Skip to main content

Betting on Illusory Patterns: Probability Matching in Habitual Gamblers

Abstract

Why do people gamble? A large body of research suggests that cognitive distortions play an important role in pathological gambling. Many of these distortions are specific cases of a more general misperception of randomness, specifically of an illusory perception of patterns in random sequences. In this article, we provide further evidence for the assumption that gamblers are particularly prone to perceiving illusory patterns. In particular, we compared habitual gamblers to a matched sample of community members with regard to how much they exhibit the choice anomaly ‘probability matching’. Probability matching describes the tendency to match response proportions to outcome probabilities when predicting binary outcomes. It leads to a lower expected accuracy than the maximizing strategy of predicting the most likely event on each trial. Previous research has shown that an illusory perception of patterns in random sequences fuels probability matching. So does impulsivity, which is also reported to be higher in gamblers. We therefore hypothesized that gamblers will exhibit more probability matching than non-gamblers, which was confirmed in a controlled laboratory experiment. Additionally, gamblers scored much lower than community members on the cognitive reflection task, which indicates higher impulsivity. This difference could account for the difference in probability matching between the samples. These results suggest that gamblers are more willing to bet impulsively on perceived illusory patterns.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

Notes

  1. Note that the education was slightly higher among community members, t(1,159) = 1.82, p = .071. Including education as a control variable in any of the subsequent analyses did not alter the results in any important way.

  2. Note that actual guessing would be at about 50 %, and most participants in that category were around that value. Yet the extremely few participants who consistently predicted the less event more often (i.e., below 50 %) were included in this category as (1) there were so few of them that an extra category was not warranted and (2) their behavior is similar to guessing in the sense that they have not learnt to perform well in the task.

  3. d expresses the difference between two means in terms of its (pooled) standard deviation. See Cohen (1992) for details.

  4. “The \(\upeta_{\text{p}}^{2}\) statistic is simply the ratio of the sum of squares for the particular variable under consideration divided by the total of that sum of squares and the sum of squares of the relevant error term. It describes the proportion of variability associated with an effect when the variability associated with all other effects identified in the analysis has been removed from consideration.” (Fritz et al. 2012, p. 8).

References

  • Bar-Hillel, M., & Wagenaar, W. A. (1991). The perception of randomness. Advances in Applied Mathematics, 12, 428–454.

    Article  Google Scholar 

  • Bechara, A. (2001). Risky business: Emotion, decision-making, and addiction. Journal of Gambling Studies, 19, 23–51.

    Article  Google Scholar 

  • Blanchard, T. C., Wilke, A., & Hayden, B. Y. (2014). Hot hand bias in rhesus monkeys. Journal of Experimental Psychology: Animal Learning and Cognition, 40, 280–286.

    Google Scholar 

  • Clark, L., Studer, B., Bruss, J., Tranel, D., & Bechara, A. (2014). Damage to insula abolishes cognitive distortions during simulated gambling. Proceedings of the National Academy of Sciences of the USA, 111, 6098–6103.

    PubMed Central  Article  CAS  PubMed  Google Scholar 

  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155–159.

    Article  CAS  PubMed  Google Scholar 

  • Croson, R., & Sundali, J. (2005). The gambler’s fallacy and the hot hand: Empirical data from Casinos. Journal of Risk and Uncertainty, 30, 195–209.

    Article  Google Scholar 

  • Ellery, M., & Stewart, S. H. (2014). Alcohol affects video lottery terminal (VLT) gambling behaviors and cognitions differently. Psychology of Addictive Behaviors, 28, 206–216.

    Article  PubMed  Google Scholar 

  • Falk, R., & Konold, C. (1997). Making sense of randomness: Implicit encoding as a basis for judgment. Psychological Review, 104, 301–318.

    Article  Google Scholar 

  • Fawcett, T. W., Fallenstein, B., Higginson, A. D., Houstan, A. I., Mallpress, D. E. W., Trimmer, P. C., & McNamara, J. M. (2014). The evolution of decision rules in complex environments. Trends in Cognitive Sciences, 18, 153–161.

    Article  PubMed  Google Scholar 

  • Fortune, E. E., & Goodie, A. S. (2012). Cognitive distortions as a component and treatment focus of pathological gambling: A review. Psychology of Addictive Behaviors, 26, 298–310.

    Article  PubMed  Google Scholar 

  • Frederick, S. (2005). Cognitive reflection and decision making. Journal of Economic Perspectives, 19, 25–42.

