Numerical Reasoning Ability and Irrational Beliefs in Problem Gambling

Abstract

Numerous studies have shown that pathological gamblers are particularly prone to various cognitive biases that may explain why they continue to gamble despite having occurred substantial losses. A common explanation advanced to account for this finding is that pathological gamblers may have poorer numerical or statistical knowledge than other people. Addressing these deficits is therefore seen as one possible way in which to assist pathological gamblers or prevent the development of problematic behaviour within the broader community. The aim of this study was test this assumption by assessing the numerical reasoning skills, objective gambling knowledge and tendency towards biased reasoning in a sample of 90 regular poker-machine gamblers (pathological and non-pathological) and a non-gambling comparison group (n = 45). Analyses based on both group comparisons and regression analyses controlling for differences in educational attainment showed that pathological gamblers scored significantly higher on the cognitive biases measure than other gamblers. However, this difference could not be attributed to poorer knowledge of gambling odds or limited numerical ability among pathological gamblers. The findings suggest that educating pathological gamblers with greater knowledge about the odds of gambling is unlikely to be an effective harm minimisation strategy.

Introduction

In Australia, as in almost all major westernised countries, it is well documented that between 1 and 2% of the adult population experience significant problems with gambling (Productivity Commission, 1999). Problem1 or pathological gambling is thought to be a progressive disorder characterised by an increasing commitment of time and money to gambling that can lead to harmful consequences to the gambler, those around them and the broader community (Dickerson et al., 1997; Lesieur and Blume, 1987; Neal et al., 2005; National Council on Problem Gambling, 2004). Since the 1970s, a variety of explanations have been advanced to understand pathological gambling, ranging from applications of the established principles of operant and classical conditioning to addiction models adapted from the DSM-IV classification for psychiatric disorders (American Psychiatric Association, 1994), or neurophysiological models relating to dysfunctional patterns of physiological and cortical activation associated with gambling reinforcers (Blaszczynski and Nower, 2002; Griffiths and Delfabbro, 2001; Petry, 2005). However, perhaps one of the most influential in terms of its impact on recent public policy, educational programs and clinical interventions for pathological gamblers, has been the increasing body of research relating to the application of cognitive theory to the study of gambling behaviour.

The principal tenet of the cognitive approach is that pathological gambling results from various forms of erroneous information processing. Since almost all forms of gambling are designed to have a negative return to players, long periods of play virtually(assure monetary loss and accordingly, prolonged play should be aversive and rare (Dowling et al., 2005; Walker, 1992). Accordingly, it follows that any gamblers who persist despite heavy losses must be irrational or playing against their better judgement.2 Dysfunctional gambling of this type is thought to arise because pathological gamblers frequently fall victim to a variety of well-documented decision-making errors, heuristics or biases (Corney and Cummings, 1985; Delfabbro, 2004; Ladouceur, 2004; Presson and Benassi, 1996; Wagenaar, 1988), all of which either encourage gamblers to continue playing, or make them overly confident about the potential profitability of gambling. A very comprehensive list of all these biases is provided by Wagenaar (1988), but perhaps the most important of these and the ones most strongly supported by empirical research into gambling, are the representation bias or gambler's fallacy (Tversky and Kahneman, 1971, 1973), availability bias (Tversky and Kahneman, 1973); beliefs about the role of luck (Griffiths, 1994, 1995), the illusion of control (Langer, 1975; Thompson et al., 1998) and personalisation of the outcomes, e.g. a belief that gaming machines are unfair or that players deserve to win (Griffiths, 1995).

The representation bias refers to the belief that short-term sequences of evidence should reflect long-run probabilities and often leads to the well-known gamblers' fallacy in which one event (e.g. reds in roulette, tails in coin-tosses, or wins in general) is seen as more probable if it has not occurred for some time. Availability refers to a tendency to base judgements (e.g. the profitability of gambling) on salient cues such as large wins rather than objective assessments of all wins and losses. In much the same way, beliefs in personal luck can also contribute to the view that one's personal odds of winning are better than the objective odds, or that outcomes are influenced by particular conjunctions of events or circumstances such as the right person or atmosphere being present at the gambling venue. All three of these biases do not necessarily lead to a belief that one can control outcomes, but can lead to a belief that one can predict or anticipate outcomes and this has been often considered as a form of predictive control (Raylu and Oei, 2004).

