Cash-Out Gambling and The Illusion of Control
Ross Gorrie - 11374195 Supervisor - Aljaz Ule
Economics Master’s Thesis: Specialisation - Behavioural Economics & Game Theory
Abstract:
Findings in psychology point to a systematic bias, “the Illusion of Control”, by which certain preconditions lend agents to overestimate their degree of control over chance outcomes. This thesis proposes that the increased level of active involvement associated with cash-out betting contributes to illusory control among gamblers, making bets with an option to cash-out more attractive. Using data collected from an online gambling experiment, the paper fails to prove that subjects preferred cash-out gambles to non-cash-out gambles. Illusory beliefs that a cash-out gamble pays more were present, however. Beliefs were correlated with preference over gambles, although this effect was insignificant. Beliefs were found to be significantly determined, in part, by subjects’ previous success at a cash-out gamble but not by subjects’ previous gambling experience. Risk aversion was not found to be a significant determinant of preferences over gambles.
Statement of Originality:
This document is written by Ross Gorrie who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
1 Section 1 – Introduction
Firms routinely look for new methods to influence the behavior of their existing and potential customers. The more traditional ways include changes in price or quality of the product as well as persuasion of an inherent need for the product. Increasingly, as new findings and greater data sets make them easier to quantify, firms have made use of cognitive and emotional biases to influence the decision process. Betting companies notoriously use marketing strategies to encourage increased risk taking in lotteries – primarily targeting young males. Advertisements prime customers by depicting unlikely winners as the norm; clouding one’s predisposition to betting by showing that winning is not only possible, but also probable. Framing is common, with adverts that depict the act of betting on the outcome of an event as an opportunity to take part in the event itself. In the UK, the growth of the social norm is encouraged with “The Ladbrokes Life”1 style advertisements. This depiction of reckless gambling as a part of everyday life normalizes the betting world. In a sense, one cannot be ‘in’ unless they gamble. This effect is magnified by the relentless sponsorship by gambling companies that surrounds the sport of football making the two almost synonymous (MacInnes 2017).
Aside from advertising, betting firms have taken advantage of behavioral biases through modifying the design of their product. Advancements in technology have provided opportunities on this front: with the introduction of online betting accounts, firms make it easier to deposit funds than to withdraw winnings. Withdrawals are accompanied by longer processing times and more thorough security checks than deposits, making the immediate gratification of placing winnings on a new bet more attractive than the time-discounted withdrawal amount. Also, the development of betting applications for mobile devices has made it possible to place bets from anywhere, reducing the effort associated with betting at designated locations.
This thesis will focus on ‘Bet In Play’ markets (those with opportunities to place bets on events that are currently ongoing) and in particular the option to ‘cash-out’ on unresolved bets for their current value. Findings in psychology state that increasing the level of active involvement in pure chance games can lead to increased risk taking (Langer 1975, Thompson
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1999). This phenomenon is often attributed to the cognitive bias “the illusion of control” (IOC) as gamblers irrationally associate the increased control they have over their decision with having a greater personal influence on their probability of winning, i.e. they believe they can play the game skillfully to win more. An alternative explanation is that gamblers are aware of their probability of winning, but gain utility from active involvement and so inherently prefer a gamble with more control.
The aim of the thesis is to provide evidence of the IOC and demonstrate how betting firms use it to encourage customers to take up bets. Although studied thoroughly in psychology literature, results surrounding the bias in economics are less clear (Filippin, Crosetto 2016). The study aims to address whether the option to cash-out, controlling for risk preferences, makes a gamble more attractive, and whether this effect can be attributed to the IOC. An online gambling experiment using 55 participants was conducted to study the effects of the cash-out option on betting habits. No evidence was found that cash-out gambles are preferred to non-cash-out gambles when risk preferences are controlled for. In fact, non-cash-out gambles were preferred. There is suggestive evidence, however, that subjects believed a cash-out gamble would earn more than an equivalent non-cash-cash-out gamble, implying some form of illusory beliefs. Results were affected by a multitude of issues that are discussed further in Section 4.
The thesis proceeds as follows. Section 2 will provide an overview of IOC literature in the fields of both psychology and economics. Section 3 describes the design of the experiment and procedures taken, while Section 4 analyses the results of the study in full. Section 5 discusses the implications of the study and suggests avenues for further research before concluding the paper.
Section 2 – Literature Review
Most theories of why gamblers make irrational decisions focus on the characteristics of the individual. Kahneman & Tversky (1972) argued that the representativeness heuristic leads to incorrect probability estimations that internally rationalize these decisions. The IOC is often characterised as a representativeness heuristic that associates active involvement (or control over an unrelated factor) with influence over the probability of success in a game or event.
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The IOC is defined by Langer (1975) as “an expectation of a personal success probability inappropriately higher than the objective probability would warrant”. The term captures a bias towards believing that an outcome determined purely by chance can be controlled. This discrepancy arises when factors from skill situations (competition, choice, familiarity, and involvement) are introduced into chance situations. Langer cites an experiment in which subjects selected a path to move a stylus across a wooden board. The confidence of choosing the correct path was reported higher when subjects were allowed to move the stylus themselves as opposed to dictating the path to the experimenter. From this, Langer confirms active involvement as a determinant of the bias. In a lottery prize draw, passive involvement was also found to affect the bias. Treated subjects were encouraged to think about the lottery on three separate occasions. Compared to a non-encouraged control group, encouraged subjects were more confident of winning the prize and less likely to trade their ticket for a lottery ticket with a higher probability of winning. Dixon (2000) provides an example of how the IOC can be manipulated through increased involvement in a roulette game. Similarly to Langer’s lottery numbers experiment, it showed that subjects were willing to pay for the right to select a number (as opposed to the number being selected by the experimenter) when playing a game of roulette. The statistical significance of the observed effect is not documented, and the small sample size (5), as well as the ambiguity surrounding why subjects preferred to pick their number – because they believed they could earn more this way or for some other reason – makes it impossible to draw any definitive conclusions.
