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International Gambling Studies
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Personal Luck Usage Scale (PLUS): psychometric validation of a measure of
gambling-related belief in luck as a personal possession
Michael J. A. Wohla; Melissa J. Stewarta; Matthew M. Younga
a Department of Psychology, Carleton University, Canada
Online publication date: 31 March 2011
To cite this Article Wohl, Michael J. A. , Stewart, Melissa J. and Young, Matthew M.(2011) 'Personal Luck Usage Scale
(PLUS): psychometric validation of a measure of gambling-related belief in luck as a personal possession', International
Gambling Studies, 11: 1, 7 — 21
To link to this Article: DOI: 10.1080/14459795.2010.541270
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Personal Luck Usage Scale (PLUS): psychometric validation of
a measure of gambling-related belief in luck as a personal possession
Michael J.A. Wohl*, Melissa J. Stewart
†
and Matthew M. Young
Department of Psychology, Carleton University, Canada
Luck is by definition a random event. However, many people believe luck to be
something it is not – an internal, personal quality. An obstacle for understanding
personal luck and its sequelae among gamblers has been the lack of a psychometrically
sound measure. The current paper reports the development of the Personal Luck Usage
Scale (PLUS). In Studies 1 and 2 (Ns¼347 and 361, respectively), a one-dimensional,
eight-item scale emerged and was subsequently confirmed among university-aged
gamblers. Importantly, the PLUS was distinguishable from a general belief in luck
(Study 2). In Study 3 (N¼60), a behavioural consequence of belief in personal luck
was assessed among a community sample of gamblers. Specifically, PLUS scores were
positively associated with the average amount of money spent in a gambling session.
The implications of a belief in gambling-related personal luck for the progression and
maintenance of problem gambling are discussed.
Keywords: behaviour; beliefs; cognition; irrational beliefs; psychology; sociology
According to causal theories of attribution (Kelley, 1973; Weiner, 1974), luck is a random
environmental factor that is independent of human volition or individual effort. Therefore,
when a person experiences good luck, it is not the result of personal actions, rather a
confluence of external, situational causes. As such, people’s expectations of future success
should not be influenced by luck occurrences of the past. Although experiencing luck may
have positive consequences for the self, the self-perceived lucky individual cannot
influence events determined by chance – luck is not an existing force that can be possessed
to maximise outcomes. Despite this reality, many people (and gamblers more specifically)
use the word ‘luck’ in reference to personal attributions of both individuals (e.g. a ‘lucky
stiff’) and groups (e.g. the ‘luck of the Irish’). While quaint in a colloquial sense, such
perceptions may have negative consequences within a context that involves games of pure
chance. Walker (1992), for example, reported that during a speak-aloud procedure while
playing slot machines, one participant spontaneously announced, ‘I’m lucky today, I
should buy a lotto ticket’. Observers often greet such statements with a smile or nod of
agreement. These self-perceptions, however, have the potential to be more than mere
benign, colloquial statements. Indeed, believing the self to be a lucky person (i.e. personal
luck) may lead gamblers to bet more on games of chance (Wohl & Enzle, 2002, 2003) and
may be a predictor of pathological gamblers’ reluctance to seek treatment (Wohl, Young
& Hart, 2007).
ISSN 1445-9795 print/ISSN 1479-4276 online
q2011 Taylor & Francis
DOI: 10.1080/14459795.2010.541270
http://www.informaworld.com
*Corresponding author. Email: michael_wohl@carleton.ca
†
Now at Dalhousie University, Halifax, NS Canada
International Gambling Studies
Vol. 11, No. 1, April 2011, 7–21
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One reason for the association between personal luck and problematic gambling may
be that some gamblers believe they can use their luck to maximise gambling-related
outcomes. Wohl and Enzle (2002), for example, showed that gamblers acted as though
luck could be transmitted from the self to a wheel-of-fortune and thereby positively affect
their perceived chance of winning. Specifically, participants would rub gambling-specific
paraphernalia when that object was involved in a given wager (e.g. they handled a
numbered ping-pong ball that corresponded to the number they wagered a wheel-of-
fortune would stop on). The current research examined such non-rational views of luck
and its consequences though (a) the creation of a psychometrically sound scale to assess
gambler’s perceived ability to use personal luck, (b) an examination of whether
pathological gamblers differ from recreational gamblers in their perceived ability to use
personal luck, and (c) an assessment of the relationship between perceived personal luck
and wagering in a given gambling session.
Luck as a psychological construct
People are typically motivated to see themselves as causal agents of their environment (see
Bandura, 1989). Thus, a sense of discomfort or tension is generally experienced when
confronted with an event with an uncertain outcome (see Gordon, 2003; Van den Bos,
2001). As a result, people become motivated to engage in uncertainty reducing thoughts or
actions (Hogg, 2000). Gambling is, by definition, a wager of money or something of value
on an uncertain outcome. Indeed, gamblers cannot, with any accuracy predict when a
given spin of a slot machine will result in a win or loss. Despite this statement of fact,
many gamblers erroneously believe they can affect the likelihood of winning in chance
games (see Langer, 1975; Wohl, Christie, Matheson & Anisman, 2010). Instead of
perceiving outcomes as the result of pure chance, these individuals have a tendency to
believe that effort or skill can be used to help improve their chances of winning.
