metadata: authors: 0: author: Abel,Simon Martin
1: author: Cole,Shawn Allen
2: author: Zia,Bilal Husnain
count: Southern Africa
docna: 0: docna: Debiasing on a roll: changing gambling
            behavior through experiential learning
docty: Policy Research Working Paper
subtopic: Inequality,Educational Sciences
teratopic: Education,Poverty Reduction
abstracts: cdata!: This paper tests experiential learning
            as a debiasing tool against gambling and lottery behavior in
            South Africa. The study implemented a simple, interactive
            dice game that simulates worsening winning odds of rolling
            sixes as more dice are added to the game. The analysis
            exploits two levels of exogenous variation, first from
            random assignment into the debiasing game, and second from
            the number of rolls it takes to obtain the sixes. Treated
            individuals who needed above-median number of rolls to
            obtain simultaneous sixes are significantly less likely than
            the control group to gamble or play the lottery in the
            following year. The converse is true for individuals who
            needed below-median number of rolls, suggesting a perverse
            treatment effect among this group. The analysis also finds
            suggestive evidence that the debiasing affected the
            sensitivity to varying winning odds. Changes in
            entertainment utility or risk preferences cannot explain
            these findings, rather the results are consistent with
            changes in risk beliefs.
repnme: repnme: Debiasing on a roll: changing gambling
            behavior through experiential learning
display_title: Debiasing on a roll: changing
            gambling behavior through experiential learning
listing_relative_url: /research/2015/02/23990597/debiasing-roll-changing-gambling-behavior-through-experiential-learning
topicv3: Poverty m1326687 695,Education m1327048 470,Financial Sector Development m1327681 1920
publishtoextweb_dt: 2015-02-01T00:00:00Z
historic_topic: Education,Poverty Reduction
no_of_pages: 43
author_keys: 0: author_key: 1373021
1: author_key: 1003669
2: author_key: 642766
model_extractions: WPS7195 Policy Research Working Paper 7195 Debiasing _on a Roll_ Changing Gambling Behavior through Experiential Learning _Martin Abel Shawn Cole Bilal Zia_ Development Research Group Finance and Private Sector Development Team February 2015
Policy Research Working Paper 7195

# **Abstract**

This paper tests experiential learning as a debiasing tool against gambling and lottery behavior in South Africa. The study implemented a simple, interactive dice game that simulates worsening winning odds of rolling sixes as more dice are added to the game. The analysis exploits two levels of exogenous variation, first from random assignment into the debiasing game, and second from the number of rolls it takes to obtain the sixes. Treated individuals who needed above-median number of rolls to obtain simultaneous sixes are significantly less likely than the control group to gamble or play the lottery in the following year. The converse is true for individuals who needed below-median number of rolls, suggesting a perverse treatment effect among this group. The analysis also finds suggestive evidence that the debiasing affected the sensitivity to varying winning odds. Changes in entertainment utility or risk preferences cannot explain these findings, rather the results are consistent with changes in risk beliefs.

This paper is a product of the Finance and Private Sector Development Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at bzia@worldbank.org. .

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Debiasing _on a Roll_ : Changing Gambling Behavior through Experiential Learning

Martin Abel<sup>_∗_</sup> Shawn Cole<sup>_†_</sup> Bilal Zia<sup>_‡§_</sup> February, 2015

### **Abstract**

This paper tests experiential learning as a debiasing tool against gambling and lottery behavior in South Africa. The study implemented a simple, interactive dice game that simulates worsening winning odds of rolling sixes as more dice are added to the game. The analysis exploits two levels of exogenous variation, first from random assignment into the debiasing game, and second from the number of rolls it takes to obtain the sixes. Treated individuals who needed above-median number of rolls to obtain simultaneous sixes are significantly less likely than the control group to gamble or play the lottery in the following year. The converse is true for individuals who needed below-median number of rolls, suggesting a perverse treatment effect among this group. The analysis also finds suggestive evidence that the debiasing affected the sensitivity to varying winning odds. Changes in entertainment utility or risk preferences cannot explain these findings, rather the results are consistent with changes in risk beliefs.

