9484c8e3f58b97b244d15 |
| institution | Directory Open Access Journal |
| issn | 1930-2975 |
| language | English |
| last_indexed | 2024-03-12T04:39:00Z |
| publishDate | 2010-04-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Judgment and Decision Making |
| spelling | doaj.art-4f11bfc206d9484c8e3f58b97b244d152023-09-03T09:46:15ZengCambridge University PressJudgment and Decision Making1930-29752010-04-01512413210.1017/S193029750000098XGambler’s fallacy, hot hand belief, and the time of patternsYanlong Sun0Hongbin Wang1University of Texas Health Science Center at HoustonUniversity of Texas Health Science Center at HoustonThe gambler’s fallacy and the hot hand belief have been classified as two exemplars of human misperceptions of random sequential events. This article examines the times of pattern occurrences where a fair or biased coin is tossed repeatedly. We demonstrate that, due to different pattern composition, two different statistics (mean time and waiting time) can arise from the same independent Bernoulli trials. When the coin is fair, the mean time is equal for all patterns of the same length but the waiting time is the longest for streak patterns. When the coin is biased, both mean time and waiting time change more rapidly with the probability of heads for a streak pattern than for a non-streak pattern. These facts might provide a new insight for understanding why people view streak patterns as rare and remarkable. The statistics of waiting time may not justify the prediction by the gambler’s fallacy, but paying attention to streaks in the hot hand belief appears to be meaningful in detecting the changes in the underlying process.https://www.cambridge.org/core/product/identifier/S193029750000098X/type/journal_articlegambler’s fallacyhot hand beliefheuristicsmean timewaiting time |
| spellingShingle | Yanlong Sun Hongbin Wang Gambler’s fallacy, hot hand belief, and the time of patterns Judgment and Decision Making gambler’s fallacy hot hand belief heuristics mean time waiting time |
| title | Gambler’s fallacy, hot hand belief, and the time of patterns |
| title_full | Gambler’s fallacy, hot hand belief, and the time of patterns |
| title_fullStr | Gambler’s fallacy, hot hand belief, and the time of patterns |
| title_full_unstemmed | Gambler’s fallacy, hot hand belief, and the time of patterns |
| title_short | Gambler’s fallacy, hot hand belief, and the time of patterns |
| title_sort | gambler s fallacy hot hand belief and the time of patterns |
| topic | gambler’s fallacy hot hand belief heuristics mean time waiting time |
| url | https://www.cambridge.org/core/product/identifier/S193029750000098X/type/journal_article |
| work_keys_str_mv | AT yanlongsun gamblersfallacyhothandbeliefandthetimeofpatterns AT hongbinwang gamblersfallacyhothandbeliefandthetimeofpatterns |