Thompson (1999) builds on Langer’s description of the bias and concludes that control is overestimated when certain situational or person-based factors are met. The situational factors described are similar to Langer’s skill-based factors, but are extended to include foreknowledge of the desired outcome and success at the task. Success is demonstrated to be a relevant factor through an experiment where subjects flick a light switch that works either 75% or 25% of the time. Those in the 75% group reported higher estimates of their control over the light. While a link to the original study is not provided, we can assume that the light did not switch on for no reason, i.e. only 25% / 75% of the time when the switch was
activated. If so, those from the 75% group did exert more control and so an IOC was not
present. It does seem a reasonable notion, though, that prior success at a task could determine IOC. The person-based factors introduced by Thompson include one’s need for control and
one’s mood. Need for control was manipulated experimentally with subjects that were
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task for which the prize was a hamburger. Alloy et al. (1981) assessed the effect of mood and observed that non-depressed individuals overestimated their level of control while those that suffered from depression were more realistic. This is consistent with psychological findings on similar optimistic biases such as overconfidence and the self-serving bias (Dunning, Story 1991).
Harrigan et al. (2014) discuss an example of how the IOC is manipulated by gambling companies. Adding more winnable lines to slot machines creates more gambling options and so greater control over “celebratory feedback rate” (how likely the gambler is to receive a prize) which includes legitimate wins, as well as losses disguised as wins - a payout that is less than the wagered amount. The overall effect is a less varied gambling experience that takes longer to exhaust funds and includes more instances of receiving payment. Audiovisual feedback accompanies payment and is likely to encourage winning feelings and increase dopamine levels in the same way gaming and receiving text messages have proven to (Kuss 2013). This control over celebratory feedback creates a bias where gamblers feel like they can influence their chances of a legitimate win. Gambling strategies are tested and shown to be equally profitable, i.e. proving that the bias is irrational. While a compelling argument, the paper fails to assess gambler behaviour or beliefs and indeed concludes by pointing towards testing these hypotheses experimentally.
Presson and Benassi (1996) carried out a meta-analysis of 53 experiments on the IOC and distinguished between illusory control and illusory prediction. Robust effects of a systematic bias are found under a variety of circumstances and designs. The effect, however, is found to be much stronger in experiments that measure subjects’ beliefs about their ability to predict outcomes rather than their ability to control outcomes. They point out the fact that few experiments are framed in a way that correctly measures IOC in that subjects are asked to judge the extent to which they directly affect outcomes. There is, however, a clear preference for direct control observed in some experiments, e.g. craps players who prefer to roll the dice themselves.
Martinez et al. (2009) distinguish between the influences of choice (choosing between gambles) and involvement (interaction with the gambling device) to determine the principal force surrounding irrational risk taking in gambling and assess whether either can be mediated by the IOC. The experiment involved subjects picking urns to draw a ball from and
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betting on whether they would draw a winning ball. Involvement was manipulated by having the player or the dealer draw from the chosen urn while choice was manipulated by having the player or dealer choose which urn to draw from. IOC was measured with an un-incentivised questionnaire that asked subjects how much they expected to win at the end of each game while risk taking was measured crudely by the average bet amount and more precisely by the average investment (ratio of bet amount to current amount of chips in possession). Results of the experiment suggest that increased choice does translate to greater IOC, but the effect did not correlate with greater risk-taking. Increased involvement did not correlate with IOC reports, but did so with greater risk-taking. The findings suggest any bias instigated by increased choice is not large enough to encourage greater risk taking, while the increased risk taking observed with the greater involvement condition cannot be attributed to the bias. Possible explanations are that active involvement leads to greater arousal, which is commonly linked to risk taking (Fernandez-Duque, Wifall 2007). As the measurement for risk taking is confined to betting amounts, it cannot be ruled out that IOC beliefs are linked to greater risk taking in other ways - such as the decision of whether to take up a gamble.
The effect of the IOC, when compared to biases commonly tested in behavioural economics (confirmation bias, status quo bias, anchoring effects etc.) is more ambiguous, and as such, the effect and strength of the bias are doubted. There have been attempts, both successful and unsuccessful, however, to prove the effect of the IOC in a robust experimental setting. Filippin and Crosetto (2016) discuss the differing consensuses surrounding the IOC among economists and psychologists. One explanation is that findings in psychology would be crowded out by monetary incentives. Another is that economists tend to test the influence of control over the resolution of uncertainty (active involvement), rather than over the choice of lottery as is often looked at by psychologists. Using a Bomb Risk Elicitation Task - a game in which subjects collect boxes to earn cash by clicking on them, where one box contains a ‘bomb’ that discards the subjects’ earnings - the authors were able to manipulate both types of control. Active involvement was manipulated by allowing the subject (rather than the experimenter) to roll the die that determined the position of the bomb. Choice was manipulated by altering the method for collecting boxes. Rather than a mechanism that continually collected boxes, subjects would click boxes individually. Choices were generally consistent with risk neutrality across treatments (picking 50% of the boxes before quitting) and, in fact, those subjected to the control over choice of lottery treatment displayed beliefs in the opposite direction predicted with an IOC - but not significantly so. The results suggest
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that the type of control is not a significant reason for the differing conclusions observed across economics and psychology literature. The authors conclude that a hypothetical bias may exist: The IOC may occur with hypothetical decisions commonly used in psychological papers, but become crowded out by the monetary incentives used in economic studies.