## **JEL Codes: D03, D12, D81, G02**

**Keywords: Debiasing, Experiential Learning, Behavioral Economics, Financial Education**

> _∗_ Harvard University. Email: abel@fas.harvard.edu. Corresponding author. 79 John F. Kennedy Street, Cambridge, MA 02138, United States. Phone: (207) 319 2967

> _†_ Harvard Business School and NBER. Email: scole@hbs.edu

> _‡_ World Bank. Email: bzia@worldbank.org

> _§_ Acknowledgments: This paper greatly benefited from discussions with and comments from Xavier Gine, David Laibson, David McKenzie, Matthew Rabin, Andrei Shleifer, Richard Zeckhauser, and conference participants at Yale University, the University of Cape Town, the Rotterdam Behavioral Finance Conference, and the World Bank. Megan Blair, Reinhard Schiel, and Sarah van Vliet provided excellent research assistance. Special thanks to Luke Crowley for creative contibutions to the debiasing intervention. We also thank the International Labor Organization and the World Bank for financial support. All errors and omissions are our own.

<mark>1</mark>
# **1 Introduction**

Gambling is an ancient human activity practiced in many world cultures, and serves as an important everyday pastime in both developed and developing countries (Custer and Milt 1985, McMillan 1996).<sup>1</sup> Gambling is also costly. In the United States for example, gambling losses comprise almost 2% of household consumption (Kearney 2005). The popularity of gambling poses a challenge to the classical theory of decision-making under risk and uncertainty, which posits that risk-averse individuals should avoid gambles with negative expected value (Tversky and Wakker 1995).

One explanation for gambling that is consistent with rational utility maximization is that individuals understand winning probabilities, but receive utility from gambling which offsets the negative expected utility of the lottery (Kearney 2005). An alternative set of explanations argues that individuals have cognitive biases that lead to systematic misjudgments of risk, in particular overestimation of small probability events (Kahneman and Tversky 1992; Barberis 2013). This second strand of literature shows that people’s risk _beliefs_ are affected by heuristics that rely on psychological cues such as ease of retrieval, familiar scenarios, or personal similarities (Jones et al. 1995). One example particularly relevant for assessing winning probabilities of gambling is the availability heuristic – the tendency to “ _assess the likelihood of an event. . . by assessing the ease with which the relevant mental operation of retrieval, construction, or association can be carried out_ ” (Kahneman and Tversky 1979). While availability is generally a useful cue for assessing probabilities as more frequent events are usually recalled better and faster, it can easily lead to the overestimation of the likelihood of emotionally arousing (Nisbett and Ross 1980) or unusual and salient events (Miller and McFarland 1986; Plous 1993; Bordalo et al. 2012). This phenomenon is readily apparent in the gambling industry – advertisements of lotteries often emphasize large jackpots, casinos typically have bells that ring if somebody wins a major prize, and betting houses strategically place slot machines in large clusters so gamblers can hear the sound of others winning (Clothfelter and Cook 1989).<sup>2</sup> Distinguishing between these explanations is important not only for assessing welfare effects of gambling

> 1 Gambling can be defined as “the act of risking a sum of money on the outcome of a game or event that is determined by chance” (Bolen & Boyd, 1968). It takes many forms, from betting on cockfights in the Philippines, to playing mahjong for money in China, to buying lottery tickets virtually in any part of the world.

> 2Three advertisement schemes are particularly common in the lottery industry in the U.S. (Clothfelter et al 1999): (i) advertizing the size of the jackpot, (ii) emphasizing the fun and excitement of playing, and (iii) highlighting lifestyles of past winners. Example radio advertisement in Arizona: “Every single second, the lottery makes someone very happy. Every single second, someone is cashing a winning ticket.”

