Journal of Gambling Studies

, Volume 29, Issue 1, pp 109–118 | Cite as

Winning or Losing a Bet and the Perception of Randomness

Original Paper

Abstract

This study examines the potential effects of random gain, loss, or neutral outcomes on individuals’ judgments of randomness in life and in unpredictable life events. Based on existing evidence, we hypothesize that experiencing gain would decrease the perception of randomness, whereas loss would have the opposite effect. One-hundred and ten students participated in a random bet for academic credit required for their introductory psychology course, where they could experience gain (bonus credit), loss (no credit), or neutral (exact credit as promised) outcomes. In addition, they filled out a questionnaire on their beliefs in randomness in general and in various everyday life events, as well as their judgment of the extent to which each event was pre-determined. The results provide partial support for our hypotheses. The participants experiencing a ‘neutral’ result report the highest level of randomness in general and in everyday life events, as well as the highest extent to which the events were judged as pre-determined. Randomness was judged as lower in both the ‘loss’ and ‘gain’ conditions. These patterns only emerge after controlling for gender and religiosity. The results are discussed in light of existing evidence and directions for future studies.

Keywords

Randomness Unpredictable events Framing Priming Perception of random events Experimental design 

Introduction

Individuals’ ability to understand and assess randomness is the subject of much interest, not only in psychology but also in philosophy and theology (Wolfram 2002) as well as numerous other fields of research and practice. Although the notions of randomness and unpredictability are often used interchangeably in cognitive science, the difference between the two should be noted. Randomness may have numerous definitions and operationalizations in varying contexts (Bar-Hillel and Wagenaar 1991). In psychological research it is often defined as a condition in which various events have the same (known in advance) chance of occurrence. As a result, one random event is as likely as any other random event to take place. Unpredictability, on the other hand, is a condition in which the chances of an event or a set of events are simply unknown or perceived as beyond one’s ability to control and predict (Kimhi and Zysberg 2009; Nickerson 2004; Wolfram 2002). In this case, events may differ in their chance of occurrence, but are perceived as uncontrollable.

Existing evidence on the perception of randomness links it with various personal attributes and variables. For example, studies have found a tendency to perceive randomness associated with internal locus of control; male gender; and natural events, as opposed to man-made events (Kimhi and Zysberg 2009). While unpredictability has received far less research attention than randomness, it may be more relevant to everyday situations and human behavior in real-life settings. The current study examined the influence of situational factors (i.e., winning, losing, or neutral outcomes of a bet) on the perception of unpredictability and randomness in more general terms than has been studied in previous research.

There is some literature exploring the antecedents of the perception of unpredictability, of which the most well-known are the studies focusing on the “hot hand fallacy” and the “gambler’s fallacy” (Nickerson 2004; Rapoport and Wallsten 1972; Kahneman and Tversky 1972). These explore how people perceive predictability in an unpredictable series of events, usually attributed to motivational and perceptual biases. Findings suggest that depending on the circumstances, individuals will perceive higher or lower chances of scoring in sports or of winning a bet based on the results of previous attempts. Other studies have explored other examples of life events in which unpredictability is high, but there is no known chance of occurrence. Two factors are mentioned in the literature on randomness cognition in actual and fictitious life events. The first consists of previous beliefs and perceptions that are typical of the individual. For example, there is a line of studies showing that people who report believing in paranormal events tend to perceive other unpredictable or random events as less random and perceive more illusory associations between life events (Rogers et al. 2009). The second factor comprises of the setting and format in which the data are presented (e.g., graphic or numerical). Studies have shown that the format of the presentation of data or events may have an influence on the perceived randomness (Wright et al. 2009). Other studies have focused on how information alters or fails to alter perceptions of the likelihood of random events, especially in gambling settings (Boutin et al. 2009; Caruso et al. 2010).