Support for this contention can be found in the large body of work on the illusion
of control (see Thompson, Armstrong & Thomas, 1998, for a review). Originally
conceptualised by Langer (1975), it was claimed that people are often subject to the belief
that they can influence chance events. Langer’s work on the illusion of control rests on the
argument that people fail to understand the randomness of chance games and thus believe
effort or skill can be used to influence outcomes, i.e. belief in an ability to control truly
mutable events is sometimes overextended to truly immutable ones. Not surprisingly,
Wohl, Young and Hart (2005) showed that pathological gamblers whose preferred game
had a component of skill (e.g. poker) were less likely to have positive attitudes toward
treatment seeking than pathological gamblers who preferred to play games of pure chance
(e.g. slot machines). It was argued that the more elements of skill that are incorporated into
a game of chance, the more likely gamblers are to blur the lines between the skill and
chance. This blurring might lead to problematic play because losses might be attributed to
a lack of effort or practice. The only way to win would thus be to exert more effort or
practice to learn how best to use their skill. Gamblers are thus under no illusion about the
random nature of the game, but instead over generalise their abilities and believe that with
effort and practice they can use their ‘skill’ to exert control over the chance as well as the
non-chance elements of the game.
Indeed, a growing body of literature (see Darke & Freedman, 1997; Friedland, 1998;
Griffiths & Bingham, 2005; Wagenaar & Keren, 1988; Wohl & Enzle, 2002, 2003; Wohl
et al., 2007) has shown that some people believe in luck as a means of controlling the
uncontrollable forces in games of chance (for a review on the psychology and philosophy
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of luck, see Pritchard & Smith, 2004). Wohl and Enzle (2002, 2003), for example, have
argued that a segment of gamblers believe in an a priori causal contingency or ‘personal
luck’ that undermines or reduces the effects of randomness. In this case, the perception of
causal contingency during games of chance would not be an erroneous inference from
evidence of simple connection, but would reflect a belief that the gambler has a relevant,
albeit unconventional, personal attribute. In other words, rather than thinking of luck as
external and unstable, some people think about luck as a personal quality that can be used
and deployed to maximise outcomes in games of chance.
According to Wagenaar and Keren (1988), a conceptual distinction is often made
between chance and luck. Whereas chance is random, luck is viewed as a causal agent that
sometimes overrules the effects of chance. In other words, luck is perceived as an intrinsic,
personal quality or a dispositional skill that can be strategically used to influence gambling
outcomes. As a result of this misconception of luck, wins may be attributed to the self
(because of their personal luck) rather than external, random forces. Thus, while engaged
in play, games of chance might be perceived as less random than objective, cause –effect
logic would allow (Wohl, 2008).
Personal luck might therefore provide explanatory power to the established link
between illusory control and positive outcome expectancy. The more luck a person
believes him or herself to possess, the more that person perceives the self as able to
influence the outcomes of chance games. Should gamblers believe themselves able to use
personal luck, their gambling may persist because the threat of loss is counteracted by
gamblers’ perceived personal luck. As a result, elevated expectancies of success that stem
from the perceived ability to use personal luck might result in prolonged and excessive
betting.
Measuring perceptions of luck
Despite the potential significance of perceptions of gambling-related personal luck in the
development and maintenance of gambling problems, there is a lack of an adequate
measure of this construct. As a result, other related measures have been used, such as
scales that assess a general belief in luck (Darke & Freedman, 1997; Wiseman & Watt,
2004) or gambling relevant beliefs in luck (Steenbergh, Meyers, May & Whelan, 2002).
Scales assessing a general belief in luck have used items such as, ‘I believe in luck’ (from
Darke & Freedman, 1997) or ‘Do you sometimes carry a lucky charm or object’ (from
Wiseman & Watt, 2004). Although agreement with these items is meant to reflect a
general belief in luck, such scales are broad scoped and thus do not assess luck in relation
to gambling. That is, these extant scales are one step removed from a measurement tool
that assesses luck in relation to gambling and the ability to harness this luck to maximise
outcomes. For researchers wishing to assess personal luck or clinicians who might benefit
from improved insight into their client’s specific non-rational patterns of thought, a
general belief in luck does not necessarily equate with a belief that self-perceived personal
luck can influence outcomes in games of pure chance, i.e. I can believe that luck might
benefit me, but not necessarily that I possess a personal luck-relevant ability that I can use
to help me win while playing games of chance.
A scale that gets closer to our conceptualisation of personal luck is the Gambler’s
Belief Questionnaire (GBQ; Steenbergh et al., 2002). This scale was designed to assess an
array of erroneous beliefs about gambling, one of which being the belief that luck,
perseverance, or both, will eventually lead to gambling wins. For example, participants are
asked how strongly they agree to statements such as ‘I have a “lucky” technique that I use
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when I gamble’. While positive endorsement of such an item reflects a greater belief that
luck can influence chance outcomes, it does not directly capture the subjective belief
that luck is a personal ability that can be used to increase one’s odds of success while
gambling. Instead, measures of gambling-related erroneous cognitions, such as the GBQ,
conceptualise luck as an external entity rather than a personal ability that gamblers believe
they possess and can use to increase their luck when gambling.
To directly assess self-perceived personal luck, Wohl and Enzle (2002) asked
participants, ‘If you were to say that you were “lucky” in terms of some event, to what
extent do you mean that you are a lucky type of person or that a lucky thing happened to
you?’ This item was anchored at (1) a lucky thing happened to me and (7) I am a lucky type
of person. It was found that increases in the belief that luck was a personal quality (as
opposed to something attributable to the situation) was associated with heightened
confidence that they would win at games of pure chance. While this item was associated
with a general belief in luck, it was not redundant with such a general belief. Although this
study lends credence to the notion that some people believe themselves as possessing
personal luck, single-item measures have been criticised for their limited accuracy and
reliability and underlying assumption that perceptions of gambling-related personal luck
can be adequately assessed with only one item (Gardner, Cummings, Dunham & Pierce,
1998).