Sloof and von Siemens (2016) conducted an experiment that aimed to test whether the bias is a manifestation of intrinsic value for authority. Subjects were asked to make a choice in which each option corresponded to a different task. Subjects are aware of the tasks but unaware of which option corresponds to which task. The experiment uses an incentivised willingness to pay and belief elicitation method to test whether subjects are willing to pay for the right to choose which task will be undertaken and whether they believe their choice is more likely to correspond to their preferred task. Although most subjects rationally reported the probability of choosing their preferred task as 50%, a sizeable portion reported beliefs that their choice could increase their probability of success (and a small amount predicted that their choice would decrease their probability of success). A Wilcoxon signed-rank test rejected the hypothesis that the median of this illusion was zero providing evidence of a systematic bias rather than noise in the belief reports. Furthermore, while many subjects who reported rational beliefs about their probability of success were willing to pay for control - suggesting some intrinsic preference for authority, the amount subjects were willing to pay was significantly more for those who reported positive illusory beliefs and the two were indeed correlated.
Charness and Gneezy (2009) tested for the presence of the IOC, among other behavioural phenomena (ambiguity aversion and myopic loss aversion), and studied their effect on portfolio choices. A roll of a six-sided die determined the value of the asset. The four treatments were: the subject rolls the die, the experimenter rolls the die, the subject chooses who rolls the die, and the subject chooses who rolls the die, but must pay 5 units from their 100 unit allocation to roll themselves. Comparing the last two treatments, 68% of subjects prefer to roll themselves without cost - tested to be significantly different from 50% (the randomisation level), while only 22% were willing to pay for the right to roll themselves. This change was tested to be significant. These findings back up the hypothetical bias notion of Filippin and Crosetto (2016). Although it is not tested, one would assume 22% to be significantly different to the rational response of zero, suggesting a weaker preference for control still exists with opposing monetary incentives. The amounts invested were almost
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identical for all treatments. If the IOC leads to greater confidence in investment decisions, one would expect a larger proportion to be invested when the subject rolls the die. The authors conclude that although a preference for control is observed, it is not strong enough to influence investment decisions.
Li (2011) investigates different directions of preferences towards control: preference for control, preference for no control, and preference for randomisation, as well as how each of these affects risk taking, and the reasons behind such preferences. The study is unique when compared to the examples previously discussed in that it is not framed in a way to encourage a bias in one direction. It is suggested that the reasoning behind control preferences are not biases in probability belief but preferences over sources of uncertainty (e.g. a preference for numbers being generated by a computer rather than choosing themselves). In a similar experiment to Charness and Gneezy (that concerns balls being drawn from an urn rather than a roll of a die), Li finds that subjects significantly prefer control to no control. The type of control measured is choice of numbers rather than who physically draws the balls (choice over active involvement). Interestingly, conditional on preferring to choose their numbers (a factor that Charness and Gneezy failed to assess), subjects do invest significantly more into the gamble. For those who preferred the experimenter to choose, this difference disappears. As expected, adding a cost to the control condition again lowers the number of subjects that choose to control. At 30%, this again suggests some preference for control strong enough to survive an opposing monetary incentive. Of those that paid for control, only one reported beliefs that the probability of winning was higher with control, and indeed, all other subjects reported beliefs that the probability of success was the same under both methods. These observations suggest that source preference rather than an IOC determined the preference for control observed. Similar results were found when subjects had to pay to lose control or for randomisation, i.e. those that paid to lose control (or randomise) did not report beliefs that they could earn more this way. The implications of the paper are that firstly, preferences over control can operate in both directions - looking at control in only one direction previously could potentially explain results biased towards an IOC. Secondly, it seems preferences towards control may be governed by source preferences rather than biased beliefs about probability, making it imperative for any IOC study to accurately measure beliefs as well as preferences.
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Cash-out betting, when compared with standard bets, can be described as an increase in the level of active involvement. The IOC may also be influenced by an increased presence of choice due to the fact gamblers decide if / when to withdraw their gamble, as well as their decision to take up a out gamble over a standard one. It is also possible to view a cash-out gamble as an opportunity for gamblers to increase Harrigan’s (2014) “celebratory feedback rate”. Cashing out replaces both wins and losses with smaller ‘wins’ that may or may not be greater than the wagered amount (losses disguised as wins). Presson and Bennassi (1996) may dismiss any bias afforded by cash-out betting as illusory prediction over the outcome of the gamble rather than illusory control. It should be noted, though, that the illusion tested in this paper is of controlling the probability of being successful rather than controlling or predicting the outcome of the event. Cash-out gambling has not been previously examined as a manifestation of IOC and has not been used as a method to test the bias. This thesis aims to provide insight, not only into the existence and strength of the IOC but on whether it is a useful tool for betting companies to influence gambling behavior.
Section 3 – Experimental Design and Procedures
The aim of this paper was to determine firstly, whether subjects preferred a gamble with a cash-out option to one without, controlling for risk preferences. The second objective was to verify whether the IOC mediated said preferences. Data was collected using an online Qualtrics survey. Subjects were recruited through an online group for economics masters students at The University of Amsterdam. At the beginning of the experiment, subjects were told that they were participating in an individual choice experiment and would be exposed to a series of gambles. It was made clear which gambles were paid and which were not. Payment was decided by randomly selecting one participant for every ten responses, i.e. participants had a 10% chance of receiving any winnings earned from the experiment. As there were 55 subjects, this meant that 5 were randomly selected for payment. The payment procedure was made clear in the instructions. Next, the individual rounds were explained:
In the first part, subjects engage in three unpaid gambles. For each gamble, subjects are shown an image of six differently coloured balls and asked to select one. Each ball was randomly assigned an unobserved value – although subjects were aware of the value
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distributions. The goal was for participants to select the ball with the highest value. The value distributions (in euro amounts) were as follows:
Gamble 1 Gamble 2 Gamble 3
0,0,0,6,6,6 0,3,3,3,3,6 2,2,2,4,4,4
These gambles acted as the non-cash-out treatment. As cash-out gambles are less risky than non-cash-out gambles, it was imperative to distinguish between genuine preferences for control and preferences due to risk aversion. Each ball value set represents the possible cash-out values from every round of gamble 4. As such, all 3 gambles were necessary comparisons. This will be expanded upon in the description of gamble 4. After experiencing the three gambles, subjects are directed to Choice 1 – in which they are asked to select their preferred gamble to complete once more for real euro amounts. This choice would provide the basis for comparison against the cash-out treatment. If a preference for cash-out is observed, we can infer a preference for cash-out against all three gambles and so can rule out risk aversion as a rational determinant of said preference.