    Article  Google Scholar 

  • Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations, and interpretation. Journal of Experimental Psychology: General, 141, 2–18.

    Article  Google Scholar 

  • Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416–422.

    Article  PubMed  Google Scholar 

  • Gaissmaier, W., Schooler, L. J., & Mata, R. (2008). An ecological perspective to cognitive limits: Modeling environment-mind interactions with ACT-R. Judgment and Decision Making, 3, 278–291.

    Google Scholar 

  • Gaissmaier, W., Schooler, L. J., & Rieskamp, J. (2006). Simple predictions fueled by capacity limitations: When are they successful? Journal of Experimental Psychology. Learning, Memory, and Cognition, 32, 966–982.

    Article  PubMed  Google Scholar 

  • Gal, I., & Baron, J. (1996). Understanding repeated choices. Thinking and Reasoning, 2, 81–98.

    Article  Google Scholar 

  • Gervais, W. M., & Norenzayan, A. (2012). Analytic thinking promotes religious disbelief. Science, 336, 493–496.

    Article  CAS  PubMed  Google Scholar 

  • Goodie, A. S. (2005). The role of perceived control and overconfidence in pathological gambling. Journal of Gambling Studies, 21, 481–502.

    Article  PubMed  Google Scholar 

  • Goodie, A. S., & Fortune, E. E. (2013). Measuring cognitive distortions in pathological gambling: Review and meta-analyses. Psychology of Addictive Behaviors, 27, 730–743.

    Article  PubMed  Google Scholar 

  • Green, D. M., & Swets, J. A. (1966). Signal detection theory and psychophysics (Vol. 1). New York, NY: Wiley.

    Google Scholar 

  • Haselton, M. G., Bryant, G. A., Wilke, A., Frederick, D. A., Galperin, A., Frankenhuis, W. E., & Moore, T. (2009). Adaptive rationality: An evolutionary perspective on cognitive bias. Social Cognition, 27, 733–763.

    Article  Google Scholar 

  • Healy, A. F., & Kubovy, M. (1981). Probability matching and the formation of conservative decision rules in a numerical analog of signal detection. Journal of Experimental Psychology: Human Learning and Memory, 7, 344–354.

    Google Scholar 

  • James, G., & Koehler, D. J. (2011). Banking on a bad bet: Probability matching in risky choice is linked to expectation generation. Psychological Science, 22, 707–711.

    Article  PubMed  Google Scholar 

  • Jefferson, S., & Nicki, R. (2003). A new instrument to measure cognitive distortions in video lottery terminal users: The informational biases scale (IBS). Journal of Gambling Studies, 19, 387–403.

    Article  PubMed  Google Scholar 

  • Joukhador, J., Blaszczynski, A., & MacCallum, F. (2004). Superstitious beliefs in gambling among problem and non-problem gamblers: Preliminary data. Journal of Gambling Studies, 20, 171–180.

    Article  PubMed  Google Scholar 

  • Kareev, Y., & Trope, Y. (2011). Correct acceptance weighs more than correct rejection: A decision bias induced by question framing. Psychonomic Bulletin and Review, 18, 103–109.

    Article  PubMed  Google Scholar 

  • Kessler, R. C., Hwang, I., LaBrie, R., Petukhova, M., Sampson, N. A., Winters, K. C., et al. (2008). DSM-IV pathological gambling in the National Comorbidity Survey Replication. Psychological Medicine, 38, 1351–1360.

    PubMed Central  CAS  PubMed  Google Scholar 

  • Koehler, D. J., & James, G. (2009). Probability-matching in choice under uncertainty: Intuition versus deliberation. Cognition, 113, 123–127.

    Article  PubMed  Google Scholar 

  • Koehler, D. J., & James, G. (2010). Probability matching and strategy availability. Memory and Cognition, 38, 667–676.

    Article  PubMed  Google Scholar 

  • Lakey, C. E., Rose, P., Campbell, W. K., & Goodie, A. S. (2008). Probing the link between narcissism and gambling: The mediating role of judgment and decision-making biases. Journal of Behavioral Decision Making, 21, 113–137.

    Article  Google Scholar 

  • Lopes, L. L. (1982). Doing the impossible: A note on induction and the experience of randomness. Journal of Experimental Psychology. Learning, Memory, and Cognition, 8, 626–636.

    Article  Google Scholar 

  • MacLaren, V. V., Fugelsang, J., Harrigan, K. A., & Dixon, M. J. (2011). The personality of pathological gamblers: A meta-analysis. Clinical Psychology Review, 31(6), 1057–1067.