An illusion of control can also have much the same result as beliefs about luck, but refers more specifically to over-estimations of the personal capacity to influence outcomes, so that people have a subjective probability of winning that is greater than the objective odds. As Thompson et al. (1998) show, this perception typically arises in situations where people have a strong intention to achieve outcomes and where people are likely to perceive a link between their actions and outcomes such as when people are personally involved, or have to make choices, when participating in chance-based activities. This illusion is often maintained by biased attributional styles (Gilovich, 1983; Gilovich and Douglas, 1986) that lead gamblers to attribute failures to external factors such as bad luck and successes to their personal skill so as to maintain their perception of control despite clear evidence to the contrary. Finally, many gamblers may also continue to gamble because of a strong belief in a sense of fairness, or greater personalisation of the experience. Gamblers may come to believe that croupiers or gaming machines are ‘unfair’ or personally against the gambler, or may personalise the task by talking or shouting at gaming machines as if they were genuine competitors or rivals (Delfabbro and Winefield, 2000; Griffiths, 1994). Griffiths (1995) found that this latter class of beliefs was the one that differed most strongly between very frequent and infrequent slot-machine players.

Such heuristics, mental shortcuts or beliefs are a common feature of everyday life and can facilitate more efficient information processing and, in the case of biased attributions and illusions of control can be psychologically beneficial (Alloy and Clements, 1992). However, when applied(in a gambling context, any or all of these heuristics can lead to over-confidence or over-estimations of success and may lead to excessive gambling. Evidence in support of this view emerged from a number of studies employing a speaking aloud methodology, in which subjects were required to verbalise all uncensored(thoughts and rationalisations aloud while gambling (Coulombe et al., 1992; Gilovich and Douglas, 1986). Studies using this method(have consistently demonstrated that over 70% of verbalisations recorded during gambling(sessions are irrational and that many of the biases described above were clearly being used (Gaboury and Ladouceur, 1988; Ladouceur et al., 1988). Similar findings have also been obtained in recent studies using psychometric instruments (e.g. Joukhador et al., 2004; Toneatto et al., 1997; Jefferson and Nicki, 2003; Raylu and Oei, 2004), which have also confirmed a positive relationship between scores on standardised measures of problem or pathological gambling and people's susceptibility to cognitive biases related to gambling.

As a result of these findings, it has been argued that a potentially effective way in which to treat pathological gambling might be to address these biased cognitions by asking pathological gamblers to elucidate their thoughts, or by providing them with objective information concerning the true nature of the odds, probabilities and other relevant mathematical concepts (e.g. Ferland et al., 2002; Ladouceur and Sylvain, 1999; Ladouceur et al., 2003). Based on this logic, education programs have also been developed in schools (e.g. Shaffer et al., 1995; Williams et al., 2004) to provide young people with objective information about gambling in the hope that it will protect them against irrational beliefs and therefore make them more informed about the true nature of gambling. Central to all of these programs is the belief that irrational beliefs arise from a lack of knowledge about mathematics, gambling odds, so that it might be possible to reduce pathological gambling through appropriate education strategies that draws people's attention to the design of gambling activities and their inevitable unprofitability.