Afterwards, subjects were introduced to gamble 4, the cash-out treatment, in another unpaid trial. For this gamble, subjects are shown an image of four balls (two red, two blue) and asked to select a winning colour – the colour of the last remaining ball. A correct guess earns €6, while an incorrect guess earns €0. Subjects are informed that they will receive an offer to withdraw their bet in-between rounds as balls are removed one by one. The amount offered for withdrawal corresponded to the current value of the bet, e.g. if a subject chose to bet on blue, and a red ball is removed in the first round. The withdrawal offer will be:
Pr(Last remaining ball is blue) × €6 =23× €6 = €4
Here we can observe how the possible cash-out offers in each round correspond to gambles 1, 2, and 3 to rule out preferences for cash-out mediated by risk aversion:
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Probabilities of offer amounts Non-cash-out gamble equivalent
Cash-out in Round 1
Pr(2) =12 , Pr(4) = 12 Gamble 3
Cash-out in Round 2
Pr(0) =16 , Pr(3) =23 , Pr(6) = 16 Gamble 2
Reject cash-out offers
Pr(0) =12 , Pr(6) = 12 Gamble 1
In the next part of the experiment, subjects are directed to Choice 2, a decision between Gamble 4 and their induced preferred gamble from Gambles 1, 2, and 3. The purpose of this choice was to answer the question of whether, controlling for risk preferences, subjects found cash back gambles more attractive than standard gambles of the same expected value.
For Choice 3, subjects were informed that they would play both gambles again (preferred gamble 1, 2, or 3, and gamble 4) but would decide which one to receive payment from. The intention, here, was to determine whether subjects preferred cash back due to a genuine belief that they could earn more this way (an indication of IOC) or due to an inherent preference for active involvement.
For Choice 4, subjects again played both gambles with the decision of which one would be paid. A cost of €0.50 was added to the control treatment. So, the prize for choosing the correct colour was reduced to €5.50, and every withdrawal offer was reduced by €0.50. The only exception was if subjects earned €0: to avoid subjects earning negative payoffs, these were not reduced. Again, the aim here was to provide stronger evidence that subjects believed they could earn more with an option to cash-out.
In the final part of the experiment, subjects participated in a questionnaire. They were asked for their gender, whether they would describe themselves as an experienced gambler, whether they thought it was easier to win money with a withdrawal option, and whether they thought the withdrawal option was less risky. Finally, subjects provided their email address if they wished to enter the draw to receive payment. Those that were successful in the draw were contacted and paid through bank transfer after the results had been collected.
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Langer (1975) refers to competition as one of the four factors that influence the IOC. Betting markets can certainly be described as a competitive environment, and because of this (as well as the fact that the goal of the study was to observe an IOC) the experiment instructions and feedback was deliberately worded in a way that inspired competitive feelings. Examples of this include “unlucky” when losing, “congratulations” when winning, as well as referring to the experiment as a “game”.
This paper’s objective was to prove that betting companies’ introduction of an option to cash-out encourages betting due to the IOC. The first hypothesis, then, was that subjects would be more likely to choose to play the gamble with a cash-out option than their preferred choice without a cash-out option. While this observation alone would prove that subjects prefer betting with an option to cash-out, it does not prove that the IOC mediated this preference. What was then addressed is whether they gained utility from the active involvement in the gamble or whether they believed they would earn more this way. The second hypothesis predicted that subjects would be more likely to choose a bet with a cash-out option for payment than one without the option. The third hypothesis concerns the strength of the bias, and predicted that a significant amount of subjects would be willing to choose a bet with a cash-out option for payment over a bet without a cash-out option but with a higher expected value.
Section 4 – Results
Observed variables were calculated in the following ways:
Risk Level: A crude measurement of risk aversion was assigned through subjects' responses to Choice 1. The values range from 0 (most risk averse) – for subjects that chose the 2,2,2,4,4,4 gamble, to 2 (most risk loving) – for subjects that chose the 0,0,0,6,6,6 gamble.
Preference: An indicator of whether the subject prefers to partake in a gamble with an option to cash-out over one without the option. Derived from whether the subject chose the gamble with an option to cash-out in Choice 2.
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Weak Belief: An indicator of whether the subject believes the probability of winning a high amount is greater when there is an option to cash-out. Derived from whether the subject chose to take payment from the gamble with an option to cash-out in Choice 3.
Strong Belief: A stronger indicator of whether the subject believes the probability of winning a high amount is greater when there is an option to cash-out. Derived from whether the subject chose to take payment from the gamble with an option to cash-out with added cost in Choice 4.
Male: 1 if the subject was male, 0 otherwise.
Experienced: Whether the subject answered “yes” to the question “Would you describe yourself as an experienced gambler?”
CB More: Whether the subject answered “yes” to the question “Did you think it was easier to make money from a gamble with an option to withdraw?”
CB Risk: Whether the subject answered “yes” to the question “Did you find gambling with a withdraw option to be less risky?”
Earnings: Earnings from all paid gambles (although only 10% of subjects received them)
NCO Payoff: Payoff from Choice 1, subjects preferred non-cash-out gamble.