    Article  PubMed  Google Scholar 

  • MacLaren, V. V., Fugelsang, J. A., Harrigan, K. A., & Dixon, M. J. (2012). Effects of impulsivity, reinforcement sensitivity, and cognitive style on pathological gambling symptoms among frequent slot machine players. Personality and Individual Differences, 52, 390–394.

    Article  Google Scholar 

  • Marmurek, H. H. C., Switzer, J., & D’Alvise, J. (2015). Impulsivity, gambling cognitions and the gambler’s fallacy in university students. Journal of Gambling Studies, 31, 197–210.

    Article  PubMed  Google Scholar 

  • Mata, R., Schooler, L., & Rieskamp, J. (2007). The aging decision maker: Cognitive aging and the adaptive selection of decision strategies. Psychology and Aging, 22, 796–810.

    Article  PubMed  Google Scholar 

  • Michalczuk, R., Bowden-Jones, H., Verdejo-Garcia, A., & Clark, L. (2011). Impulsivity and cognitive distortions in pathological gamblers attending the UK National Problem Gambling Clinic: A preliminary report. Psychological Medicine, 41, 2625–2635.

    PubMed Central  Article  CAS  PubMed  Google Scholar 

  • Miedl, S. F., Buechel, C., & Peters, J. (2014). Cue-induced craving increases impulsivity via changes in striatal value signals in problem gamblers. Journal of Neuroscience, 34, 4750–4755.

    Article  CAS  PubMed  Google Scholar 

  • Myers, J. L. (1976). Probability learning and sequence learning. In W. K. Estes (Ed.), Handbook of learning and cognitive processes: Approaches to human learning and motivation (pp. 171–205). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Navarette, G., Santamaria, C., & Froimovitch, D. (2015). Small samples in evolution: Did the law of small numbers arise as an adaptation to environmental challenges? Frontiers in Evolutionary Psychology and Neuroscience, 6, 1–3.

    Google Scholar 

  • Newell, B. R., Koehler, D. J., James, G., Rakow, T., & van Ravenzwaaij, D. (2013). Probability matching in risky choice: The interplay of feedback and strategy availability. Memory and Cognition, 41, 329–338.

    Article  PubMed  Google Scholar 

  • Newell, B. R., & Rakow, T. (2007). The role of experience in decisions from description. Psychonomic Bulletin and Review, 14, 1133–1139.

    Article  PubMed  Google Scholar 

  • Otto, A. R., Taylor, E. G., & Markman, A. B. (2011). There are at least two kinds of probability matching: Evidence from a secondary task. Cognition, 118, 274–279.

    Article  PubMed  Google Scholar 

  • Pennycook, G., Cheyne, J. A., Seli, P., Koehler, D. J., & Fugelsang, J. A. (2012). Analytic cognitive style predicts religious and paranormal belief. Cognition, 123, 335–346.

    Article  PubMed  Google Scholar 

  • Rakow, T., Newell, B. R., & Zougkou, K. (2010). The role of working memory in information acquisition and decision making: Lessons from the binary prediction task. Quarterly Journal of Experimental Psychology, 63, 1335–1360.

    Article  Google Scholar 

  • Rogers, P. (1998). The cognitive psychology of lottery gambling: A theoretical review. Journal of Gambling Studies, 14, 111–134.

    Article  PubMed  Google Scholar 

  • Scheibehenne, B., & Studer, B. (2014). A hierarchical Bayesian model of the influence of run length on sequential predictions. Psychonomic Bulletin and Review, 20, 211–217.

    Article  Google Scholar 

  • Scheibehenne, B., Wilke, A., & Todd, P. M. (2011). Expectations of clumpy resources influence predictions of sequential events. Evolution and Human Behavior, 32, 326–333.

    Article  Google Scholar 

  • Shaffer, H. J., Hall, M. N., & Bilt, J. V. (1997). Estimating the prevalence of disordered gambling behavior in the United States and Canada: A meta-analysis. Boston, MA: Harvard Medical School.

    Google Scholar 

  • Shaffer, H. J., Peller, A. J., LaPlante, D. A., Nelson, S. E., & LaBrie, R. A. (2010). Toward a paradigm shift in internet gambling research: From opinion and self-report to actual behavior. Addiction Research and Theory, 18, 270–283.

    Article  Google Scholar 

  • Shanks, D. R., Tunney, R. J., & McCarthy, J. D. (2002). A re-examination of probability matching and rational choice. Journal of Behavioral Decision Making, 15, 233–250.