Despite the intuitive appeal of these suggestions and some promising results to suggest that the provision of information to pathological gambling may be therapeutically useful (e.g. Ferland et al., 2002), the empirical evidence available to support the fundamental ‘information deficit’ assumption of these approaches remains very sparse. In fact, those studies that have been conducted so far to test for the relationship between knowledge and people's susceptibility to cognitive biases have generally produced equivocal results. Benhsain and Ladouceur (2004), for example, conducted a comparative study involving humanities and statistics students gambling on a simulated roulette task. The results showed no significant difference in the prevalence of irrational cognitions. Another study by Smith (2003) also using university students found only a very small relationship (r < 0.20) between pathological gambling scores and student scores on a test of numerical reasoning and questions relating to their understanding of probabilities. Similarly, in a survey study of over 900 adolescents, Delfabbro et al. (2006) found that young pathological gamblers were actually more accurate in their responses to questions about objective probabilities (e.g. the odds of getting outcomes in coin-tossing), despite having a tendency to over-estimate the amount of skill involved in purely chance-based activities and other questions relating to specific types of gambling. Taken together, these results suggested that differences in numerical reasoning or objective knowledge may not be the primary source of differences in the prevalence the differences in cognitive reasoning observed between pathological gamblers and other gamblers.

The Present Study

Although the studies of gambling knowledge conducted so far involving student samples are not without value, such studies may be limited in that the prevalence of pathological gambling may be so low as to make it difficult to draw clear comparisons between the responses of pathological gamblers and others in the community. Accordingly, the principal aim of the current study was to extend these previous studies by conducting comparisons of gambling beliefs, numerical reasoning and knowledge of gambling odds with clearly defined samples of adult gamblers with varying levels of gambling involvement and which included a substantial sample of genuine pathological gamblers. Using these measures, it was possible to investigate two principal issues. The first, based on the research described above (e.g. Raylu and Oei, 2004), was whether pathological gamblers would more endorse the important types of irrational beliefs describe above, including the illusion of control, predictive control and a personalisation of gambling outcomes. The second, based on the recent preliminary research by Benhsain and Ladouceur (2004) and Delfabbro et al. (2006), was to investigate whether pathological gamblers differed in terms of their knowledge of basic gambling odds, or their ability to process numerical information as assessed by a formal test of this ability. Based on the studies described above, it was hypothesised that pathological gamblers would score more irrational on questions relating to the nature of gambling outcomes, but would not differ in terms of their knowledge of general gambling odds, or in terms of their numerical reasoning ability.

Method

Participants

The study involved 135 participants (males = 68, females = 67) ranging in age from 19 to 64 years, with a mean age of 39.08 (SD = 13.16). To be involved in the study, an individual had to be over 18 years old (the legal age for gambling in South Australia) and have had some experience with playing poker machines. Poker machine gambling3 was chosen as the basis for selection because it is the most popular continuous and high intensity form of gambling available in Australia (between 35 and 40% of the population gambles at least once per year, Productivity Commission, 1999). Approximately 70% of all pathological gamblers report that poker machines are the primary cause of their difficulties. Gaming machines have also been the major focus of investigation in previous studies of irrational cognitions (Delfabbro and Winefield, 2000; Joukhador et al., 2004; Jefferson and Nicki, 2003; Ladouceur et al., 1991).

Three groups of gamblers were recruited. A pathological gambler sample (n = 44) was recruited using newspaper advertisements and through access to new clients at local counselling agencies. All participants had to score five or more on the South Oaks Gambling Screen (SOGS) and gamble on poker machines at least once per week. The second group, also sampled from the community, comprised regular gamblers (n = 46) matched for age, gender, playing frequency and education level. A third sample comprised 45 infrequent gamblers (n = 45) recruited from the general community. All respondents in the infrequent sample had a SOGS score of less than five, gambled on poker machines less than once a fortnight and were significantly younger, F(2, 132) = 9.30, p < 0.001 and contained significantly more tertiary educated individuals, χ²(2, N = 135) = 24.76, p < .001, than the other two samples (Table 1). The principal purpose of the third sample was to test the validity of the numerical reasoning measure (scores should be higher in a tertiary educated sample) and to provide a wider range of scores on the measure of educational attainment for the purpose of the multivariate analyses described below.