CO Payoff: Unpaid payoff from subjects first exposure to gamble 4. The reason a paid gamble was not used, here, is that all paid cash-out gambles concerned choices between gambles. As such, not all subjects chose the cash-out option and, indeed, the variable is used to explain these choices.
Difference: The difference between NCO Payoff and CO Payoff – positive when CO Payoff was greater.
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Variable N Mean SD Range
Risk Level 55 0.945 0.848 0-2 Preference 55 0.127 0.336 0-1 Weak Belief 55 0.600 0.494 0-1 Strong Belief 55 0.164 0.373 0-1 Male 55 0.618 0.490 0-1 Experienced 55 0.236 0.429 0-1 CB More 55 0.582 0.498 0-1 CB Risk 55 0.691 0.466 0-1 Earnings 55 11.88 3.50 5-21 NCO Payoff 55 3.04 2.13 0-6 CO Payoff 55 3.02 1.96 0-6 Difference 55 -0.02 3.03 (-6)-6
The sample consisted of 34 males and 21 females, of which 13 described themselves as experienced gamblers. On average, subjects earned slightly less than €12, which is consistent with expectations (four paid gambles with expected value €3 – one with expected value €2.50 if cash-out was paid for in Choice 4). The means for NCO Payoff and CO Payoff were both close to the expected value of €3, proving that there was no monetary advantage to be gained from choosing either option. There was a mix of risk levels observed, with 21 subjects choosing the least risky gamble, 16 subjects choosing the medium-risk gamble, and 18 choosing the riskiest gamble. Most subjects, it seemed, preferred to gamble without an option to cash-out, with only 7 subjects choosing to partake in the cash-out gamble over the non-cash-out gamble. Conversely, 33 subjects preferred to take payment from the non-cash-out gamble (with 9 of those willing to pay for this right) suggesting decisions to partake in the non-cash-out gamble were due to reasons other than beliefs about their probability of success.
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This observation is strengthened by the questionnaire responses with 32 (38) reporting that they believed they could earn more (reduce risk) through taking a cash-out gamble.
When assessing whether an option to cash-out makes gamblers more likely to take up a bet, what must first be considered is whether subjects preferred a cash-out gamble to a gamble without this option. For this to be true, we should observe a mean for the Preference variable that is significantly higher than 0.5 (the expected level if participants randomised). A mean of 0.13 with 95% confidence interval of [0.04, 0.22] – that is significantly lower than 0.5 – suggests that, in fact, the opposite was true. Subjects preferred to participate in a gamble without an option to cash-out over one with an option to cash-out. Reasons behind this observation are difficult to explain, especially given responses to the other choices and the questionnaire. One possible explanation is that the cash-out gamble in this experiment was more time consuming and involved more rounds / decisions. It is conceivable that subjects were more concerned with completing the survey than extracting the highest possible payment (especially as there was a fairly low chance of receiving said payment).
Although this study cannot provide evidence that cash-out gambles are preferred to non-cash-out gambles, it is still useful to assess whether those that did prefer a cash-non-cash-out gamble did so in conjunction with illusory beliefs. A Weak Belief mean of 0.86 for those that preferred to play the cash-out gamble, with 95% confidence interval [0.60, 1.12] is significantly greater than the randomisation level of 0.5. This suggests a systematic belief among those that preferred to partake in a cash-out gamble that the probability of earning a greater payoff is higher with an option to cash-out. When comparing to those that preferred to play a non-cash-out gamble we observe a mean of 0.56 with 95% confidence interval [0.42, 0.70] that is not significantly different to 0.5. We cannot, then, reject the hypothesis that those subjects were randomising their choice of gamble for payment. Although as both confidence intervals overlap, we also cannot reject the hypothesis that the two means are equal and that the level of (illusory) beliefs are equal for both groups. With a larger sample size, however, it seems reasonable to assume that the two means could be proven to be significantly different. This observed discrepancy between reports of beliefs and preferences contradicts the view that gamblers inherently prefer active involvement. Although most subjects did not prefer to take a cash-out gamble, IOC seems a more likely explanation than active involvement for those that did. In fact, for those that preferred the cash-out gamble, only one believed that the non-cash-out gamble would pay more.
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The observed effect was, understandably, lower when a cost was introduced to the cash-out option. A Strong Belief mean for those that preferred a cash-out gamble of 0.29 with 95% confidence interval [-0.49, 0.62] is not significantly greater than the rational choice of zero (to pick the non-cash-out gamble). Interestingly, the Strong Belief mean for those that preferred to play the non-cash-out gamble, while lower (0.15), was significantly greater than zero – 95% confidence interval, [0.05, 0.24] suggesting a significant amount of subjects were biased towards the belief that a cash-out gamble earns more. In fact, 7 of the 9 subjects that reported a Strong Belief that cash-out paid more preferred to partake in the non-cash-out gamble. It is reasonable to believe that this result could be achieved for those that did prefer to partake in a cash-out gamble with a larger sample size (only 7 subjects preferred to partake in the cash-out gamble). Indeed, the Strong Belief mean for all subjects, 0.16, had a 95% confidence interval of [0.06, 0.26] pointing towards a systematic bias across all subjects towards believing cash-out are more likely to earn more.
