Journal of Gambling Studies

, Volume 31, Issue 1, pp 133–160 | Cite as

Erroneous Gambling-Related Beliefs as Illusions of Primary and Secondary Control: A Confirmatory Factor Analysis

  • Anastasia EjovaEmail author
  • Paul H. Delfabbro
  • Daniel J. Navarro
Original Paper


Different classification systems for erroneous beliefs about gambling have been proposed, consistently alluding to ‘illusion of control’ and ‘gambler’s fallacy’ categories. None of these classification systems have, however, considered the how the illusion of control and the gambler’s fallacy might be interrelated. In this paper, we report the findings of a confirmatory factor analysis that examines the proposal that most erroneous gambling-related beliefs can be defined in terms of Rothbaum et al.’s (J Pers Soc Psychol, doi: 10.1037/0022-3514.42.1.5, 1982) distinction between ‘primary’ and ‘secondary’ illusory control, with the former being driven to a large extent by the well-known gambler’s fallacy and the latter being driven by a complex of beliefs about supernatural forces such as God and luck. A survey consisting of 100 items derived from existing instruments was administered to 329 participants. The analysis confirmed the existence of two latent structures (beliefs in primary and secondary control), while also offering support to the idea that gambler’s fallacy-style reasoning may underlie both perceived primary control and beliefs about the cyclical nature of luck, a form of perceived secondary control. The results suggest the need for a greater focus on the role of underlying processes or belief structures as factors that foster susceptibility to specific beliefs in gambling situations. Addressing and recognising the importance of these underlying factors may also have implications for cognitive therapy treatments for problem gambling.


Gambling-related beliefs Illusion of control Gambler’s fallacy Luck Factor analysis 



We thank Nancy Briggs for invaluable help with fine-tuning the CFA, and members of our Computational Cognitive Science Lab, especially Dinis Gokaydin, Matthew Welsh and Rachel Stephens, for very fruitful discussions of the gambler’s fallacy.