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but for designing interventions aimed at changing gambling behavior. In this paper, we address this important area of research by studying the impact and discerning mechanisms of a gambling debias experiment in a sample of 840 poor households in the Eastern Cape and KwaZulu-Natal province of South Africa. This location choice was deliberate – the national lottery in South Africa is very popular especially among the poor, is widely advertised, and has extremely low odds associated with the jackpot prize.

Our debiasing tool was an experiential dice game based on the fundamentals of a four-stage learning cycle model common in psychology (Zull 2002). We started by asking participants to roll a six-sided die until they obtained a six. We then handed them two dice and asked them to roll till they obtained two sixes, which on average took them much longer. This iteration offered them a concrete experience on assessing probabilities. Moreover, depending on how fast participants were able to roll two sixes, they could reflect and update their beliefs about winning odds. We then informed them that the chance of winning the South African national lottery jackpot was smaller than them rolling _nine_ dice with all nine showing up sixes.

Experiential learning methods have the potential to be more effective than standard lectures for several reasons. First, experiential debiasing techniques tend to be simpler and more intuitive and thus do not tax cognitive resources like memory or attention (Bell et al. 1988). Our debiasing game conveyed the concept of probability by having participants experience rolling one die versus two dice, without the feeling of sitting through a math lesson. Second, experiential learning designs can be more novel and thus more memorable, while still building on preexisting knowledge (Heath et al. 1998). Our debiasing game provided participants a useful and powerful benchmark to assess the likelihood (or lack of chance) of being able to simultaneously roll sixes on nine dice, having just experienced the difficultly of rolling just two sixes. Third, experiential learning can leverage cognitive biases to induce desired behavioral change, a strategy referred to as ‘counter-biasing’ (Jolls and Sunstein 2006). Likewise, experiential learning caters to the the human tendency to put too much weight on single events in the process of belief updating (Griffin and Tversky 1992, Rabin 2002), a phenomenon that Kahneman (1998) dubbed the ‘ _power of the particular_ ’. Hence, in our intervention the dice rolling experience may have become the basis of a new availability heuristic.

Our research design features two levels of exogenous variation. First, half the study sample was randomly assigned to receive the debias treatment at the end of a baseline survey on financial access, 3
while the other half received a more traditional financial education module on avoiding expensive credit. Both the debiasing and credit modules took an average of 10 minutes and covered mutually exclusive topics. Second, the number of rolls it took for participants in the treatment group to get two sixes provides additional variation in the intensity of treatment. Moreover, the longer it took to roll two sixes, the clearer it became to the participants that their chance of winning was low.<sup>3</sup> This research design allows us not only to report primary impacts of experiential learning on gambling, but importantly to distinguish mechanisms of impact. Specifically, we can test whether impacts were driven by changes in entertainment utility or risk preferences versus changes in risk beliefs. Theoretically, a change in risk preferences as a result of the debiasing treatment would represent a level shift of individuals’ decision weighting function. Hence, empirically we would expect a change in gambling regardless of treatment intensity. However, if debiasing affected individual beliefs of winning odds for example by forming a new availability heuristic, then there would be variation based on how well these heuristics were influenced, or in other words the strength of treatment.

We find strong support for heuristic based belief updating in our analysis. Specifically, there is substantial variation in outcomes based on treatment intensity – individuals who took more than the median number of rolls to obtain two sixes (high intensity) gambled 19 percent less in a lottery offered after the debiasing intervention and were 34 percent less likely to have played the lottery after one year compared to the control group. Conversely, the low treatment intensity group (below median number of rolls) gambled 29 percent more in a lottery offered immediately after the intervention and was 45 percent more likely than the control group to have played the lottery after one year. These differences are statistically significant at the 5 percent level.