95% mean confidence intervals for Preferred Gamble, and Beliefs about payment for subjects that preferred or did not prefer a cash-out gamble
Thompson (1999) described how the IOC is affected by success at the task with a light switch experiment, the results of which were rejected by this paper. Although it does not answer the research question, it was useful to test the mediating effect of subjects’ previous success rate
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
Preferred Weak Belief
(Preferred) Weak Belief(Non) Strong Belief(Preferred) Strong Belief(Non)
Upper Lower Mean
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of the cash-out gamble on their beliefs that they would earn more from this gamble. OLS regressions of the Weak Belief variable on CO Payoff and Difference both give positive and significant coefficients – 0.103 and 0.046 respectively. This suggests that prior success from a cash-out gamble positively affected subjects’ likelihood to believe that it will pay more than a non-cash-out gamble. The fact that CO Payoff has a stronger and more significant effect than Difference suggests subjects put more weight on the cash-out payoff than the difference between the two payoffs (and by definition, the non-cash-out payoff). This observation adds weight to the theory that increased control reduces the accuracy of probability judgments. The results state that an increase in CO Payoff of €1 is associated with an increase of over 10% in probability of choosing to take payment from the cash-out gamble without cost. When regressing Strong Belief on the same variables, we observe smaller and insignificant coefficients, suggesting the misjudgment of probabilities caused by previous success is not strong enough to encourage payment for the option to cash-out.
Those that viewed themselves as experienced gamblers were more likely to believe the probability of winning was higher with a cash-out gamble, but less likely to believe so when having to pay for this option. As both of these coefficients are insignificant, however, we cannot reject the hypothesis that that subjects’ were affected equally by the bias regardless of experience. Predictably, possession of Weak and Strong Beliefs that the cash-out gamble paid more were associated with an increase in the likelihood of preferring to partake in the cash-out gamble (14% and 11% respectively). Although as both effects are insignificant, we cannot reject the hypothesis that illusory beliefs had no effect on gamble preference.
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Weak Belief Strong Belief Preference
(1) (2) (3) (4) (5) (6) (7) (8) (9) Weak Belief 0.136 (0.092) Strong Belief 0.114 (0.113) CO payoff 0.103** 0.038 (0.032) (0.026) Difference 0.046* 0.021 (0.022) (0.017) Risk Level -0.042 (0.054) Experienced 0.121 -0.114 (0.158) (0.119) Constant 0.288* 0.601** 0.571** 0.049 0.164** 0.190** 0.045 0.109* 0.167* (0.114) (0.065) (0.077) (0.092) (0.050) (0.058) (0.071) (0.050) (0.069) N 55 55 55 55 55 55 55 55 55 𝐑𝐑𝟐𝟐 0.168 0.078 0.011 0.039 0.028 0.017 0.040 0.016 0.011
Significance levels are denoted: 95% *, 99% **
All regressions are OLS with non-clustered standard errors.
The observed results, then, shed no real light on the influence of cash-out gambling regarding its usefulness as a tool to influence consumers. They do, however, provide some suggestive evidence of biased beliefs about the advantages of cash-out gambles that may manifest as an IOC. It would be shortsighted, though, to take these results completely at their nominal value as a number of factors limitedthe experimental process. Firstly, it is certainly conceivable that observations were biased by the particular sample selected. Participants were recruited through a group for economics masters students at The University of Amsterdam. Clearly, a sample like this cannot account for a systematic bias amongst the population as many of the participants had good knowledge of behavioural biases and the IOC. Further to this, some participants were class members who had viewed presentations about the study and so knew what was being tested for. We cannot rule out (and, in fact, would expect) Hawthorne effects as subjects realised what was expected of them and may have adjusted behaviour - although this would also be the case with random sampling, as the experiment was not conducted in the field. The results, then, should not be considered externally valid in terms of representing the population of gamblers and potential gamblers affected by available options to cash-out.
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Limited funds meant that it was impossible to promise payment for every survey response. As such, subjects were aware that even if they won, their chance of receiving payment was only 10%. This may explain the observed preference to play non-cash-out gambles (they did not take as long to complete and required less effort) and casts doubt over all incentivised induced preference and belief variables and so makes the study less internally valid. This effect was compounded by the fact that all incentivized variables were determined by one decision, and so, are unlikely to accurately represent the true profile of every subject. The variables, then, should be seen as crude indicators of what they are supposed to represent: Preference, Belief, and Risk Level.
Regarding the original research question, the experiment aims to prove that cash-out bets are preferred to non-cash-out bets (although this was, in fact, not observed). The assumption, here, is that if cash-out bets are preferred, then the addition of an option to cash-out will lead to either a greater amount of gamblers taking up bets or existent gamblers risking more money. While a preference for cash-out may indicate this, it does not prove it, as there was no option to adjust the stake or refrain from betting. To distinguish between IOC-related preferences for cash-out and inherent preferences for active involvement, the Belief variables were constructed from subjects’ choice of which gamble to receive payment from and compared to the Preference variable constructed from subjects’ choice of which gamble to engage in. The difference in means of the two variables accounts for those that preferred cash-out due to increased involvement but did not believe they would earn more this way. It does not, however account for those who preferred cash-out due to the active involvement in a salient feature of the game. Another limitation of the study that has been discussed by Li (2011) is the one-directional nature of the testing for strong beliefs. A mean that was significantly greater than zero suggests an irrational bias towards the belief that cash-out gambles earn more, however, the absence of the option to pay for less control only allows for irrationality in one direction. It is possible that some subjects would be willing to pay for the right to collect payment from the non-cash-out gamble, which may have guided the mean towards zero.
19 Section 5 – Discussion
It is unclear whether betting firms target behavioural biases consciously, and in particular, whether they target the IOC. It seems unlikely, though, that cash-out gambling was introduced for the benefit of gamblers. There is an argument to be made that many past successful marketing strategies have unconsciously taken advantage of behavioural biases. From this study, it is impossible to conclude that the introduction of the option to cash-out on bets should be viewed as a viable tactic to encourage gamblers to risk greater amounts or to take up more gambles. The study, in fact, revealed a preference for playing gambles without an option to cash-out. The fact that the cash-out option requires more time and effort to complete, coupled with the fact that subjects had a small chance of receiving payment, can explain this observation.