  1. Aasved, M. (2002). The psychodynamics and psychology of gambling: The gambler’s mind. Springfield, Illinois: Charles C. Thomas Publisher, Ltd.Google Scholar
  2. Anderson, J. R. (1993). Problem solving and learning. American Psychologist. doi: 10.1037/0003-066X.48.1.35.
  3. Atran, S., & Norenzayan, A. (2004). Religion’s evolutionary landscape: Counterintuition, commitment, compassion, communion. Behavioral and Brain Sciences. doi: 10.1017/S0140525X04000172.PubMedGoogle Scholar
  4. Ayton, P., & Fisher, I. (2004). The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness? Memory & Cognition. doi: 10.3758/BF03206327.Google Scholar
  5. Bar-Hillel, M., & Neter, E. (1996). Why are people reluctant to exchange lottery tickets? Journal of Personality and Social Psychology. doi: 10.1037/0022-3514.70.1.17.
  6. Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment Research & Evaluation.
  7. Cummins, R. A., & Nistico, H. (2002). Maintaining life satisfaction: The role of positive cognitive bias. Journal of Happiness Studies. doi: 10.1023/A:1015678915305.Google Scholar
  8. Curran, P. J., West, S. G., & Finich, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods. doi: 10.1037/1082-989X.1.1.16.Google Scholar
  9. Darke, P. R., & Freedman, J. L. (1997). The belief in good luck scale. Journal of Research in Personality. doi: 10.1006/jrpe.1997.2197.
  10. Delfabbro, P. H. (2004). The stubborn logic of regular gamblers: Obstacles and dilemmas in cognitive gambling research. Journal of Gambling Studies. doi: 10.1023/B:JOGS.0000016701.17146.d0.
  11. DiStefano, C., Zhu, M., & Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation. Accessed 20 November 2012.
  12. Ejova, A., Delfabbro, P., & Navarro, D. (2010). The illusion of control: Structure, measurement and dependence on reinforcement frequency in the context of a laboratory gambling task. In W. Christensen, E. Schier, & J. Sutton (Eds.), ASCS09: Proceedings of the 9th conference of the Australasian society for cognitive science (pp. 84–92). Sydney: Macquarie Centre for Cognitive Science. doi:  10.5096/ASCS200914.
  13. Estes, W. K. (1964). Probability learning. In A. W. Melton (Ed.), Categories of human learning (pp. 88–128). New York: Academic Press.Google Scholar
  14. Ferris, J., & Wynne, H. (2001). The Canadian problem gambling index: Final report. Ottawa: Canadian Centre on Substance Abuse.Google Scholar
  15. Floyd, F. J., & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment. doi: 10.1037/1040-3590.7.3.286.
  16. Fortune, E. F., & Goodie, A. S. (2012). Cognitive distortions as a component and treatment focus of pathological gambling: A review. Psychology of Addictive Behaviors. doi: 10.1037/a0026422.PubMedGoogle Scholar
  17. Fox, J., Nie, Z., & Byrnes, J. (2012). sem: Structural Equation Models. R package version 3.0-0.
  18. Goodie, A. S., & Fortune, E. F. (2013). Measuring cognitive distortions in pathological gambling: Review and meta-analyses. Psychology of Addictive Behaviors. doi: 10.1037/a0031892.PubMedGoogle Scholar
  19. Griffiths, M. D. (1994). The role of cognitive bias and skill in fruit machine gambling. British Journal of Psychology. doi: 10.1111/j.2044-8295.1994.tb02529.x.Google Scholar
  20. Hahn, U., & Warren, P. A. (2009). Perceptions of randomness: Why three heads are better than four. Psychological Review. doi: 10.1037/a0015241.PubMedGoogle Scholar
  21. Henslin, J. M. (1967). Craps and magic. American Journal of Sociology. Accessed 20 November 2012.
  22. Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural equation modelling: Guidelines for determining model fit. Electronic Journal of Business Research Methods, 6(1), 53–60.Google Scholar
  23. Jahoda, G. (1969). The psychology of superstition. London: Allen Lane, Penguin Press.Google Scholar
  24. 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. doi: 10.1023/A:1026327926024.PubMedGoogle Scholar
  25. Joukhador, J., Blaszczynski, A., & Maccallum, F. (2004). Superstitious beliefs in gambling among problem and non-problem gamblers: Preliminary data. Journal of Gambling Studies. doi: 10.1023/B:JOGS.0000022308.27774.2b.
  26. Joukhador, J., Maccallum, F., & Blaszczynski, A. (2003). Differences in cognitive distortions between problem and social gamblers. Psychological Reports. doi: 10.2466/pr0.2003.92.3c.1203.
  27. Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology. doi: 10.1016/0010-0285(72)90016-3.Google Scholar
  28. Keren, G., & Wagenaar, W. A. (1985). On the psychology of playing blackjack: Normative and descriptive considerations with implications for decision theory. Journal of Experimental Psychology: General. doi:  10.1037/0096-3445.114.2.133.
  29. King, J. M. (1990). Neutralizing marginally deviant behaviour: Bingo players and superstition. Journal of Gambling Studies. doi: 10.1007/BF01015748.PubMedGoogle Scholar
  30. Kline, R. B. (2010). Principles and practice of structural equation modeling (3rd ed.). New York: The Guilford Press.Google Scholar
  31. Ladouceur, R., Sylvain, C., Boutin, C., & Doucet, C. (2002). Understanding and treating the pathological gambler. London: Wiley.Google Scholar
  32. Ladouceur, R., Sylvain, C., Boutin, C., Lachance, S., Doucet, C., Leblond, J., et al. (2001). Cognitive treatment of pathological gambling. Journal of Nervous and Mental Disease. doi: Scholar
  33. Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology. doi: 10.1037/0022-3514.32.2.311.Google Scholar
  34. Leotti, L. A., Iyengar, S. S., & Ochsner, K. N. (2010). Born to choose: The origins and value of the need for control. Trends in Cognitive Sciences. doi: 10.1016/j.tics.2010.08.001.
  35. Livingstone, C., Wooley, R., & Borrell, J. (2006). The changing electronic gambling machine (EGM) industry and technology. Melbourne, Australia: Australian Institute of Primary Care. Accessed 20 November 2012.