The study design also tests whether the treatment changed individuals’ sensitivity to odds by offering lotteries at midline with randomly assigned winning probabilities. Orthogonal to original treatment status, half the sample was offered a lottery with a low winning probability and the other half was offered a lottery with a higher winning probability. Hence, we can employ a difference-in-difference strategy to test whether there was a greater sensitivity to winning odds based on treatment intensity. In the analysis, we find that the high treatment intensity group indeed showed greater sensitivity to probabilities, and in contrast the low intensity group was less odds-sensitive than the control group. While these coefficients are large in magnitude they are not statistically significant at conventional lev-

> 3In the analysis, we also exploit the reverse feature of this design. That is, if by chance the players rolled two sixes right away or in a few number of tries, then their biases may be reinforced.

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els. Nonetheless, these results provide additional suggestive evidence for the channel of belief updating for given risk preferences.

Finally, the analysis addresses the important and complementary question of how individuals learn. Specifically, we exploit the exogenous variation in the number of rolls in both the first and second rounds to study whether the reinforcement effect (difficulty rolling sixes in both rounds) led to a stronger impact than the exponential learning effect (easy first round followed by difficult second round). We find that the debiasing effect is larger for participants with a reinforcing treatment of needing many rolls to get sixes in both rounds compared to those experiencing the more complex lesson that rolling sixes is exponentially more difficult with each die added.

Overall, our research is one of the first field studies that shows experiential learning in general and experiential debiasing in particular have the potential to be promising alternatives to the traditional method of conveying information. Insights from educational theory suggest that experiential learning may be a particularly promising strategy in the context of developing countries. The four-stage learning cycle model used in the psychology literature posits that learning is most effective if participants can test relationships between experiential learning (e.g. dice rolling) and abstract concept (winning probabilities) through active experimentation (Zull 2002). To the extent that developing country economies have less division of labor, producers may be more likely to observe, and attempt to infer, the relationship between actions and outcomes, though they may not do so optimally. For example, Hanna, Mullainathan and Schwarzstein (2014) find that Indonesian farmers fail to learn as much as they might about their production technologies. Finally, experiential learning is less taxing on cognitive resources, which is conducive in environments where people are less likely to have developed analytical skills in school (Bell et al. 1988).

The rest of this paper is structured as follows. Section 2 provides the conceptual framework for our study and derives testable implications. Section 3 discusses the study background, debiasing treatments, and outcome measures, and introduces the empirical strategy. Section 4 reports and discusses findings and Section 5 concludes.

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# **2 Game Design and Conceptual Framework**

## **2.1 Debiasing through Experiential Learning**

The effectiveness of teaching financial concepts in standard classroom settings is often constrained by limited numeric skills, low arithmetic intuition, and general lack of interest among participants. As a result, many evaluations of financial education programs have found only limited impacts on financial outcomes (see Fernandes et. al 2014; Xu and Zia 2013; and Miller et. al 2014 for literature reviews).

While standard financial education has failed to establish a stronghold in the literature on savings and credit decisions, the domain of gambling presents an even greater hurdle as understanding the pitfalls of gambling requires knowledge of probabilities. In developing countries where poor individuals have limited or no formal schooling, even understanding simple math problems is a substantial challenge (see for example, Cole, et al. 2011). Insights from behavioral economics, however, can help design interventions that address cognitive biases rather than focusing on pure knowledge transmission. One of the main insights of this literature is that a wide range of factors such as framing or context affect individuals’ assessment and internalization of knowledge. Consequently, it is unlikely that there is ‘ _one way to perfect intuitive judgment_ ’ (Griffin and Buehler 1999: 75). Rather than finding a general method to improve decision making, Heath, et al. (1998) conclude that different interventions may be effective in different circumstances. These insights are important in the context of financial decision making, where simply telling people about their cognitive biases has not proven to be effective. Debiasing interventions have tried three types of methods: (i) repeat interaction with immediate unambiguous feedback, (ii) consider the opposite, and (iii) counter-biasing (Willis 2008, Jolls and Sunstein 2006).<sup>4</sup> The first method of immediately providing feedback on an action has been used successfully in the lab to address overconfidence (Lichtenstein and Fischhoff 1980). However, getting feedback on financial decision making in a classroom setting has not proven to be effective (Prabhu and Tellis 2000). Likewise, applying this method through educational financial games has led to some improvement in financial knowledge, but does not appear to have translated into improvements in financial decision making