Table 1. Descriptive statistics for age, gender and tertiary education across the three gambling groups

Group	M (SD) Age	n (%) Male	n (%) Female	n (%) Tertiary educated
Pathological gamblers (n = 44)	43.48 (11.5)	22 (50.0)	22 (50.0)	3 (6.82)
Regular gamblers (n = 46)	41.11 (12.8)	23 (50.0)	23 (50.0)	5 (10.87)
Infrequent gamblers (n = 45)	32.71 (12.9)	23 (51.1)	22 (48.9)	21 (46.67)

Measures

The survey was divided into five components: (i) demographics and gambling habits; (ii) understanding of gambling odds; (iii) a cognitive biases scale; (iv) the SOGS; and (v) a standardised numerical reasoning test.

Demographics and Gambling Habits

The first section addressed demographic details including age, gender and educational status. Subjects were also asked to indicate how often they played poker machines, how many years of experience they had playing poker machines and how long was typically spent gambling on each occasion. A significant difference was also observed for years of gambling experience, F(2, 132) = 3.84, p < 0.05. A Fisher LSD post hoc test indicated that pathological gamblers (M = 8.41, SD = 6.07) and regular gamblers (M = 7.90, SD = 5.83) had more previous gambling experience than infrequent gamblers (M = 5.04, SD = 6.68), p < 0.05. Reported average session length (in minutes) was also significantly higher for pathological gamblers (M = 132.73, SD = 81.99) than for regular gamblers (M = 81.52, SD = 59.44) and infrequent gamblers (M = 15.62, SD = 17.90), F(2, 132) = 43.85, p < 0.001.

Understanding of Odds

Five general questions were included to assess participants' understanding of the odds of common gambling activities that would be familiar even to those with little in vivo playing experience.

• The first question asked participants which set of odds was closest to those associated with winning X-Lotto. This was specified as having six correct numbers. Five options were provided ranging from 1 in 100,000 to 1 in 10 million, with the closest answer being 1 in 8 million.

• The second question provided information regarding roulette and asked subjects the odds of red spinning up on two consecutive rounds. The options included 4/16, 9/18, 1/37, 1/18 and 2/18, with the closest answer being 4/16.

• The third question asked the chances of getting two heads when two fair coins were tossed. The options ranged from 10 to 50%, however the correct response was 25%.

• The next question informed subjects that a typical poker machine returned 87% to the player and asked how much money they would expect to lose on average if they played A$20 through the machine. Five options were provided with the correct response being A$2.60.

• The final question asked the chances of drawing an ace from a deck of 52 cards. The options included 1 in 52, 2 in 52, 4 in 52, 2 in 26 or none of the above, with the correct response being 4 in 52. The content of these questions were very consistent with those typically included in quizzes for high school students exposed with gambling knowledge education programs (Crites, 2003).

Measuring Irrational Beliefs

Several existing scales have been developed to measure irrational beliefs (e.g. Jefferson and Nicki, 2003; Joukhador et al., 2004; Raylu and Oei, 2004; Steenbergh et al., 2002), although only one of these (Raylu and Oei, 2004) has been validated in Australia and only one (Jefferson and Nicki, 2003) was specifically designed to examine beliefs relating only to gaming machines. Moreover, only Steenbergh et al.'s and Raylu and Oei's measures classify items into specific classes that allow one to measure the illusion of control, or predictive control in separate subscales. No measure has specifically examined the personalisation of outcomes. Since Raylu and Oei's Australian scale included items relating to other types of gambling (number and colours), as well as items relating to behaviours that might not be observed in all gamblers (e.g. use of prayer), a revised pool of items relating to poker machines was derived.

• Five items relating to an illusion of control were developed: certain ways to play to get a better chance of winning; presence of objects and people can influence winning; concentration and winning can influence outcomes; superstitious rituals; and picking winning machines.

• Nine items were selected to measure predictive control as based on a reliance on the availability, representation bias or beliefs about luck: e.g. play machines where people are winning; early outcomes determine latter outcomes; avoid machines that have recently paid out; playing until your luck changes.

• Three items related a personalisation of outcomes: e.g. the person talks to machines (one wins more if one is ‘nice’ to machines, or machines ‘have it in for me personally’). For each item, players were asked to indicate on a scale of 0 (strongly disagree) to 10 (strongly agree) whether they endorsed the statement or belief.