These findings may lead us to ask whether judgment regarding unpredictable events is affected by priming and framing. However, to the best of our knowledge, this issue has never been directly examined in laboratory settings. The phenomenon of framing has been at the center of perception and decision-making research for quite some time now (Kareev and Trope 2011). From a cognitive perspective, a frame is a psychological device offering context, activating cognitive schemas, and raising the salience of specific features in the perceptual field, thus shaping judgment and decision making (Gabriel and Williamson 2010; Kareev and Trope 2011; Tversky and Kahneman 1981). The existing evidence suggests that framing may influence individual and group judgments beyond the time-point and specific context in which it is presented. This has been demonstrated in fields ranging from the perception of everyday events to health-related decision making and career choices (Hodginson et al. 2002; Kareev and Trope 2011; Romanek et al. 2005). In studies looking at the perception of odds in a betting context both the priming-framing theoretical framework and the mere perceptual dynamics and biases of multi-stage bets were studied—suggesting most people fail in assessing realistic utility functions in such settings (Diecidue et al. 2004; Rapoport and Jones 1970).

Two experimental paradigms dominate the research in such judgment tasks. In the first, framing is manipulated or operationalized through the presentation of information. Typical results from such experiments show that the same problem induces different patterns of judgments when presented in varying ways (i.e., Gabriel and Williamson 2010; Tversky and Kahneman 1981). The second has to do with time sequencing as the mode of manipulation. In such settings, typical results demonstrate that a framing task influences judgments made in a different task following it (e.g., Nickerson 2004; Rapoport and Wallsten 1972; Kahneman and Tversky 1972). This phenomenon may also be referred toand conceptualized as priming.

The literature on priming provides a broad understanding of the phenomenon in diverse settings—from memory and basic perceptual tasks to social behavior (e.g., Epley and Gilovich 1999; Tipper 1985). Despite the differences in operationalization and settings applied, the evidence consistently suggests that priming is a powerful factor in producing perceptual and judgmental biases (Tipper and Cranston 1985). We sought to further explore how random outcomes prime our perception of predictability and randomness in general and in various everyday life events, beyond the popular use of equal-chance events and beyond the scope of a specific judgment task. Based on the literature describing the “gambler’s fallacy”, we hypothesized that experiencing a random gain would increase individuals’ sense of control over events, leading them to perceive less randomness in life. Thus the present study goes beyond traditional paradigms (e.g.: Rapoport and Jones 1970) in that it examines how one event may or may not influence people’s judgment of odds in a completely different type of activity or judgment call. Based on the literature on framing (e.g., Tversky and Kahneman 1981) we hypothesized that experiencing a random loss would decrease the sense of control, leading them to perceive more randomness in life.

In addition, the literature on the perception of predictability or randomness in everyday life events points to both gender and religiosity as having an influence on the perception of randomness. Females tend to perceive less randomness in various everyday unpredictable life events than males (Kimhi and Zysberg 2009). Religiosity is associated with a tendency to perceive less randomness and unpredictability (Beck and Miller 2001; Orenstein 2002) as well as a stronger belief in the meaningfulness of coincidence (Bressan et al. 2008).

Based on the above, we hypothesized that gender and religiosity would significantly affect people’s perception of randomness. Specifically, we hypothesized the following: (a) People experiencing random gain will tend to perceive less randomness in the world around them than people experiencing random neutral results. (b) People experiencing random loss will tend to perceive more randomness than those experiencing neutral results, and (c) Gender and religiosity will influence the relationships between experiencing random gain or loss and the perception of randomness.

Method

Sample

Participants were 110 freshman and sophomore students, who were offered credit required for their introductory psychology course in an academic college in northern Israel. Of the 110 participants, 69 (63%) were women and 41 (37%) were men. They ranged in age from 19 to 54 years old (M = 25.37; SD = 4.20). Ninety-three percent were Jewish, 4% were Christian and 3% were Druze.

Instruments

Perceptions of Randomness

Perception of randomness was assessed using a questionnaire developed by the authors to assess individuals’ perception of randomness and the extent to which various rare life events are pre-determined. The questionnaire included brief descriptions of eight events (four can be considered positive, e.g., winning a prize or finding a valuable raw gemstone while hiking, and four can be considered negative, e.g., home burglary). For each event, participants were requested to assess its randomness as well as the extent to which it was pre-determined, to the best of their judgment, on semantic-differential type scales. The reliability and content validity of this measure were good and reported as such in previous studies (Kimhi and Zysberg 2009). In the current study, we used three measures of perception of randomness. The first was the mean score of the participants’ responses to the question “to what extent is this event random” for each of the eight events depicted in the questionnaire (mean randomness) (Cronbach’s Alpha = .86). The second was the mean score of the responses to the question “to what extent is this event pre-determined”, again calculated for each of the eight events described (mean pre-determinedness, Cronbach’s Alpha = .92). The third was the participants’ perceptions of randomness in general, as assessed through a simple question: “to what extent is randomness a part of our lives?”, which was rated on a seven-point semantic interval scale ranging from “not at all” to “very much” (randomness in life).

