Probability, Random Events, and the Mathematics of Gambling

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produces a very slow accumulation of money. Eventually, however, the player experiences a disastrous losing streak One final reason for errors in judging random events is that our minds tend to segment events in ways that are consistent with what we expect. Given a heads and tails sequence of H, H, H, H, T, H, H, H, T, T, T, T, H, we are likely to divide this string into a segment in which H was more likely to appear (H, H, H, H, T, H, H, H) and one in which T was more likely to appear (T, T, T, T, H). This segmentation process is very often used by sports commentators (e.g., “The Blue Jays have now won 5 of their last 6 games,” or “A player has struck out 11 times in his last 15 at bat”). In segmenting the sequence this way, it is very easy to convince oneself that tails did in fact come up more often, to correct for the excess of heads. As noted above, our minds are predisposed to find patterns, not to discount them. Summary There are important clues regarding erroneous beliefs in the experiences of the individual who gambles. While it is unlikely that addressing the erroneous beliefs is sufficient for treatment, exploring these beliefs can be an important aid in helping the client understand their gambling experiences—both their wins and their losses. Correcting these beliefs may also help in relapse prevention. If individuals with a gambling problem still believe that they can beat the odds, the odds are they will try again. References Arnold, P. (1978). The encyclopedia of gambling: The games, the odds, the techniques, the people and places, the myths and history. Glasgow: Collins Publishers. Bass, T.A. (1985). The eudaemonic pie. Boston: Houghton Mifflin Company. De Finetti, B. (1990). Theory of probability: A critical introductory treatment (Vol. 1). (Trans. A. Machi & A. Smith.) Chichester: Wiley. Gabriel, K. (2003). Playing the gods. Gambling and spirituality: A new anthropological perspective. In G. Reith (Ed.), Gambling: Who wins? Who loses (pp. 334–347). Amherst, NY: Prometheus Books. 22
Gleick, J. (1987). Chaos: Making a new science. New York: Viking Penguin Inc. Johnson-Laird, P. (1983) Mental models. Cambridge: Cambridge University Press. Kahneman, D., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. In Kahneman, D., Slovic, P., & Tversky, A. (Eds.), Judgement under uncertainty (pp. 3– 22). Cambridge: Cambridge University Press. Ladouceur, R., & Walker, M. (1996). A cognitive perspective on gambling. In P. Salkovskis (Ed.), Trends in cognitive and behavioural therapies (pp. 89–120). U.K.: John Wiley and Sons. Merriam-Webster Online Dictionary (2006). Downloaded June 1, 2006, from www.m- w.com/cgi-bin/dictionary. Orkin, M. (2000). What are the odds? Chance in everyday life. New York: W.H. Freeman and Company. Patterson, J.L. (1990). Blackjack: A winner’s handbook. New York: Perigee Books. Reber, A.S. (1993). Implicit learning and tacit knowledge. New York: Oxford University Press. Papoulis, A. (1991). Probability, random variables, and stochastic processes (3rd ed.). New York: McGraw Hill. Ross, S. (1984). A first course in probability (2nd ed.). New York: Macmillan. Stewart, I. (1989). Does God play dice: The new mathematics of chaos. London: Penguin Books. Thorpe, E.O. (1966). Beat the dealer: A winning strategy for the game of Twenty-One (2nd ed.). New York: Vintage Books. Toneatto, T. (1999). Cognitive psychopathology of problem gambling. Substance Use and Misuse, 34 (11), 1593–1604. Toneatto, T., Blitz-Miller, T., Calderwood, K., Dragonetti, R., & Tsanos, A. (1997). Cognitive distortions in heavy gambling. Journal of Gambling Studies, 13, 253–266. Turner, N.E. (1998). Doubling vs. constant bets as strategies for gambling. Journal of Gambling Studies, 14, 413–429. Turner, N.E. (2000, July). Randomness: Does it matter? Electronic Journal of Gambling Issues [Online serial], issue 2. Available at http://www.camh.net/egambling/issue2/research/ 23
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Probability, Random Events, and the Mathematics of Gambling

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