A pilot validation study of 40 regular poker machine players (17 pathological, 24 non-pathological) was undertaken using these sets of items and found that all three subscales had acceptable internal reliability (Cronbach α > 0.70). Each was validated against the eight-item illusion of control scales developed by Steenbergh et al. (2002) and the four-item scale developed by Raylu and Oei (2004). All new subscales showed moderate to high correlations (0.54–0.72) with these previously developed measures of general irrationality, with the strongest correlation found between the newly developed illusion of control scale and Raylu and Oei's scale (0.72) (as compared with 0.58 for the Steenbergh et al. scale). All three subscales had Cronbach α reliabilities of 0.70 and higher in the current sample.

South Oaks Gambling Screen (SOGS) (Lesieur and Blume, 1987)

The SOGS (last 12-months version) was used to distinguish between probable pathological and(non-pathological gamblers. The test featured 20 items with an overall score of five or more used to classify an individual as a probable pathological gambler (Strong et al., 2004). In the present study the Cronbach α coefficient was 0.92. Regular non-problem gamblers had a score < 5. Significant differences in SOGS scores were obtained between the three groups, F (2, 132) = 228.1, p < 0.001. The scores for probable pathological gamblers (M = 9.68, SD = 3.36) were significantly higher than for the regular group (M = 2.05, SD = 1.57) and the infrequent group (M = 0.48, SD = 0.74).

Numerical Reasoning Ability

A standardised numerical reasoning test developed by Psychtech International Ltd. (1991) was used to assess participants' ability to understand numbers and the relationship between numbers. This test has been utilised extensively in both international and national samples and has been found to have very good psychometric properties. Furthermore, only a basic level of education was required to successfully complete the test, making it suitable for the general community and a measure of numerical ability rather than educational achievement. The 10-min test featured 25 questions, each with six possible multiple choice answers. As with other widely used tests of numerical aptitude, e.g. the Differential Aptitude Test (DAT) commonly used for vocational assessments of school leavers in Australia, the tests asks respondents to complete numerical sequences, calculate and convert ratios, percentages and fractions and conduct arithmetic problem solving. In the present study, the Cronbach α coefficient was 0.88.

Procedure

Infrequent and regular non-pathological gamblers who expressed interest in the study were mailed an information sheet and invited to the University of Adelaide laboratory for testing. Upon giving informed consent, subjects were asked to complete the survey that pertained to demographic information, understanding of odds and the cognitive biases scale. Following this, the SOGS was administered followed by the timed numerical reasoning test. Subjects were debriefed and received A$20 payment for their time and travel costs.

Results

Statistical Note

An α level of 0.05 was used for all statistical tests. For large effect sizes with 0.05 significance it was determined that a sample size of 135 would yield 99% power. A first series of analyses was undertaken using analysis of variance (ANOVA). In these analyses, the principal interest lay in the differences between the two groups matched for gambling frequency and education level (the pathological gamblers and the regular gamblers) because these groups only differed in terms of their SOGS scores. A second multivariate analysis was then undertaken to examine the relationship between numerical reasoning and knowledge scores and cognitive belief scores after controlling for any group differences in educational level and age and pathological gambling scores.

Individual Differences in Ability

Table 2 summarises the numerical reasoning scores for the three groups along with their score out of five on the knowledge of gambling odds questions. One-way ANOVA revealed that there was no significant difference between the groups for their knowledge of gambling odds, but a significant difference was detected for numerical reasoning ability. As might be expected, the more highly educated infrequent group scored higher than the other two groups (Fisher LSD, p < 0.001), but no significant difference was observed between pathological gamblers and regular gamblers.