Importantly, Wohl and colleagues (2007) showed that perceptions of personal luck
increase with each progressive DSM-IV level of gambling pathology. Personal luck may
therefore be a risk factor for the development of gambling problems, and as such, it is
important that researchers and clinicians alike have at their disposal a valid, reliable
measure of gambling-related personal luck. This case is further strengthened by the fact
that a belief in gambling-related personal luck has been associated with more negative
attitudes towards seeking treatment (Wohl et al., 2005, 2007). Given the relationship
between perceptions of gambling-related luck and problematic gambling, an instrument
that directly targets the belief that luck is perceived, by some people, as a personal
possession that can be used to maximise outcomes in games of chance would be helpful in
identifying those gamblers that may be at risk for developing gambling problems. Thus,
the present study focused on developing a scale that assesses perceptions of personal luck
in relation to gambling.
Overview of the current research
The purpose of Study 1 was to examine the psychometric properties of the Personal Luck
Usage Scale (PLUS). This scale was developed to assess the degree to which gamblers feel
they possess luck that can be used to maximise outcomes while gambling. Because a belief
in personal luck might lead players to believe they have a ‘skill’ that can be used to
sidestep objective probability of success at games of chance (see Wohl, 2008; Wohl et al.,
2005), such perceptions are likely to be more common among people with symptoms of
gambling pathology than gamblers with no symptoms. To this end, an initial pool of 12
items was generated to measure gambling-related personal luck.
The aim of Study 2 was to confirm the factorial structure of the PLUS by administering
the scale to a second set of gamblers. Validity of the scale was also assessed through
associations with a related construct. Specifically, by including items from a previously
validated measure of gambling-related irrational cognitions (GBQ; Steenbergh et al.,
2002), Study 2 sought to determine whether the PLUS assessed a distinct construct that
is not fully captured by other measures of gambling-related irrational beliefs. It was
10 M.J.A. Wohl et al.
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hypothesised that the factor structure of the PLUS revealed in Study 1 would be confirmed
in Study 2. It was also predicted that the PLUS would measure a unique construct that is not
completely encapsulated by other such measures of gambling-related irrational beliefs.
The purpose of Study 3 was tri-fold. First, we examined whether the factor structure of
the PLUS held in a community sample of gamblers. Second, we wanted to determine if,
among a community sample of gamblers, the PLUS could discriminate between
recreational and pathological gamblers. Third, Study 3 afforded the opportunity to assess
whether the PLUS predicted gambling behaviour. Specifically, we examined whether
participants who had exaggerated perceptions of personal luck spent more money in a
gambling session.
The sample size for all three studies were determined to provide sufficient power (0.80)
with p¼0.05 to detect a medium effect size (
h
2
¼0.10) as significant. In addition, prior to
conducting the studies reported herein, the purpose and methodology were reviewed and
approved by the Carleton University, Department of Psychology Ethics Committee.
Study 1
Method
Participants and Procedure
Over a span of three years, students enrolled in a broad range of first year classes at a large
Eastern Canadian University were asked to complete the DSM-IV checklist for
pathological gambling (American Psychiatric Association [APA], 1994) and a single
question asking them ‘Do you gamble’ (yes or no). In total, 3419 students completed the
questionnaire.
From this participant pool, 347 people (154 males and 193 females) were randomly
selected (within each category of gambling pathology – according to the DSM-IV – so as
to have a distribution across levels) to participate in the current study. Using the DSM-IV
checklist for pathological gambling (APA, 1994), the current sample consisted of 254
(73.20%) recreational gamblers (85 males and 169 females), 80 (23.05%) at-risk
pathological gamblers (58 males and 22 females), and 13 (3.75%) pathological gamblers
(11 males and 2 females). The majority of participants were Caucasian (77.2%), whereas
other participants were East Asian (4.9%), other or multi-ethnic (4.9%), and South Asian
(4.6%). The remainder of participants (8.4%) identified themselves as African-Canadian,
Native Canadian, Hispanic and Middle Eastern. In terms of preferred form of gambling,
participants reported playing slot machines (39.9%) and cards (34.4%) as their favourite
form of gambling. A smaller percentage of those surveyed cited roulette (7.7%), other
gambling activities (7.4%), horse races (4.6%), dice games (4.6%) and video lottery and
poker machines (1.2%) as their favourite form of gambling. Participants ranged in age
from 17 to 49 (M¼21.00, SD ¼5.18).
The study was administered online via a link provided to participants on the online
recruitment tool used by the department of psychology at the university. Upon clicking on
the link, participants were taken to a webpage that contained an online consent form. When
consent was granted, they were automatically taken to a webpage that contained, among
other measures, those of interest for the current investigation. Once the questionnaire battery
was completed, participants were taken to another webpage that debriefed them about the
purpose of the study. As compensation for taking part in the study, participants were given
Can$10 or if enrolled in an introductory psychology course, they had the option of either
Can$10 or one bonus percent that could be used towards their final grade in the course.
International Gambling Studies 11
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Measures
Personal luck
Based on existing conceptualisations of gambling-related personal luck (Darke &
Freedman, 1997; Griffiths & Bingham, 2005; Wagenaar & Keren, 1988; Wohl, 2008), as
well as discussion with experts in the field, an initial pool of 12 items was formulated.