> 4One additional method previously proposed by supporters of the ‘ecological rationality’ theory is to specifically address poor understanding of probabilities is to use frequencies rather than probabilities to communicate odds (Hoffrage and Gigerenzer, 1998). Gigerenzer (1998) called this “ _the strongest and most consistent debiasing method known today_ ”. However, other research has shown that under most real-life circumstances, intuitive judgments are equally biased regardless of whether are presented in frequencies or probabilities (Griffin and Buehler 1999).

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(Mandell 2006). The ‘consider the opposite’ method has been implemented by asking participants to list alternative choices before making a financial decision. Theory predicts that participants place increasing weight on these alternatives as they become more mentally available. However, the few studies that have tested the effectiveness of this method have found little or no results (Trout 2005). The third method of ‘counter-biasing’ builds on the premise that cognitive biases may be used to induce desired behavior (Jolls and Sunstein 2006). One example is the well-known ‘save-more-tomorrow plan’ that is built on the premise that people do not change saving rates they initially chose as a default (Thaler and Benartzi 2004).

The experiential learning approach contrasts to traditional forms of financial education based on cognitive learning theories that ‘ _emphasize cognition over effect_ ’ (Boyatzis et al. 1999). Kolb (1984: 194) argues that ‘ _learning is not just the result of cognition,_ [it] _involves the integrated functioning of the total person - thinking, feeling, perceiving, behaving._ ” This insight is captured in the concept of the four-stage learning cycle which posits that learning is most effective if it involves four aspects: an (i) immediate experience forms the basis for (ii) observations and reflections which are then (iii) distilled into abstract concepts (Boyatzis et al. 1999). These concepts are subsequently (iv) actively tested which leads to new experiences.<sup>5</sup> Lecture-based learning is less likely to activate all stages in the learning cycle. Traditional forms of financial education interventions may only convey abstract concept that are not actively tested and thus do not lead to new experiences. A reflection on the lesson learned is unlikely and the content may be quickly forgotten amidst the daily challenges and obligations people face. In contrast, the starting point of our intervention is the active experience of rolling dice and the game incorporates elements from each of the learning methods discussed above. Rolling dice provides the participants with immediate feedback on probabilities of winning in a lottery (presented by getting a certain number of sixes) and the intervention serves as a memorable event that can form the basis of a new decision heuristic. Participants are able to reflect on the difficulty of obtaining sixes and the facilitator explains the link between dice rolling and the abstract concept of lottery winning probabilities. Likewise, playing a game with dice allows the complex notion of probability to be conveyed in a low-key setting

> 5Neuroscience research shows that the different stages of the cycle of experiential learning corresponds to the structure and process of brain functioning. Zull (2002: 18-19) explains that “... _concrete experiences come through the sensory cortex, reflective observations involves the integrative cortex at the back, creating new abstract concepts occurs in the frontal integrative cortex, and active testing involves the motor brain. In other words, the learning cycle arises from the structure of the brain_ .”

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without taxing the cognitively heavy systems of attention and memory.

# **2.2 Game Design**

In this study we play a simple dice game with participants to provide an experience-based learning forum to convey low probabilities of gambling. Gambling prevalence is often explained by the fact that individuals do not understand how low probabilities translate into the frequency of winning as probabilities such as 14 million to one are unlikely to lie within the range of everyday experiences (Smith and Walker 1993). Hence, our game was meant to provide an intuitive mapping of probabilities through active experimentation.

The game used regular six-sided dice as props and was administered in the field at the conclusion of a baseline survey on financial access. The game was administered by our trained staff and at the individual respondent level (see Appendix A for the exact protocol used). We first let participants roll one die until they obtained a six. Then we added another die and let them roll until they simultaneously obtained two sixes, which took them much longer. The participants were then told the equivalence of number of dice and the odds of winning different prizes in the lottery. The chance of having four right numbers in the lottery, for example, was equivalent to rolling all sixes with five dice and the odds of winning the jackpot was smaller than getting all sixes with nine dice.