Demographic Questionnaire

A short demographic questionnaire included items on gender (male = 1; female = 2); program of study (coded numerically to represent the relevant programs); age; socioeconomic status, reported on an ordinal scale ranging from 1 (much below average) to 5 (much above average), with the average income for a household in Israel used as the reference point; ethnic group (self-report); and the level of religiosity in the nuclear family. The item on religiosity was “what would best describe your nuclear family in terms of religiosity?”, and responses were scored on a four-point ordinal scale: “secular”, “traditional”, “religious”, and “orthodox”. These definitions correspond with widely acceptable terms referring to religious groups in Israeli society (e.g., Hobfoll et al. 2009).

Manipulation of Gain, Loss, or Neutral Outcomes (Priming)

The participants entered a room in groups of three. They agreed to participate in a simple bet based on rolling a die. This allowed for randomly choosing a winner (the one with the highest number), a loser (the one with the lowest number), and one who did not win or lose (the one with the middle value). They were told that the winner would receive 150% of the participation credit promised (bonus credit), the loser would lose all the credit for participation in the study (no credit), and the one in the neutral position would receive the original participation credit (exact credit as promised). Since the participation credit was required for the students’ completion of the Introduction to Psychology course (mandatory 10 h credits), gain or loss of this credit was evidently important and valuable to the students. Each participant threw the die once, and a research assistant documented the results, declaring who won, who lost, and who was ‘neutral’.

Decoy Questionnaire

Immediately following the throw of the die and announcement of the results, the students were asked to complete a short “decoy” self-image questionnaire. The questionnaire, which was constructed by two research assistants, consisted of basic demographic data (e.g., age, gender, program) and eight items assessing self-image (e.g.: “I think I am a worthy person”) that were rated on a seven-point Likert scale. The data from this questionnaire were not used in the analysis.

Procedure

Participants were recruited for the experiment through ads posted on a departmental bulletin board, disguising it as a “study on self-perception”. They were informed about the study procedure and were told that they could withdraw from the study at any point should they feel uncomfortable (students could choose from a wide range of different studies to earn the required credit). The researchers obtained approval from the college’s IRB for the study, and participants were asked to sign an informed consent form.

The participants first completed the study questionnaires and the gambling task, followed by the short “decoy” self-image questionnaire. At the end, the participants were asked to fill out one final questionnaire as a “personal favor” to the research assistants, who presented it as part of their own seminar project. No additional information was provided on the subject of the questionnaire. Except for one participant, all agreed to fill out the questionnaire, which was used to assess their perception of randomness in general (the perceived randomness measure).

The entire procedure took about 10–12 min to complete. After the experiment was completed, the participants were contacted by telephone and debriefed on the actual research question. Those who had “lost the bet” were reimbursed for the participation credit, as promised during recruitment.

Results

Before testing our hypotheses, we examined the distributions of the main study variables. Descriptive statistics suggested that the main dependent variables were distributed in a near normal manner and showed adequate range allowing for parametric data analysis. Core family religiosity in our sample was reported as 58% ‘secular’, 26% ‘traditional’, 13% ‘religious’, and 3% ‘orthodox’. This pattern resembles the distribution of self-reported religiosity levels in the general population in Israel (Israel Bureau of Statistics 2008) and therefore retained its original coding despite the relatively low number of participants in the “Orthodox” group.