Specifically, we conducted a non-exhaustive review of the literature for articles that
examined colloquial understandings of luck. Importantly, both empirical and
philosophical articles on luck were included in the review. From the empirical articles
we adapted items that reflected the Wohl and Enzle (2002, 2003) notion of personal luck
(i.e. a misperceived ability to influence non-controllable events). From philosophical
papers on luck, we constructed items based on discussions regarding people’s non-rational
understanding of luck. We also asked four researchers/clinicians for examples of
expressions of personal luck by pathological gamblers. From these sources, a list of 12
items was constructed to assess the belief that luck is an internal quality of the self as
opposed to a random event that happened to befall the self. For example, participants were
asked to indicate their agreement with statements such as ‘I am likely to win when
gambling because I am lucky’ and ‘I try to use my luck when I gamble’ (see Table 1 for a
full list of items). Responses were anchored at 1 (strongly disagree) and 5 (strongly agree).
In order to control for response biases, two items were negatively worded. We then
contacted four expert researchers to obtain feedback on the content validity of a 12-item
version of the personal luck usage measure under development (for a discussion on this
method of scale development, see DeVellis, 1991; Kazdin, 1992). Based on the experts’
feedback, all items were retained.
Level of gambling pathology
The 10-item gambling checklist from the Diagnostic and Statistical Manual of Mental
Disorders, 4th edn (DSM-IV; APA, 1994) was used to assess symptoms of pathological
gambling. Participants were instructed to indicate ‘Yes’ if the statement applied to them
and ‘No’ if it did not. For example, item 7 asks, ‘Have you made repeated unsuccessful
attempts to control, cut back or stop gambling?’ This checklist was used to identify
recreational gamblers (0 items endorsed), at-risk gamblers (1 –4 items endorsed), and
Table 1. Study 1: Factor Loadings on the Personal Luck Usage Scale (PLUS).
Items Factor loading
I believe some people are luckier than others 0.43
I consider myself to be a lucky person 0.45
My wins are evidence that I have luck related to gambling 0.68
My luck helps me win 0.84
I am really lucky when I gamble 0.68
My luck plays an important part in my gambling 0.78
I feel secure about gambling, because I am a lucky person 0.73
I am not a lucky person*0.17
My luck influences the probability that I will win 0.82
I try to use my luck when I gamble 0.75
I am likely to win when gambling because I am lucky 0.81
I am not any luckier than other gamblers*0.33
*Reversed keyed items. Items in bold are items that make up the final scale.
12 M.J.A. Wohl et al.
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pathological gamblers (5 þitems endorsed). It should be noted that ‘at-risk’ is not a
recognised DSM-IV category for gambling pathology. Instead the term ‘sub-threshold
pathological gambler’ is used for people who report three to four symptoms of gambling
pathology. We use the term ‘at-risk’ to make a clear differentiation between our
categorisation schemes and that used in the DSM-IV. It can, of course, be argued that a
cut-off of one symptom for identifying a person as being at risk of pathological gambling
is too liberal. However, it can also be argued that the use of scores of three or four DSM-IV
symptoms may be too conservative. That said, three or four symptoms might be more
representative of clinically significant gambling problems than those who report one or
two symptoms. We (see Wohl et al., 2005), as well as others (e.g. Cox, Enns & Michaud,
2004), believe that people who report even one symptom of gambling pathology should be
considered to have experienced some degree of problem with their gambling and
therefore cannot justifiably be referred to as recreational gamblers. Although we included
participants with one or two symptoms of pathology for the analyses reported, we also
conducted all analyses excluding people who reported having only one or two symptoms
of gambling pathology. Importantly, the factor structure of the PLUS was not altered and
all reported associations between the measured variables were maintained.
Results
Analysis of scale structure
An unrestricted factor analysis (FA) with principal axis extraction was performed to
explore the dimensionality of the data collected from the initial 12 items of the PLUS. The
Kaiser– Meyer – Olkin measure of sampling adequacy (0.89); Bartlett’s test of sphericity,
x
2
¼(66, N¼347) ¼2220.67, p,0.001; and determinant of the matrix (0.001) each
indicated that the correlation matrix was appropriate for such an analysis. An oblique
rotation (promax) was selected in order to allow factors to correlate and increase
interpretability of the factors. In order to determine the number of non-trivial factors to be
retained various criteria were used: eigenvalues greater than one, the Scree test (Cattell,
1966) and parallel analysis (Horn, 1965). Further, in order to produce a succinct final scale
that selected only the purest measures of the factor (Comrey & Lee, 1992), a stringent
factor loading criteria of .0.63 was employed.
The factor analysis produced two factors with eigenvalues greater than one (5.72 and
1.47) that explained 52.93% of the variance. Both the eigenvalue criterion and the Scree
plot suggested the presence of two, non-trivial factors. Parallel analysis was also used to
determine the correct number of factors to retain (Horn, 1965; O’Connor, 2000; Zwick &
Velicer, 1986). We generated 1000 random data sets for 347 participants and 12 variables.
The eigenvalues of the two observed factors exceeded the eigenvalues of the random data
sets, suggesting the presence of two distinct factors. However, while eight items loaded
highly on the first factor (eigenvalue 5.72), only two items loaded on the second factor
(eigenvalue 1.47) and the remaining two items failed to load on either two factors.