The study sample consisted of 840 poor households in the Eastern Cape and KwaZulu-Natal province of South Africa. Half the study sample was randomly assigned to receive the debias treatment while the other half received a more traditional financial education module on avoiding expensive credit. (For the expensive credit treatment protocol see Appendix B.) Both the debiasing and credit modules took an average of 10 minutes and did not have any overlapping content. Second, the number of rolls it took for participants in the treatment group to get two sixes provided additional variation in the intensity of treatment. Moreover, the longer it took to roll two sixes, the clearer it became to the participants that their chance of winning was low.

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# **2.3 Framework and Testable Implications**

## **2.3.1 Framework**

The intuition and conceptual framework of our study builds on Kahneman and Tversky’s prospect theory. We derive testable predictions that inform our empirical analysis and help distinguish mechanisms for results reported in Section 4.

A decade after introducing the concept of heuristics and cognitive biases, Kahneman and Tversky (1982) suggested a second reason for why people systematically misjudge probabilities. Analyzing data on gambling, they noticed that the increase in winning odds from 0% to 5% had a larger effect on the inclination to gamble than the increase from 30 to 35% which in turn had a lower effect than an increase in odds from 95% to 100%. They concluded that the “ _psychophysics of chance induce over-weighting of sure things and of improbable events, relative to events of moderate probability_ ” (Kahneman and Tversky 1982), and introduced the concept of a probability weighting function that translates objective probabilities _p_ into weights _π_ ( _p_ ) used in decision making.<sup>6</sup> Figure 1 shows the shape of the decision weighting function that corresponds to Kahneman and Tversky’s observations. Decision weights lower than objective probability values near _p_ = 1 corresponds to the tendency to be risk averse in dealing with unlikely losses. By contrast, decisions weights higher than actual probability values near _p_ = 0 reflect that the tendency to be risk seeking in dealing with improbable gains such as winning the lottery. Several subsequent empirical studies have provided evidence consistent with this shape of the probability weighting function (Tversky and Kahneman 1992, Camerer and Ho 1994, and Gonzales and Wu 1996).

Gonzales and Wu (1999) note that there are two distinct features that characterize the probability weighting function: the degree of curvature and the elevation (level). The curvature of the weighting function, also referred to as _discriminability_ in the psychophysics literature, reflects how sensitive people’s decisions are to a change in (objective) probabilities _p_ . A flatter slope than 45% degree line means that people are too insensitive to a change in probability.<sup>7</sup> Conversely, the steeper the curvature

> 6Quiggin (1982) pointed out that KT’s originally proposed probability weighting function can lead to violations of stochastic dominance. Subsequently, the concept of cumulative prospect theory was developed in which agents transform cumulative instead of individual probabilities and base decisions on the ranking of outcomes (Tversky and Kahneman 1992).

> 7The extreme form of a step function corresponds to the case in which people lump probabilities into categories in which they perceive events to be equally likely (Piaget and Inhelder 2013).

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of the weighting functions the more sensitive individuals are to changing probabilities. The observed inverse-S-shape of the probability function implies diminishing sensitivity to probabilities further away from the two reference points of uncertainty ( _p_ = 0) and certainty ( _p_ = 1).<sup>8</sup> The level of the weighting function, referred to as _attractiveness_ , can be interpreted as the interpersonal preference of individuals to take risk and bet on chance events (Gonzales and Wu 1999).<sup>9</sup> The concepts of attractiveness and discriminability are two independent psychological properties. This distinction helps understand different mechanisms through which debiasing interventions may reduce people’s inclinations to gamble.