Conversely, the preference for payment from the cash-out bet suggests subjects may have believed the extra control over the bet could influence their likelihood of being successful (an IOC) and indeed those who displayed these beliefs were more likely to prefer to partake in the cash-out bet. This theory is strengthened by the fact a significant amount of subjects preferred payment from the cash-out bet when this option included a cost. The results suggest an IOC may be present, but it did not affect subjects’ preferences over gambles. The discrepancy between induced reports of preferred gamble and beliefs about the probabilities of success across gambles suggests that subjects did not prefer cash-out gambles due to an inherent preference for control. The observed correlation between success rate from subject’s first exposure to the cash-out gamble, and subjects’ likelihood to prefer payment from the cash-out gamble gives weight to Thompson’s theory that success at a task mediates the IOC.
The study was limited in that the experiment does not fully reflect a betting market in the field. In the experiment, the offered odds are clearly representative of the likelihood of a chosen ball being selected, while betting companies that offer odds on more complicated events such as sports fixtures calculate odds with algorithms along with the opinions of experts. The external validity of the experiment rests on the assumption that betting companies offer prices that accurately reflect the probabilities of the occurrence of a particular event. This is not always the case, and even when it is, it is reasonable to assume that some gamblers prefer cash-out gambles due to a belief that they can judge probabilities
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faster, or more accurately, than the company can update them, rather than a belief that the increased control over the bet translates directly to a greater probability of success.
While the study did not prove that a cash-out option encourages gamblers to take up gambles, suggestive evidence of an IOC was observed and as such, further research on the topic is encouraged. A larger data set would assist in forming more significant results, while greater monetary incentives may alleviate concerns about subjects’ effort. Gambling behavior, though, is notoriously difficult to measure in the lab. As such, a field experiment that takes into account real gambling decisions is likely to be necessary to form any externally valid conclusions.
21 References
Alloy, L.B., Abramson, L.Y., & Viscusi, D. (1981). Induced Mood and The Illusion of Control.
Journal of Personality and Social Psychology, 41(6), 1129-1140.
Biner, P.M., Angle, S.T., Mellinger, A.E., Barber, B.C., & Park, J.H. (1995). Need State and the Illusion of Control. Personality and Social Psychology Bulletin, 21(9).
Charness, G., & Gneezy, U. (2009). Portfolio Choice and Risk Attitudes: An Experiment. Economic
Inquiry, 48(1), 133-146.
Chóliz, M. (2010). Cognitive Biases and Decision Making in Gambling. Psychological Report,
107(1), 15-24
Clark, L. (2009). Decision-making during gambling: an integration of cognitive and
psychobiological approaches. Philosophical Transactions of the Royal Society B: Biological
Sciences, 365(1538), 319-330.
Dixon, M. R., Hayes, L. J., & Ebbs, R. E. (1998). Engaging in “Illusory Control” during Repeated Risk-Taking. Psychological Reports, 83(3), 959-962.
Dixon, M. R. (2000). Manipulating the Illusion of Control: Variations in Gambling as a Function of Perceived Control Over Chance Outcomes. The Psychological Record, 50(4), 705-719.
Dunning, D., &Story, A.L. (1991). Depression, realism, and the overconfidence effect: are the sadder wiser when predicting future actions and events? Journal of Personality and Social
Psychology, 61(4), 521-532
Fast, N.J., Gruenfeld, D.H., Sivanathan, N., & Galinsky, A.D. (2009) Illusory Control: A
Generative Force Behind Power’s Far-Reaching Effects. Psychological Science, 20(4), 502-508 Fernandez-Duque, D., & Wifall, T. (2007). Actor / Observer Asymmetry in Risky Decision
Making. Judgment and Decision Making, 2(1), 1-8
Fenton-O’Creevy, M., Nicholson, N., Soane, E., & Willman, P. (2003). Trading on Illusions: Unrealistic perceptions of control and trading performance. Journal of Occupational and
Organizational Psychology, 76(1), 53-68
Filippin, A., Crosetto, P. (2015). Click’n’Roll: No Evidence of Illusion of Control. IZA Discussion
Papers, 9030.
Harrigan, K., Maclaren, V., Brown, D., Dixon, M. J., & Livingstone, C. (2014). Games of chance or masters of illusion: multiline slots design may promote cognitive distortions. International
Gambling Studies, 14(2), 301-317.
Kahneman, D., & Tversky, A. (1972). Subjective Probability: A Judgment of Representativeness.
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Korn, C. W., Sharot, T., Walter, H., Heekeren, H. R., & Dolan, R. J. (2013). Depression is related to an absence of optimistically biased belief updating about future life events. Psychological
Medicine, 44(3), 579-592.
Kuss, D. (2013). Internet gaming addiction: current perspectives. Psychology Research and
Behavior Management, 125.
Langer, E. J. (1975). The illusion of control. Journal of Personality and Social Psychology, 32(2),
311-328.
Levitin, D.J. (2015, January 18). Why the modern world is bad for your brain. Retrieved from https://www.theguardian.com/science/2015/jan/18/modern-world-bad-for-brain-daniel-j-levitin-organized-mind-information-overload
Li, K. K. (2011). Preference towards control in risk taking: Control, no control, or randomize?
Journal of Risk and Uncertainty, 43(1), 39-63.
MacInnes, P. (2017, February 22). Pie-gate leaves nasty smell – and it’s footballs links with betting industry. Retrieved from https://www.theguardian.com/football/blog/2017/feb/22/gambling-wayne-shaw-sutton-united-pie
Martinez, F., Bonnefon, J., & Hoskens, J. (2009). Active involvement, not illusory control,
increases risk taking in a gambling game. The Quarterly Journal of Experimental Psychology,
62(6), 1063-1071.