Given that a factor with less than three items is generally weak and unstable (Costello
& Osborne, 2005), it was decided to eliminate the two-item second factor (‘I consider
myself to be a lucky person’; ‘I am not a lucky person’). In addition, the two items from the
initial pool that did not load onto either factor (‘I believe some people are luckier than
others’ and ‘I am not any luckier than other gamblers’) were also culled. Thus, a single
factor structure was determined to be the best fit. This eight-item PLUS demonstrated
excellent reliability,
a
¼0.92.
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Differences in PLUS scores by level of gambling pathology and gender
In order to examine whether the PLUS was capable of discriminating between those with
differing levels of gambling pathology and to assess whether there were any gender
differences, we conducted a 2 (gender) £2 (level of gambling pathology: recreational vs
at-risk gamblers) analysis of variance (ANOVA) on the PLUS. Given the small number of
pathological gamblers in the sample (n¼13), we decided to exclude pathological
gamblers from the analysis.
The ANOVA revealed a significant main effect of level of gambling pathology,
F(1, 330) ¼14.28, p,0.001,
h
p
2
¼0.04. Specifically, at-risk gamblers (M¼2.27,
SD ¼0.89) scored significantly higher than recreational gamblers (M¼1.88, SD ¼0.72)
on the PLUS. However, no significant differences were found between males (M¼2.06,
SD ¼0.86) and females (M¼1.91, SD ¼0.72) on the PLUS, F(1, 330) ¼0.11, p¼0.74.
There was also no significant interaction between gender and level of gambling pathology
on the PLUS, F(1, 330) ¼1.77, p¼0.19.
Discussion
Study 1 examined the psychometric properties of a scale developed to assess personal luck in
relation to gambling. Results revealed the emergence of a one dimensional, eight-item scale
that specifically assesses a belief in luck as a personal skill that can be used to maximise
positive gambling outcomes. As predicted, increased levels of gambling pathology were
associated with higher levels of gambling-related personal luck. Although support for our
contention that some people believe they possess a personal attribute of luck, a second study
was conducted to confirm the factorial structure of the PLUS and thus provide further
validation of this new measure of personal luck. Furthermore, it was of import to determine
whether items from the PLUS assessed a construct distinct from measures that purportedly
measure belief in luck. Recall, although there exists scales that assess luck, these scales do
not directly tap luck perceived as a personal possession, nor do they necessarily target luck as
it relates to gambling. As such, in Study 2 we examined whether the PLUS was empirically
distinguishable from the GBQ (Steenbergh et al., 2002), which measures belief that luck,
perseverance, or both, will eventually lead to gambling wins.
Study 2
Method
Participants
Three-hundred and sixty-one people (160 males and 201 females) from our pool of 3419
gamblers were randomly selected (within each category of gambling pathology – according
to the DSM-IV – so as to have a distribution across levels) to participate in Study 2. None of
the participants in Study 2 participated in Study 1. Two-hundred and fifty-five (70.64%)
participants were categorised, based on the DSM-IV checklist, as recreational gamblers (81
males and 172 females), 88 (24.38%) were at-risk gamblers (64 males and 24 females) and
18 (4.99%) were pathological gamblers (15 males and 3 females). The majority of
participants were Caucasian (77.2%), whereas other participants were East Asian (5.0%),
other or multi-ethnic (5.0%), and South Asian (4.4%). The remainder of participants (8.4%)
identified themselves as African-Canadian, Native Canadian, Hispanic and Middle Eastern.
In terms of preferred form of gambling, participants reported playing slot machines (38.9%)
and cards (34.5%) as their favourite form of gambling. A smaller percentage of those
14 M.J.A. Wohl et al.
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surveyed cited roulette (8.0%), other gambling activities (6.5%), horse races (5.3%), dice
games (5.3%), and video lottery and poker machines (1.5%) as their favourite form of
gambling. Participants ranged in age from 17 to 49 (M¼20.83, SD ¼5.12). Remuneration
for this study was the same as that offered in Study 1.
Procedure and measures
The procedure and measures were identical to those in Study 1, with the exception that
participants also completed the 10-item ‘skill orientation towards gambling’ subscale of
the GBQ (Steenbergh et al., 2002), which measures gamblers’ core beliefs in luck. This
subscale was used because, according to Steenbergh and colleagues (2002), items assess a
belief that personal skill can help maximise outcomes in games of chance. Participants
were instructed to respond to statements such as ‘I have a “lucky” technique that I use
when I gamble’ on a scale ranging from 1 (strongly disagree)to5(strongly agree).
Results
Confirmatory factor analysis (CFA) using LISREL 8.80 software (Joreskog & Sorbom,
2007) and maximum likelihood estimation was employed to assess whether the proposed
factorial structure of the PLUS fit the data, as well as to determine whether the PLUS and
10-item subscale of the GBQ (Steenbergh et al., 2002) comprised distinct factors as
expected. As the items on each scale were related, correlated error terms were introduced.
To accomplish this end, two CFAs were conducted. The first was a two factor model,
which was then compared against a one factor model.
Model fit was assessed by a number of indices, including the chi-square test, the
normed fit index (NFI), the non-normed fit index (NNFI), the comparative fit index (CFI),
the standardised root mean residual (RMR), and the root mean square error of
approximation (RMSEA). Values greater than 0.90 on the NFI, NNFI and CFI are
indicative of a good fit (Bentler, 1995; Joreskog & Sorbom, 1993), while RMR and
RMSEA values of less than 0.08 indicate an acceptable model fit (Hu & Bentler, 1999).