# **2.3.2 Changing Beliefs or Preferences?**

Kahneman and Tversky (1979) observe that people have “ _limited ability to comprehend and evaluate extreme probabilities._ ” It is commonly overlooked that this statement captures two distinct concepts: comprehension and evaluation of unlikely events. Fox and Tversky (1998) model decision making as a two-step framework: first, individuals assess the probability of events and second, they make decisions based on the assessed likelihood (Barberis 2013). In the context of our study, the question is whether people changed their beliefs of winning odds and/or whether, conditional on assessed probabilities, participants over-weighted the chances of this event in their decision-making. The difference between these two mechanisms is visualized in Figure 1. We may observe a decrease in gambling because people change their _beliefs_ about the odds of winning (depicted by a change from _b_ to _a_ due to a change in assessed probability _p_ ) or because participants change their risk _preference_ for given winning odds (depicted by a change from _a_ to _c_ and _b_ to _d_ due to a vertical change in decision weight _π_ ( _p_ )).

The distinction between changes in beliefs and preferences is important because “ _overestimation is a mistake; it is less clear that over-weighting is a mistake_ ” (Barberis 2013: 9). These two mechanisms have different predictions. A change in _risk preference_ would be regarded as a change in the decision weights or the inclination of people to accept any lottery (‘attractiveness’).<sup>10</sup> Importantly, the

> 8Available evidence suggests that experts often have relatively linear weighting functions in their specific area of expertise. Thaler and Ziemba (1988) find that decisions of experienced racetrack betters are sensitive to small differences in probabilities. By comparison, inexperienced betters disproportionately bet on long-shot horses. Likewise, Fox, Rogers and Tversky (1996) show that the median option trader in their sample shows equal sensitivity throughout the probability interval. However, it is unclear if discriminability varies intra-personally, i.e. whether the option trader also has a linear probability weighting function when he bets at the race track (Gonzales and Wu 1999).

> 9 There may also be intra-personal difference of chance domains: holding winning odds constants, individuals may prefer betting on sporting events compared to outcomes of political elections (Heath and Tversky 1991). This is related to the concept of ‘illusion of control’ (Langer 1975): gamblers prefer to choose their own numbers in a lottery rather than playing with assigned numbers even though the winning odds of each combination is identical.

> 10Attractiveness may also be affected by changes in salience bias (Bordalo et. al 2012, Gennaioli and Shleifer 2010).

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treatment effect would be observed across varying treatment intensities and range of (low probability) winning odds. Alternatively, changes in _beliefs_ or risk perception would affect people’s sensitivity to winning odds (‘discriminability’), i.e. individuals’ inclination to base gambling decision on the odds offered. The behavioral economics literature offers concrete explanations why our treatment may affect _beliefs_ of winning the lottery. Prior research has shown that individuals often put too much weight on single events in the process of belief updating (Rabin 2002). In our study, the treatment could have affected beliefs of winning odds by forming a new availability heuristic where those who rolled two sixes fairly quickly may believe lottery winnings are attainable whereas those who rolled two sixes very slowly may adopt the opposite heuristic. Importantly, the direction of belief updating underlying these behavioral mechanisms would depend on the intensity of treatment.

Our study design allows us to empirically test for heterogeneity in outcomes based on treatment intensity and thus shed light on the underlying mechanism. Due to the two stages of randomization, there is natural variation in the strength of treatment offered to individuals. The first empirical test is whether behavior change varies across treatment intensities; if yes, this would provide evidence against risk preference as the driving mechanism of behavior change. Second, we test whether the treatment changed individuals’ sensitivity to winning odds by offering lotteries with randomly assigned winning odds. Half the sample was offered a lottery with a low winning probability ( _pl_ ) and the other half were offered a lottery with a higher winning probability ( _ph_ ). As per Table 1, the difference between cells [ _a, b_ ] and [ _c, d_ ] after the intervention would show how the debiasing treatment affected the odds sensitivity, with a larger difference in _d − c_ relative to _b − a_ indicating a greater change in risk beliefs for given risk preferences (Figure 1). We implement this test empirically through a difference-in-difference strategy.