We then examined the general associations between the various measures of randomness perception in our study across the experimental conditions. Table 1 provides descriptive statistics and Pearson’s correlations for the three measures, including religiosity.
Table 1

Descriptive statistics and intercorrelations among the outcome measures in the study (n = 110)

 

1

2

3

4

1. Randomness in life

   

2. Religiosity

−.20**

  

3. Mean randomness

−.46**

.13*

 

4. Mean pre-determinedness

.36**

−.15*

−.51**

Mean (SD)

4.22 (1.65)

***

2.91 (1.35)

4.84 (1.75)

Cronbach’s Alpha

.86

.92

Higher ratings in both measures of perceived randomness reflect higher levels of randomness. Higher ratings in perceived pre-determinedness reflect lower judgments of pre-determinedness in life events (reverse scaling)

P < .05

** P < .01

*** Religiosity distribution is provided in the text

The results suggest the expected correlation between various indicators of the participants’ assessment of randomness in life in general and in the various events described in our questionnaire. However, the moderate levels found may indicate that people assess randomness in specific events differently from their global assessment of “randomness in people’s lives”. Moreover, there were moderate, yet significant, correlations found between self-reported core family religiosity and the indices of randomness perception. Given the literature on the association between religious beliefs and the perception of randomness, this finding is in line with previous findings in adjacent fields, such as religiosity and belief in the paranormal and fate (see, for example, Beck and Miller 2001; Orenstein 2002).

After exploring the preliminary association patterns between the main measured variables, we proceeded to test our hypotheses by using ANCOVA to compare perceptions of randomness across the experimental conditions with gender as a second independent variable and religiosity as a covariate. Tables 2 and 3 summarize the results of these analyses.
Table 2

ANCOVA analysis with condition and gender as independent variables and core family religiosity as a covariate (n = 110)

 

F

df

Effect size (Eta2)

Religiosity

 Perception of randomness in life

4.73*

1

.06

 Mean randomness of life events

4.93*

.08

 Mean predictability of life events

5.07**

.10

Condition

 Perception of randomness in life

.75

2

.01

 Mean randomness of life events

3.40*

.07

 Mean predictability of life events

2.91*

.05

Gender

 Perception of randomness in life

.68

1

.00

 Mean randomness of life events

.04

.00

 Mean predictability of life events

6.15**

.11

Gender × condition

 Perception of randomness in life

.23

2

.00

 Mean randomness of life events

.73

.00

 Mean predictability of life events

.81

.01

P < .05

** P < .01

Table 3

Means and SD of randomness in life, perceived randomness and unpredictability by experimental condition and gender (after controlling for religiosity)

 

Loss

Neutral

Gain

Male

Perception of randomness in life

3.78 (1.57)

3.84 (1.77)

3.58 (2.19)

Mean randomness of life events

4.00 (1.51)

4.69 (1.70)

3.59 (2.06)

Mean predictability of life events

5.43 (1.33)

5.48 (1.59)

5.01 (2.06)

Female

Perception of randomness in life

3.65 (1.42)

4.29 (1.57)

3.96 (1.62)

Mean randomness of life events

3.84 (1.50)

4.70 (1.75)

4.16 (1.49)

Mean predictability of life events

4.09 (1.85)

5.23 (1.36)

4.25 (1.92)

Total

Perception of randomness in life

3.70 (1.46)

4.13 (1.63)

3.83 (1.80)

Mean randomness of life events

3.90 (1.48)a

4.70 (1.71)

3.97 (1.69)

Mean predictability of life events

4.64 (1.76)b

5.32 (1.43)

4.49 (1.97)

Higher ratings reflect higher perceptions of randomness in the first two measures. Higher ratings in ‘unpredictability’ reflect lower perceived levels of unpredictability in events (due to reverse scaling)

aLevel 2 versus Level 1 = .92; P < .02, Level 3 versus previous = −.74; P < .05

bLevel 2 versus Level 1 = .72; P < .05, Level 3 versus previous = −.65; P < .06

The results provide partial support for our hypotheses, indicating differences in two out of the three randomness assessment indices once we controlled for religiosity. People tended to report higher levels of perception of randomness in life events in the ‘neutral’ condition as compared to both the ‘loss’ and ‘gain’ conditions. In accordance, they also reported lower levels of perceived ‘pre-determinedness’ in various events in the ‘neutral condition.’ Gender had an effect only on the extent to which events were perceived as pre-determined, namely, females perceived various events to be more pre-determined than did males (as reflected by a lower mean in ‘pre-determinedness’, which was reverse-scaled).

Post hoc tests were used to examine the source of the significant differences found between the experimental conditions (see bottom of Table 3). The results show that the group differences in perceived randomness for various events were all significant, while the differences in perceived pre-determinedness were significant between the ‘neutral’ and the ‘loss’ groups, but marginal for the ‘gain’ group.