According to these criteria, the proposed two factor structure was a good fit to the data [
x
2
(105) ¼270.84, p,0.001, NFI ¼0.97; NNFI ¼0.98; CFI ¼0.98; RMR ¼0.08;
RMSEA ¼0.06]. A
x
2
difference test indicated that this two factor model fit the data
significantly better than a single factor model [
x
2
(119) ¼1130.35, p,0.001],
x
2
dif
(14) ¼859.51, p,0.001]. Although distinct, the PLUS and 10-item subscale of the GBQ
were positively correlated, r¼0.43. In addition, both the PLUS (
a
¼0.93) and the 10-
item subscale of the GBQ (
a
¼0.91) demonstrated excellent reliability.
Differences in PLUS scores by level of gambling pathology and gender
A 2 (gender) £2 (level of gambling pathology: recreational vs at-risk gamblers) ANOVA
on the PLUS was performed to assess differences in PLUS scores by level of gambling
pathology and gender. As the sample consisted of a small number of pathological
gamblers (n¼18), these gamblers were excluded from the analysis. The analysis revealed
a significant main effect of level of gambling pathology, F(1, 339) ¼26.67, p,0.001,
h
p
2
¼0.07. Specifically, at-risk gamblers (M¼2.37, SD ¼0.82) scored significantly
higher than recreational gamblers (M¼1.86, SD ¼0.78) on the PLUS. However, no
significant differences were found between males (M¼1.97, SD ¼0.79) and females
(M¼2.01, SD ¼0.84) on the PLUS, F(1, 339) ¼0.36, p¼0.55. There was also no
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significant interaction between gender and level of gambling pathology on the PLUS,
F(1, 339) ¼0.03, p¼0.85.
Differences in GBQ scores by level of gambling pathology and gender
A 2 (gender) £2 (level of gambling pathology: recreational vs at-risk gamblers) ANOVA
on the PLUS was conducted to examine differences in GBQ scores by level of pathology
and gender. Because of the low number of pathological gamblers (n¼18) in the sample,
these gamblers were not included in the analysis. The analysis revealed a significant main
effect of level of gambling pathology, F(1, 339) ¼12.81, p,0.001,
h
p
2
¼0.04.
Specifically, at-risk gamblers (M¼2.58, SD ¼0.94) scored significantly higher than
recreational gamblers (M¼2.19, SD ¼0.84) on the subscale of the GBQ. However,
males (M¼2.31, SD ¼0.91) and females (M¼2.27, SD ¼0.87) did not significantly
differ on the subscale of the GBQ, F(1, 339) ¼0.08, p¼0.78. Further, there was no
significant interaction between gender and level of gambling pathology on the subscale of
the GBQ, F(1, 339) ¼1.03, p¼0.31.
Discussion
Results of Study 2 confirmed the factor structure of the PLUS in a separate sample of
gamblers. Although there was a significant relationship between the PLUS and the
subscale of the GBQ (Steenbergh et al., 2002), results of the CFA suggest that the two
scales measure distinct constructs and the PLUS assesses a gambling-related irrational
belief that is not fully captured by existing measures. While Studies 1 and 2 provided
support for a measure of gambling-related personal luck, it was also important to
determine whether (a) the observed factor structure of the PLUS held among a community
sample of gamblers, and (b) the PLUS was capable of predicting gambling behaviour. We
argue that gamblers who believe themselves as possessing an ability (i.e. personal luck)
that will increase their chances of a positive outcome should be willing to wager a
relatively large sum of money while gambling. That is, gamblers who perceive themselves
as personally lucky may be more likely to wager increasing amounts of money while
gambling, as they tend to believe they can use this ‘skill’ to increase their chances of
winning (e.g. Wohl & Enzle, 2002, 2003). It was thus hypothesised that scores on the
PLUS would be positively associated with gambling expenditures. To this end, Study 3
examined the predictive validity of the PLUS. Specifically, we explored whether the
PLUS predicted the average amount of money spent in a given gambling session.
Study 3
Method
Participants and procedure
Sixty gamblers (29 males and 31 females) from the local community were recruited from a
nearby casino to participate in this study on gambling at a large Eastern Canadian
university. Specifically, we were able to recruit 28 recreational (13 males and 15 females)
and 32 pathological gamblers (16 males and 16 females). The majority of participants
were Caucasian (83.0%), whereas other participants were Asian (5.7%), and the remainder
of participants (11.3%) identified themselves as Hispanic, Native Canadian, African-
Canadian and other or multi-ethnic. In terms of preferred form of gambling, participants
reported playing slot machines (42.1%), cards (31.6%), and the lottery (19.3%). A smaller
16 M.J.A. Wohl et al.
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percentage of those surveyed cited sports betting (1.8%), horse races (1.8%), lottery and
scratch tickets (1.8%) and dice games (1.8%) as their preferred form of gambling.
Participants ranged in age from 19 to 78 (M¼49.45, SD ¼15.32).
Upon arrival at the laboratory, participants completed a questionnaire that assessed
symptoms of gambling pathology (DSM-IV checklist for pathological gambling; APA,
1994), the PLUS, and a measure of gambling involvement that included items that
assessed gambling frequency and amount of money spent in a typical gambling session. As
compensation for taking part in the study, participants were given Can$20.