Martinez, F., Le Floch, V., Gaffié, B., & Villejoubert, G. (2011). Reports of Wins and Risk Taking: An Investigation of the Mediating Effect of the Illusion of Control. Journal of Gambling
Studies, 27(2), 271-285
Moore, S. M., & Ohtsuka, K. (1999). Beliefs about control over gambling among young people, and their relation to problem gambling. Psychology of Addictive Behaviors, 13(4), 339-347.
Presson, P.K., & Benassi, V.A. (1996). Illusion of Control: A Meta-Analytic Review. Journal of
Social Behavior and Personality, 11(3), 493
Sloof, R., & Siemens, F. A. (2016). Illusion of control and the pursuit of authority. Experimental
Economics, 1-18
Thompson, S. C. (1999). Illusions of Control. Current Directions in Psychological Science, 8(6), 187-190.
23 Appendix 1 – Experiment Instructions
You are about to participate in an individual choice experiment. You will be subjected to a series of gambles and can win up to €24. For every 10 participants, one will be randomly selected for payment at the end of the experiment (50 participants expected).
The first part of this experiment will consist of 3 unpaid training gambles, so as to familiarise yourself with the types of choices you will have to make.
These will be followed by a paid choice of gamble (one of the training gambles).
You will then take part in another training gamble followed by 3 paid gamble choices and a questionnaire.
You will be reminded which gambles are paid. Please click on the arrows to continue.
Gamble 1
There are six coloured balls on the screen. Three of them are worth €6, and three of them €0.
Please select a ball by clicking on it.
Congratulations, the (green/red/blue/yellow/pink/orange) ball is worth €6! OR
Unlucky, the (green/red/blue/yellow/pink/orange) ball is worth €0.
Gamble 2
The values of the balls have now changed. One of them is worth €6, four of them are worth €3, and one of them €0.
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Please select a ball.
Congratulations, the (green/red/blue/yellow/pink/orange) ball is worth €6! OR
Congratulations, the (green/red/blue/yellow/pink/orange) ball is worth €3! OR
Unlucky, the (green/red/blue/yellow/pink/orange) ball is worth €0
Gamble 3
Now three are worth €4, and three are worth €2.
Please select a ball.
Congratulations, the (green/red/blue/yellow/pink/orange) ball is worth €4! OR
Unlucky, the (green/red/blue/yellow/pink/orange) ball is worth €2.
You are about to gamble again for real euro amounts. You can choose which of the three previous gambles to take. To remind you, the potential payoffs are displayed in the brackets next to the gamble.
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Please indicate your choice below. o Gamble 1 (6,6,6,0,0,0) o Gamble 2 (6,3,3,3,3,0) o Gamble 3 (4,4,4,2,2,2) Repeat Gamble 1 OR Repeat Gamble 2 OR Repeat Gamble 3 Gamble 4
There are now four balls shown on the screen. They will be removed randomly one by one. You are choosing which colour you think the last remaining ball will be. You will receive €6 for choosing correctly and €0 for choosing incorrectly. You will receive an offer to withdraw your gamble in between rounds.
As before, your first attempt will be a training gamble, followed by 3 paid gamble choices.
Please select a colour by clicking an option below. o Blue
o Red
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OR
Do you want to withdraw for €2?
o Yes
o No
Do you want to withdraw for €3?
o Yes
o No
OR
Congratulations, you win €6! OR
Unlucky, you receive €0.
Congratulations, you win €6! OR
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You about to gamble again. You can choose whether to take gamble 1, 2 or 3 (the ball-choice gamble you chose earlier) or gamble 4 (the colour ball-choice gamble with the option to withdraw).
There will be no more training gambles. You are playing for real euro amounts for the remaining rounds of the experiment.
Please indicate your choice of gamble.
o Gamble 1 (0,0,0,6,6,6) OR Gamble 2 (0,3,3,3,3,6) OR Gamble 3 (2,2,2,4,4,4)
o Gamble 4 (option to withdraw)
Repeat Gamble 1/2/3 OR
Repeat Gamble 4
You are about to complete two more gambles: gamble 1, 2 or 3 (the ball-choice gamble you chose earlier) and gamble 4 (the colour-choice gamble with an option to withdraw).
You will receive payment for only one of these gambles. The gamble that is chosen for payment is up to you.
Please choose which gamble you would like to be paid
o Gamble 1 (0,0,0,6,6,6) OR Gamble 2 (0,3,3,3,3,6) OR Gamble 3 (2,2,2,4,4,4)
o Gamble 4 (option to withdraw)
Repeat Gamble 1/2/3
Repeat Gamble 4
You are about to complete the same gambles again: gamble 1, 2 or 3 (the ball-choice gamble you chose earlier) and gamble 4 (the colour-choice gamble with an option to withdraw).
Again, you will receive payment for only one of these gambles. The gamble that is chosen for payment is up to you.
This time, there will be a cost of €0.50 for choosing gamble 4, i.e. any payoffs will be €0.50 less than before.
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Please choose which gamble you would like to be paid
o Gamble 1 (0,0,0,6,6,6) OR Gamble 2 (0,3,3,3,3,6) OR Gamble 3 (2,2,2,4,4,4)
o Gamble 4 (option to withdraw)
Repeat Gamble 1/2/3
Repeat Gamble 4 (cash-out values lowered by €0.50)
You have reached the end of the experiment.
Please answer the short questionnaire and provide your email address below if you would like to be entered into the draw for payment.
Those that have been selected for payment will be contacted in the coming weeks. Are you Male or Female?
o Male
o Female
Would you describe yourself as an experienced gambler?
o Yes
o No
Did you think it was easier to make money from a gamble with an option to withdraw?
o Yes
o No
Did you find gambling with a withdraw option to be less risky?
o Yes
o No
What is your email address? Thank you for your participation!