  36. MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample size in factor analysis. Psychological Methods. doi: 10.1037/1082-989X.4.1.84.Google Scholar
  37. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika. doi: 10.1093/biomet/57.3.519.Google Scholar
  38. Moore, S. M., & Ohtsuka, K. (1998). Control over gambling: Solution or problem? In G. Coman, B. Evans, & R. Wooton (Eds.), Responsible gambling: A future winner. Proceedings of the 8th national association for gambling studies conference, Melbourne, 1997 (pp. 259–267). Adelaide, Australia: The National Association for Gambling Studies.Google Scholar
  39. Moore, S. M., & Ohtsuka, K. (1999). The prediction of gambling behavior and problem gambling from attitudes and perceived norms. Social Behavior and Personality. doi: 10.2224/sbp.1999.27.5.455.
  40. Murphy, G. L., & Medin, D. L. (1985). The role of theories in conceptual coherence. Psychological Review. doi: 10.1037/0033-295X.92.3.289.PubMedGoogle Scholar
  41. Nickerson, R. S. (2002). The production and perception of randomness. Psychological Review. doi: 10.1037//0033-295X.109.2.330.PubMedGoogle Scholar
  42. Ocean, G., & Smith, G. J. (1993). Social reward, conflict, and commitment: A theoretical model of gambling. Journal of Gambling Studies. doi: 10.1007/BF01014625.
  43. Ohtsuka, K., & Ohtsuka, T. (2010). Vietnamese Australian gamblers’ views on luck and winning: Universal versus culture-specific schemas. Asian Journal of Gambling Issues and Public Health, 1, 34–46.Google Scholar
  44. Oskarsson, A. T., Van Boven, L., McClelland, G. H., & Hastie, R. (2009). What’s next? Judging sequences of binary events. Psychological Bulletin. doi: 10.1037/a0014821.PubMedGoogle Scholar
  45. Raiche, G., & Magis, D. (2010). Parallel analysis and non graphical solutions to the Cattell scree test.
  46. Raylu, N., & Oei, T. P. (2004). The Gambling Related Cognitions Scale (GRCS): Development, confirmatory factor validation and psychometric properties. Addiction. doi: 10.1111/j.1360-0443.2004.00753.x.PubMedGoogle Scholar
  47. Revelle, W. (2012). psych: Procedures for Personality and Psychological Research. Northwestern University, Evanston.,1.2.8.
  48. Rothbaum, F., Weisz, J. R., & Snyder, S. S. (1982). Changing the world and changing the self: A two-process model of perceived control. Journal of Personality and Social Psychology. doi: 10.1037/0022-3514.42.1.5.Google Scholar
  49. Rudski, J. M., & Edwards, A. (2007). Malinowski goes to college: Factors influencing students’ use of ritual and superstition. The Journal of General Psychology. doi: 10.3200/GENP.134.4.389-404.
  50. Skinner, B. F. (1948). ‘Superstition’ in the pigeon. Journal of Experimental Psychology. doi: 10.1037/h0055873.PubMedGoogle Scholar
  51. Steenbergh, T. A., Meyers, A. W., May, R. K., & Whelan, J. P. (2002). Development and validation of the Gamblers’ Beliefs Questionnaire. Journal of Addictive Behaviours. doi: 10.1037//0893-164X.16.2.143.Google Scholar
  52. Thompson, S. C., Armstrong, W., & Thomas, C. (1998). Illusions of control, underestimations, and accuracy: A control heuristic explanation. Psychological Bulletin. doi: 10.1037/0033-2909.123.2.143.
  53. Toneatto, T. (1999). Cognitive psychopathology of problem gambling. Substance Use and Misuse. doi: 10.3109/10826089909039417.PubMedGoogle Scholar
  54. Toneatto, T., Blitz-Miller, T., Calderwood, K., Dragonetti, R., & Tsanos, A. (1997). Cognitive distortions in heavy gambling. Journal of Gambling Studies. doi: 10.1023/A:1024983300428.PubMedGoogle Scholar
  55. Toneatto, T., & Ladouceur, R. (2003). Treatment of pathological gambling: A critical review of the literature. Psychology of Addictive Behaviors. doi: 10.1037/0893-164X.17.4.284.PubMedGoogle Scholar
  56. Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and probability. Cognitive Psychology. doi: 10.1016/0010-0285(73)90033-9.Google Scholar
  57. Tversky, A., & Kahneman, D. (1974). Judgement under uncertainty: Heuristics and biases. Science. doi: 10.1126/science.185.4157.1124.PubMedGoogle Scholar
  58. Ullman, J. B. (2006). Structural equation modelling: Reviewing the basics and moving forward. Journal of Personality Assessment. doi: 10.1207/s15327752jpa8701_03.PubMedGoogle Scholar
  59. Wagenaar, W. A. (1988). Paradoxes of gambling behavior. Hove: Erlbaum.Google Scholar
  60. Wagenaar, W. A., & Keren, G. (1988). Chance and luck are not the same. Journal of Behavioral Decision Making. doi: 10.1002/bdm.3960010202.Google Scholar
  61. Walker, M. B. (1992a). Irrational thinking among slot machine players. Journal of Gambling Studies. doi: 10.1007/BF01014652.Google Scholar
  62. Walker, M. (1992b). The psychology of gambling. London: Pergamon Press.Google Scholar
  63. Wellman, H. M., & Gelman, S. A. (1992). Cognitive development: Foundational theories of core domains. Annual Review of Psychology. doi: 10.1146/ Scholar
  64. Williams, L. R. S. (2007). Investigations of primary and secondary illusions of control in infrequent, frequent and problem gamblers. Unpublished Honours Thesis. Department of Psychology, The University of Adelaide.Google Scholar
  65. Wohl, M. J. A., & Enzle, M. E. (2009). Illusion of control by proxy: Placing one’s fate in the hands of another. British Journal of Social Psychology. doi: 10.1348/014466607X258696.PubMedGoogle Scholar
  66. Wood, W. S., & Clapham, M. M. (2005). Development of the Drake Beliefs about Chance Inventory. Journal of Gambling Studies. doi: 10.1007/s10899-005-5556-4.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Anastasia Ejova
    • 1
    Email author
  • Paul H. Delfabbro
    • 1
  • Daniel J. Navarro
    • 1
  1. 1.School of PsychologyThe University of AdelaideAdelaideAustralia

Personalised recommendations