Results
Analysis of scale structure
Because the nature of the sample drawn for Study 3 (community) differed from that drawn
for Studies 1 and 2 (university students), we once again conducted an unrestricted FA on
the PLUS items followed by a CFA. Specifically, a FA with principal axis extraction was
performed to further explore the dimensionality of the eight-item PLUS using a
community sample of gamblers. The Kaiser – Meyer–Olkin measure of sampling
adequacy (0.87); Bartlett’s test of sphericity,
x
2
¼(28, N¼60) ¼330.73, p,0.001;
and determinant of the matrix (0.003) each indicated that the correlation matrix was
appropriate for such an analysis. We used the same criteria as Study 1 to determine the
number of non-trivial factors to be retained.
The factor analysis produced only one factor with an eigenvalue greater than one
(4.78), which explained 59.81% of the variance. Both the eigenvalue criterion and the
Scree plot suggested the presence of one non-trivial factor. Parallel analysis was also used
to determine the correct number of factors to retain (Horn, 1965; O’Connor, 2000; Zwick
& Velicer, 1986). We generated 1000 random data sets for 60 participants and eight
variables. The eigenvalue of the observed factor exceeded the eigenvalues of the random
data sets, suggesting the presence of one factor. To be sure, we then conducted a CFA
using LISREL 8.80 software (Joreskog & Sorbom, 2007). The proposed one factor
structure was a good fit to the data:
x
2
(14) ¼36.80, p,0.001, NFI ¼0.93,
NNFI ¼0.94, CFI ¼0.95, RMR ¼0.06; RMSEA ¼0.06. Thus, coinciding with both
Study 1 and 2, a single factor structure was determined to be the best fit. This eight-item
Personal Luck Usage Scale (PLUS) demonstrated excellent reliability,
a
¼0.92.
Main analysis
Separate regression analyses were performed to determine whether the PLUS was capable
of predicting frequency of play and the average amount of money spent in a gambling
session. Results revealed that PLUS scores did not predict frequency of play, R
2
¼0.04,
b
¼20.19, t(51) ¼21.40, p¼0.17. However, PLUS scores did account for over 10%
of the variance in average amount of money spent in a gambling session, R
2
¼0.11.
Specifically, higher PLUS scores were associated with increased average amounts of
money spent in a gambling session,
b
¼0.27, t(59) ¼2.60, p¼0.01.
We then conducted a 2 (gender) £2 (level of gambling pathology: recreational vs
pathological gamblers) ANOVA on the PLUS. This analysis revealed a significant main
effect of level of gambling pathology, F(1, 56) ¼5.90, p,0.05,
h
p
2
¼0.10. Specifically,
pathological gamblers (M¼1.91, SD ¼0.80) scored significantly higher than recreational
gamblers (M¼1.43, SD ¼0.68) on the PLUS. However, no significant differences were
found between males (M¼1.74, SD ¼0.69) and females (M¼1.64, SD ¼0.85) on the
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PLUS, F(1, 56) ¼0.23, p¼0.64. There was also no significant interaction between gender
and level of gambling pathology on the PLUS, F(1, 56) ¼0.52, p¼0.48.
Discussion
Study 3 was conducted to confirm the factor structure of the PLUS among a community
sample of gamblers, to assess whether a community sample of recreational and pathological
gamblers differed in perceptions of gambling-related personal luck (as measured by the
PLUS), and to determine whether the PLUS was capable of predicting the average amount
of money spent in a gambling session. As predicted, the factor structure of the PLUS
remained stable when it was administered to a community sample of gamblers (as opposed
to the university students used in Studies 1 and 2). We were also able to show that within this
community sample, pathological gamblers scored significantly higher than recreational
gamblers on the PLUS. Importantly, results revealed that the PLUS was moderately
correlated with the average amount of money spent in a gambling session and scores on the
PLUS were capable of predicting this gambling behaviour. As spending increasing amounts
of money gambling is one of the various problematic behaviours associated with gambling
pathology (e.g. Black & Moyer, 1998), the association between the average amount of
money spent in a gambling session and perceptions of gambling-related personal luck as
measured by the PLUS lends support to the predictive validity of this new scale.
General discussion
Although a belief in luck has been shown to have an important influence on gambling
(Wohl & Enzle, 2002, 2003), it has received relatively little attention among gambling
researchers. One possible reason is the lack of a valid, reliable, psychometrically tested
scale designed to measure gambling-related beliefs that luck is a personal quality or ability
that can be used to maximise outcomes when playing games of chance. Although there are
existing measures of a belief in luck and skill orientation while gambling, they do not
specifically measure perceptions of gambling-related personal luck. The current set of
studies describes the development and psychometric properties of such a scale – the
Personal Luck Usage Scale (PLUS).
Results from Study 1 suggest that gambling-related personal luck is comprised of one
factor, which assesses a belief that luck is a personal quality that can be utilised to influence
gambling outcomes. As predicted, the PLUS discriminated between those with differing
levels of gambling pathology. Specifically, at-risk gamblers endorsed significantly higher
levels of gambling-related personal luck than recreational gamblers. These findings are
consistent with previous research conducted by Wohl and colleagues(2007), which found that
beliefs in luck were elevated among at-risk gamblers incomparison to recreational gamblers.
Results of Study 2 confirmed the factorial structure of the PLUS observed in Study 1 in
a different sample of gamblers. The results also revealed that the PLUS assesses a
gambling-related irrational belief that is not fully captured by previous measures of
gambling-related irrational beliefs (i.e. GBQ; Steenbergh et al., 2002). This finding
provides further support for a new measure of gambling-related personal luck.