Table 2. Mean (SD) knowledge and numerical reasoning scores

	Pathological gamblers (n = 44)	Regular gamblers (n = 46)	Infrequent gamblers (n = 45)	F(2,132)	η^2
	M (SD)	M (SD)	M (SD)
Knowledge of gambling odds	1.57 (1.50)	1.61 (1.48)	2.13 (1.50)	2.00	0.03
Numerical reasoning ability	13.52 (0.72)	12.30 (0.90)	16.82 (0.91)	7.74	0.11

Group Differences in Irrational beliefs

Group differences in scores on the cognitive biases scales were assessed to test the hypothesis that pathological gamblers would show greater endorsement of irrational beliefs than regular and infrequent gamblers (Table 3). As indicated in Table 3, the results were very consistent with predictions. Pathological gamblers consistently scored higher than the regular gamblers, who in turn consistently scored higher than the infrequent gamblers. Based on Cohen's (1988) classification of η² values of 0.07 as moderate and 0.14 values as large, it is clear that all three differences were large. However, it should be noted that most scores were generally towards the lower end of the scoring range for each subscale.

Table 3. Mean (SD) scores for the 3 irrational belief subscales

	Pathological gamblers (n = 44)	Regular gamblers (n = 46)	Infrequent gamblers (n = 45)	F(2,132)	Post hoc	η^2
	M (SD)	M (SD)	M (SD)
Predictive control	48.77 (15.6)	41.98 (15.4)	28.2 (14.7)	21.3	1 > 2–3, 2 > 3	0.24
Illusion of control	16.8 (11.3)	9.65 (7.7)	4.33 (5.6)	24.3	1 > 3 2 > 3	0.27
Personalisation of the machine	14.34 (9.1)	8.89 (6.0)	4.60 (6.1)	20.4	1 > 2–3 2 > 3	0.24
Note. All F-values significant at p < 0.001 and post hoc tests significant at 0.05 level. Predictive control (nine items), illusion of control (five items), personalisation of the machine (three items). Score range for each subscale = 0 – 10 × Number of items.

Pearson correlation analysis was also used to examine the relationship between scores on the SOGS and irrationality scores for each type of bias (Table 4). Scores on the SOGS significantly correlated with all but one of the subscales, with the magnitude of the correlations found to be generally consistent with other recent studies (Jefferson et al., 2004; Joukhador et al., 2004; Raylu and Oei, 2004; Jefferson et al., 2004). A positive relationship was evident where irrationality increased as the level of pathological gambling increased, demonstrating further support for the view that pathological gambling is associated with greater irrationality. Table 4 also shows that there were generally positive intercorrelations between the biases, suggesting that people who tended to endorse one class of bias were likely to endorse others.

Table 4. Pearson correlations of SOGS scores and the cognitive belief scores

	Predictive control	Illusion of control	Personalisation of machine
SOGS	0.37	0.43	0.45
Predictive control		0.57	0.42
Illusion of control			0.54
All correlations significant p < 0.001.

Multiple Regression Analysis: Pathological Gambling, Understanding of Odds and Numerical Reasoning Ability as Predictors of Irrational Belief Scores

The previous analyses indicated that pathological gamblers were more prone to cognitive biases than regular and infrequent gamblers and that the three groups were similar in terms of their knowledge of the objective odds, but also that the pathological gamblers had poorer numerical reasoning ability than the more highly educated infrequent gamblers. To gain a clearer understanding of the relationship between pathological gambling, mathematical ability, knowledge of odds and irrationality, a hierarchical multiple regression analysis was conducted using the entire sample, while controlling for the effects of tertiary/university education. Irrationality (total scores on the cognitive biases scale) was used as the dependent measure, education level was added at Step 1, SOGS scores and years of gambling experience at Step 2 and numerical reasoning ability and knowledge of odds at Step 3. Residual analysis indicated no evidence of outliers, non-normality, nonlinearity or homoscedasticity. The final model was highly significant, F(5, 129) = 7.38, p < 0.001 and accounted for 19% of the variance in irrationality. As indicated in Table 5, the adjusted R ² change value for the final step was 0, indicating that numerical reasoning and understanding of odds explained no variance in irrationality scores and that by far the strongest predictor of irrationality was a person's SOGS score. In other words, the differences observed in Table 3 were unlikely to have been significantly influenced by differences in the level of educational attainment. Pathological gambling appears to be the primary predictor of irrational cognition scores.