Discussion

We hypothesized that a priming experience of random gain, loss, or neutral outcomes in a bet would influence people’s judgments of randomness in a broader context. The results lend only partial support to our original hypotheses. Two out of the three measures of perceived randomness used in our study show a similar pattern, according to which participants who experienced a ‘neutral’ bet result showed higher levels of perceived randomness in the events described in our questionnaire and perceived them as less pre-determined than did people who experienced ‘loss’ or ‘gain’.

Gender differences were apparent in only one of the three measures, namely the perception of “the extent to which events are pre-determined” in the life events described in our questionnaire. Generally, the female participants reported more perceived pre-determinedness than their male counterparts. Importantly, these effects were revealed only after controlling for self-reported core family religiosity level. This finding is consistent with the literature indicating that religiosity is associated with an external locus of control and with an assumption of systematic cause-and-effect relationships for events that others may perceive as random (Beck and Miller 2001; Bressan et al. 2008; Zangench et al. 2008). Therefore, there is a possibility that religiosity masks the relationship between situational factors and the perception of randomness.

Although the importance of gender and religiosity in the perception of randomness in life is not a new insight, our main findings support the “hot hand fallacy” and the “gambler’s fallacy” (Ayton and Fischer 2004; Burns and Corpus 2004) in a different setting. Whereas the overwhelming majority of studies have examined the effects of recent outcomes of a random task on judgments of what will happen next within the very same task, we showed that the outcomes of a random task (a bet) may influence individuals’ perceptions of randomness in fields and content areas other than the original ‘random task’. To the best of our knowledge, these results are the first of their kind within this context.

Evidence from other areas of the study of perception support the direction suggested by our results. There is some evidence showing indirect priming, crossing the boundaries of content areas, and even the sub-conscious priming influence of diverse behaviors (Bargh and Chartrand 2000; Kiesel et al. 2007). Recently, Rutjens et al. (2010) demonstrated how priming may influence peoples’ perceptions of ideas regarding the origin of life, thereby biasing perceptions and beliefs in certain content areas.

As for the pattern of results actually achieved in this study and how they deviate from our original hypotheses: though the literature never addressed this possibility directly, our results may suggest that any type of value-laden outcome (loss or gain), compared with what may be perceived as ‘no result’ can create a differential psychological response related to one’s sense of control or loss of it. Can it be that an ‘outcome’ versus ‘no outcome’ is more important that the type of outcome in this context? Existing evidence from adjacent fields of research may support this pattern (Bar-Hillel and Wagenaar 1991; Diecidue et al. 2004).

Some limitations of this study should be considered when interpreting the results. First, our sample poses a few limitations to the external validity of the results due to its relatively small size and the fact that it was recruited from the student population in Israel. A second point is that we used a measure based on the perception of randomness in unpredictable and relatively rare life events, such as a fire in one’s home or winning a prize. Additional studies will be required to address the issue of whether these results can be generalized to include more mundane random events.

Similarly, it is worthwhile looking at different manipulations of experiences of gain, loss, or neutral outcomes. Using decoy assignments and false manipulation (deception regarding loss of credit) to create an experience of gain, loss, or neutral outcomes also raises the question of whether the results can be generalized to other life events and settings. While the literature on the subject is ambiguous (Sieber 1982), there is enough evidence suggesting that indirect manipulation of this sort is a valid enough approach. Further studies need to corroborate our findings in different settings and in varying samples. Additional studies should also examine the effects of priming in the longer run: How long does the effect of priming of random life experiences last? Does it accumulate over time and various experiences? How malleable is it to change and intervention? All of these questions have yet to be empirically addressed.

Beyond the above limitations, the directions pointed to by our findings, as well as existing evidence in adjacent fields, provide insight into the mechanisms shaping our perceptions of randomness and unpredictability and how we implement them to assess various life events. Our findings link the perception of randomness and unpredictability with situational influences beyond the personal factors that are usually identified with how we perceive and judge our world. Should future studies support our results, such findings may change the way in which we look at gambling, superstition, and other social behaviors associated with the notion of randomness.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PsychologyTel Hai CollegeTel Hai, Upper GalileeIsrael
  2. 2.HaifaIsrael

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