Using a community sample of gamblers, results from Study 3 revealed that
pathological gamblers scored significantly higher than recreational gamblers on the PLUS.
Importantly, Study 3 found that the PLUS was linked to gambling behaviour. Specifically,
higher levels of gambling-related personal luck (as measured by the PLUS) were
associated with increased amounts of money spent in a gambling session.
18 M.J.A. Wohl et al.
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The excellent internal consistency of the final eight-item PLUS was exemplified by a
Cronbach’s
a
coefficient value of 0.92 in Study 1, 0.93 in Study 2 and 0.92 in Study 3.
According to DeVellis (1991), these values are judged to be ‘perfectly adequate’ for group
comparisons of the construct being measured and are approaching the mid-0.90s range that
is recommended for individual clinical assessment. The convergent validity of the PLUS
was supported by its moderate correlation (r.0.30) with a previously validated measure
of gambling-related irrational beliefs (i.e. items from GBQ; Steenbergh et al., 2002).
In addition, the predictive validity of the PLUS was supported by its association with
behaviour implicated in the development and maintenance of problematic gambling – the
amount of money spent in a typical gambling session.
It is our contention that the PLUS may be a useful instrument for treatment providers.
Specifically, administration of the PLUS may help treatment providers gain an
understanding of whether perceptions of personal luck play a role in the development and
maintenance of gambling problems among treatment seekers. In doing so, they may be
able to focus treatment on cognitive interventions designed to challenge the erroneous
perception of the ability to use personal luck to influence gambling outcomes. However,
such perceptions may be more difficult to undermine than basic erroneous cognitions
regarding how slot machines operate (e.g. Wohl et al., 2010). Unlike misperceptions of
randomness that can be corrected with improved mathematical knowledge, internal
attributions of personal luck might be relatively harder to undermine. This is because
suggesting that a gambler seek treatment for a behaviour he or she believes they are
skillful at would be akin to telling a star football player to seek treatment for being a
talented athlete. Of course, there is no skill that can be used to maximise outcomes in a
pure chance game. However, those who believe themselves to be personally luck would
tend not perceive this argument to be valid – they would likely believe personal luck is a
skill that can be used and deployed and thus with practice and effort the chance of success
at gambling is improved.
Some limitations of the current research should be noted. First, the factorial structure of
the PLUS was explored using undergraduate university students. That said, we were able to
confirm the factorial structure using a community sample of slot machine players.
Importantly, PLUS scores were associated with increased monetary expenditure during a
single gambling session. However, what is unknown is whether the PLUS has predictive
utility with regard to in session wagering. We propose that future research should examine
whether PLUS scores are associated with increased risk taking on particular types of bets. For
example, it is possible that self-perceived lucky people are more likely to place bets on risky
(low odds) bets. Moreover, it would be of interest to determine whether the PLUS is capable of
predicting an important marker of problematic play – persistence in the face of loss.
Concluding remarks
The present research is the first to assess the factorial structure of a belief in gambling-
related personal luck. Results from the studies suggest that a belief in gambling-related
personal luck is a one-dimensional construct that involves the perception that one can use
personal skill to positively influence gambling outcomes. The endorsement of such a
perception has important implications for gamblers. Indeed, heightened levels of self-
perceived personal luck may lead to problematic gambling (Wohl & Enzle, 2002, 2003) and
has also been associated with pathological gamblers’ reluctance to seek treatment (Wohl
et al., 2007). By implementing prevention and intervention programs that aim to challenge
and dispel this irrational belief, it is possible that the negative consequences stemming from
International Gambling Studies 19
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perceptions of gambling-related personal luck may be reduced among gamblers and the
development of this irrational belief may be prevented among those at-risk.
Acknowledgements
This research was supported by a research grant from the Ontario Problem Gambling Research
Centre (#2345) to the first author.
Notes on contributors
Michael J. A. Wohl, PhD is an Associate Professor of Psychology at Carleton University. He
received his PhD in Psychology at the University of Alberta in 2003. The majority of Dr Wohl’s
work has focused on erroneous cognitions (including perceptions of luck as a personal possession),
craving, and stress and coping responses, as predictors of continued gambling behavior. His work has
also focused on, among other things, prevention initiative and the factors that contribute to a refusal
to seek treatment. Dr Wohl has published over 40 peer-reviewed papers and is the receipt of
Carleton’s Research Achievement Award. Funding for his research has come from the Ontario
Problem Gambling Research Centre, Social Sciences and Humanities Research Council of Canada,
and the Australian Research Council. In 2009, Dr Wohl was awarded an infrastructure grant from the
Canadian Foundation for Innovation to build a state-of-the-art casino laboratory. This laboratory
contains card tables, slot machines, and an interactive virtual reality casino.
Matthew M. Young, PhD is Senior Research and Policy Analyst at the Canadian Centre on
Substance Abuse (CCSA) and an Adjunct Research Professor of Psychology at Carleton University.
Dr Young has been an active researcher in the area of problem gambling, conducting qualitative and
quantitative research in both academic and applied settings. His interests include craving,
prevention, and population assessment of gambling and problem gambling.
Melissa J. Stewart, MA is a doctoral student in Clinical Psychology at Dalhousie University. Her
research interests reside primarily within the area of prevention and treatment of problem gambling.
Specifically, she is interested in psychological factors (e.g., motivations to gamble, outcome
expectancies) that play a role in the development and maintenance of problem gambling, as well as
responsible gambling strategies aimed at reducing the risk of problematic slot machine play.
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