Table 5. Summary of hierarchical regression analysis for variables predicting total irrationality score (sum of the three subscales)

Variable	B	Adj R ^2	Δ Adj R ^2	β	t-value
Step 1
Education	− 2.18	0.05	0.05	–0.12	1.43
Step 2
SOGS score	46.33			0.41	4.97*
Gambling experience (yrs)	0.007	0.20	0.14	− 0.22	< 1
Step 3
Odds total score	− 0.02			− 0.02	< 1
Numerical reasoning score	− 0.07	0.20	0.00	− 0.08	< 1
*p < 0.001.

Discussion

Overall, the results of this investigation were consistent with other recent studies such as those conducted by Joukhador et al. (2004), Raylu and Oei (2004) and Jefferson and Nicki (2003). Pathological gamblers were found to be consistently more irrational than other gamblers on every type of cognitive bias that was measured and this difference was evident even after statistically controlling for differences in educational attainment between different gamblers. In previous studies, it has been argued that such biases could be addressed by providing pathological gamblers with greater information about the nature of gambling odds, or by introducing gambling topics into mathematical curricula. However, as the results of this study showed, there was little evidence to show that these deficits were related to poorer numeracy or knowledge of basic gambling odds. Consistent with the small number of recent studies that have investigated similar issues within student populations (Benhsain and Ladouceur, 2004; Delfabbro et al., 2006; Smith, 2003), pathological gamblers were, in fact, just as accurate in their understanding of gambling odds as regular gamblers involved in the same form of gambling and who had a similar number of years of gambling experience.

In attempting to explain this seemingly paradoxical result, Benhsain and Ladouceur (2004) and Sevigny and Ladouceur (2004) have introduced a concept termed ‘cognitive switching’. According to this view, pathological gamblers are thought to vacillate between two cognitive states: one that is focussed on an objective and rational assessment of the odds (what they term ‘cold information’) and another that is more primarily focused on information relevant to the activity and outcomes (termed ‘hot cognitions’). In this latter state, gamblers it is argued are more likely to eschew rational processing and become susceptible to various cognitive biases. In Benhsain and Ladouceur's view, one explanation for this change in mental states is that a strong personal involvement in the activity possibly leads to more analytic or left-hemisphere processing, in which there may a greater tendency to infer causal patterns or relationships that may not exist. However, these views still remain to be substantiated, perhaps through further investigations using appropriate neuro-imaging technology to confirm whether the patterns of brain activation differ according to gamblers' level of task involvement.

In Delfabbro et al.'s (2006) view, Benhain and Ladouceur's findings could also be parsimoniously explained in terms of Thompson et al.'s (1998) notion of the control heuristic, a term that refers to particular classes of situation in which people are more prone to over-estimating the amount of control perceived over outcomes [as per Langer's (1975) illusion of control]. Situations most likely to fall into this category include those where people have a strong personal involvement in the task and when they have a strong desire for outcomes. Thompson et al. (1998) draw specific attention to a study by Biner et al. (1995), which involved a simple gambling experiment where food deprived and non-food deprived participants gambled on a task for food rewards. Those participants who were hungry and therefore in greater need of the outcomes were significantly more likely to over-estimate their control over the task even though both had been exposed to the same series of events.

As Delfabbro et al. (2006) note, it is highly likely that pathological gamblers differ from other gamblers in much the same way. Gambling to recover previous losses is a central feature of pathological gambling (O'Connor and Dickerson, 2003), so that pathological gamblers are likely to have a stronger emotional and financial need to win money than other gamblers. In such states, they may be more likely to relinquish rational decision-making and interpret information in a way that is consistent with their underlying motivation to achieve control over outcomes and to recoup their losses. In support of this view, it is noteworthy that the tendency to endorse statements consistent with an illusion of control and a greater personalisation of gambling (e.g. that gaming machines should play fair and respond to emotional persuasion) was much more strongly observed in pathological gamblers than other gamblers. At the present time, most gambling research concerning the role of emotional states and decision-making has focused largely on people's responses to anticipated or actual outcomes (e.g. Mellers et al., 1997), or dysfunctional responses to patterns of reward (e.g. Overman et al., 2004). Thus a potentially fruitful extension of this research would be to examine emotions, not as outcomes, but as possible causal factors in influencing gambler's decision-making and, in particular, their susceptibility to various cognitive biases such as the illusion of control.