    Article  Google Scholar 

  • Shenhav, A., Rand, D. G., & Greene, J. D. (2012). Divine intuition: Cognitive style influences belief in god. Journal of Experimental Psychology: General, 141, 423–428.

    Article  Google Scholar 

  • Slutske, W. S., Moffitt, T. E., Poulton, R., & Caspi, A. (2012). Undercontrolled temperament at age 3 predicts disordered gambling at age 32: A longitudinal study of a complete birth cohort. Psychological Science, 23, 510–516.

    PubMed Central  Article  PubMed  Google Scholar 

  • Stinchfield, R. (2002). Reliability, validity, and classification accuracy of the South Oaks Gambling Screen (SOGS). Addictive Behaviors, 27, 1–19.

    Article  PubMed  Google Scholar 

  • Studer, B., Limbrick-Oldfield, E. H., & Clark, L. (2014). “Put your money where your mouth is!” Effects of streaks on confidence and betting in a binary choice task. Journal of Behavioral Decision Making. doi:10.1002/bdm.1844.

    PubMed Central  Google Scholar 

  • Tombaugh, T. N. (2004). Trail making test A and B: Normative data stratified by age and education. Archives of Clinical Neuropsycholology, 19, 203–214.

    Article  Google Scholar 

  • Toplak, M. E., Liu, E., MacPherson, R., Toneatto, T., & Stanovich, K. E. (2007). The reasoning skills and thinking dispositions of problem gamblers: A dual-process taxonomy. Journal of Behavioral Decision Making, 20, 103–124.

    Article  Google Scholar 

  • Unturbe, J., & Corominas, J. (2007). Probability matching involves rule-generating ability: A neuropsychological mechanism dealing with probabilities. Neuropsychology, 21, 621–630.

    Article  PubMed  Google Scholar 

  • Vulkan, N. (2000). An economist’s perspective on probability matching. Journal of Economic Surveys, 14, 101–118.

    Article  Google Scholar 

  • West, R. F., & Stanovich, K. E. (2003). Is probability matching smart? Associations between probabilistic choices and cognitive ability. Memory and Cognition, 31, 243–251.

    Article  Google Scholar 

  • Wilke, A., & Barrett, H. C. (2009). The hot hand phenomenon as a cognitive adaptation to clumped resources. Evolution and Human Behavior, 30, 161–169.

    Article  Google Scholar 

  • Wilke, A., Scheibehenne, B., Gaissmaier, W., McCanney, P., & Barrett, H. C. (2014). Illusionary pattern detection in habitual gamblers. Evolution and Human Behavior, 35, 291–297.

    Article  Google Scholar 

  • Wilke, A., & Todd, P. M. (2012). The evolved foundations of decision making. In M. K. Dhami, A. Schlottmann, & M. Waldmann (Eds.), Judgment and decision making as a skill: Learning, development and evolution (pp. 3–27). Cambridge: Cambridge University Press.

    Google Scholar 

  • Wolford, G., Miller, M. B., & Gazzaniga, M. (2000). The left hemisphere’s role in hypothesis formation. The Journal of Neuroscience, 20(RC64), 1–4.

    Google Scholar 

  • Wolford, G., Newman, S., Miller, M. B., & Wig, G. (2004). Searching for patterns in random sequences. Canadian Journal of Experimental Psychology, 58, 221–228.

    Article  PubMed  Google Scholar 

  • Yellott, J. I, Jr. (1969). Probability learning with noncontingent success. Journal of Mathematical Psychology, 6, 541–575.

    Article  Google Scholar 

  • Zhao, J., Hahn, U., & Osherson, D. (2014). Perception and identification of random events. Human Perception and Performance, 40, 1358–1371.

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

We thank the members of the Evolution and Cognition Lab at Clarkson University for their help in data collection, Dominique Schmidt for programming the experiment, and the executive director of the St. Regis Mohawk Tribal Gaming Commission Todd Papineau for his support. The research was supported by grants from the National Center for Responsible Gaming and the T. Urling and Mabel Walker Research Fellowship Program of Northern New York that were awarded to the second author.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wolfgang Gaissmaier.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gaissmaier, W., Wilke, A., Scheibehenne, B. et al. Betting on Illusory Patterns: Probability Matching in Habitual Gamblers. J Gambl Stud 32, 143–156 (2016). https://doi.org/10.1007/s10899-015-9539-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10899-015-9539-9

Keywords

  • Gambling disorder
  • Pathological gambling
  • Probability matching
  • Cognitive reflection task
  • Misperception of randomness