The results from this study suggest that a basic understanding of mathematics, statistics or gambling odds is unlikely to be a protective factor in pathological gambling because gamblers can pick and choose which information they chose to apply when the information is applied to activities in which they have a personal interest. Despite this, however, it does not necessarily follow that providing that information is completely without value. Although such information may have a limited impact on pathological gamblers once they are immersed in gambling, it may be that such information, if provided early enough, may provide people with the skills to approach gambling more rationally before they become too emotionally and financially involved. For this reason, the current interest in providing gambling information in schools, in venues and to the community in general may still be a worthwhile primary intervention and be useful for those who have not as yet become involved with gambling, or who gamble only infrequently. One possibility raised by Smith (2003), for example, is that the differences being observed between pathological gamblers and other gamblers in terms of cognitive biases may reflect more subtle misconceptions about statistics and probabilities that are not adequately detected by the sorts of questions utilised in any research so far. Thus, further more refined analyses of gamblers' knowledge may yield differences that enable one to identify the underlying conceptual basis for some of the apparent misconceptions relating to randomness reflected in many of the biases.

Conclusions

Although this study contained some methodological strengths, including a valid sample of pathological gamblers and the capacity to control for educational differences, it is important to recognise that there are nevertheless several limitations that need to be taken into account when interpreting the findings. First, all findings in this study were based on self-report data, so that it does not necessarily follow that participants endorsed biases to the same extent or in the same way as might be so in an actual session of gambling. Second, although the items used to measure to irrational beliefs were very similar to established measures and also highly correlated with them, further validation of these items particularly in international samples is important to confirm that the questions are interpreted the same way and are relevant to gamblers in other jurisdictions where different types of gaming machine may be available. Third, since the sample used in this study was recruited non-randomly from the community, there is always the danger that only the more competent and more educated pathological gamblers may have participated. In other words, even though the sampling was probably appropriate for the testing the hypotheses posed in this study, it does follow that the results can be generalised to all pathological gamblers in the community; in particular, those who do not have the literacy skills, time and motivation to participate in university research projects.

Finally, although differences between the regular and pathological groups were attributed to variations in gambling involvement, it may also be possible that there are broader neurophysiological or psychiatric factors that might account for the differences, e.g. greater anxiety, neurological impairments in pathological gamblers that make them more prone to drawing irrational associations between gambling events and specific behaviours. Without further evidence it is unclear as to the extent to which this might have been so in the present study. However, given that all participants were all able to complete a numerical aptitude test relatively competently, it did not appear that the sample of gamblers showed any obvious intellectual or other impairments that would explain the differences in results obtained across the groups.

Notes

1. In Australia, the term ‘problem gambler’ is usually used instead of ‘pathological gambler’ to encompass the broader aetiological basis for the disorder.

2. It is important to point out that the desire for monetary gain is not the only motivation for gambling (see Chantal et al., 1995). However, this assumption is central to cognitive theories of gambling and it can be argued other motivations such as gambling for enjoyment or excitement are not independent of monetary motives. As Walker (1992) points out, there is evidence that laboratory investigations that fail to include any genuine chance to win money do not evoke the same level of physiological arousal as those with only token rewards (e.g. Anderson and Brown, 1984; Diskin et al., 2003).

3. Poker machines or electronic gaming machines (EGMs) are the Australian equivalent of fruit machines in the United Kingdom and slot-machines in North America. Australian machines usually involve five spinning reels. Players win money based on whether specified combinations of symbols line up in a row on a particular betting line (e.g. the middle row, upper, lower or other patterns). Players can play up to 20 games per minute with a maximum bet of A$10 (equivalent to approximately £2 sterling orUS$7.5).