# **3 Empirical Setting and Identification**

## **3.1 Gambling in South Africa**

The setting for our study is South Africa, and this location choice was deliberate. Since the legalization

> Bordalo et. al’s (2012) salience theory is consistent with agents who comprehend (small) probabilities, but whose risk attitudes are affected by the salience of lottery payoffs. However, since the salience of lottery prices did not differ between treatment groups and the control group in our study, it is unlikely that this mechanism explains our results.

11
of gambling in 1996,<sup>11</sup> the South African gaming industry has grown substantially with gross revenues more than doubling between 2001 and 2009 to 18.13 billion Rand (1.57 billion USD) (Nzimande et al. 2010). The prevalence of gambling is also quite skewed – a 2003 survey found that while 43% of the population participated in some form of gambling, poorer household spent a significantly higher percentage of total income on it (Smith 2003). Further research in the country has shown that gambling is most prevalent among blacks, with 55% reporting that they gambled at least occasionally and 24% reporting they played the lottery regularly (NUPSGB, 2001). When asked why they gamble, 85% of respondents mentioned the chance of winning a large prize. This study also highlighted that gambling is quite socially acceptable in South Africa with 69% of respondents reporting that either some or all forms of gambling ’was ok’. We focus on one particular form of gambling, the national lotto. A 2009 regional study in the Eastern Cape showed that playing the lottery was by far the most common form of gambling in the area – 49% of respondents had tried it at least once and active gamblers played an average of 3.5 times per month (TNS 2009).<sup>12</sup>

# **3.2 Study Sample and Outcome Measures**

This study was part of a broader program that delivered classroom based financial education to individuals in rural and peri-urban areas.<sup>13</sup> Participants were organized in burial societies and women borrowing groups.<sup>14</sup> We conducted surveys in 13 geographic clusters in the Eastern Cape and KwaZulu Natal, two of South Africa’s most populous provinces.

A total sample of 840 was drawn from 27 women borrowing groups and 45 burial societies. Baseline characteristics of the sample were measured between July and November 2011 and are reported in Table 2. As the majority of burial society members were female, our sample consists of almost 90% women. Our sample is also older (53 years vs. the national average of 39 years), less educated (6.4 vs. 7.5 years), and less likely to be employed (7.3% vs. 23.4%). At the time of the baseline survey, 15% of

> 11During apartheid, all forms of gambling were prohibited under the 1965 National Gambling Act (no 15). The National Party denounced gambling as an “immoral evil” undermining the work ethic by encouraging reliance upon luck rather than hard work and skill (Lotter 1994, p.192).

> 12The lottery has distinctive features that distinguish it from other forms of gambling: it has large prizes and very low winning odds, is cheap to play, fair in the sense that it does not depend on skills, and regarded one of most socially acceptable forms of gambling (Rogers 1998).

> 13As part of a different study, half of the group in the sample received a half-day financial education training between March and June 2012. As the gambling debias was randomly assigned at the individual level, these two treatments are orthogonal. In addition, the financial education curriculum did not include any information on gambling. All estimations in this study control for whether participants received the financial education program.

> 14Burial Societies are a common form of associations to save for the typically large costs of funerals in South Africa.

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the sample reported that they had previously gambled.

During the course of the study we measured gambling outcomes at three stages, immediately after the treatment during baseline, after six months, and after one year.

i) Immediate outcome: Following the baseline survey, participants received 10 Rand ($1.00) and were offered to spend part of this compensation in the following game. First, they were shown a bag with fifty balls, in which five balls were red. Participants were then offered the opportunity to pay 1 Rand from their show-up fee to draw a ball (which was replaced after each round). If they drew a red ball they would receive 5 Rand in return. They were allowed to play up to ten times. On average, participants played 0.8 rounds. 57% of people decided not to play this gamble.

ii) Midline outcome: About six months after the debiasing treatment, participants were contacted via cell phone to collect an intermediate gambling outcome. Participants were offered the choice of a lottery in which they could win R250 or to receive R15 for certain (all prizes were delivered as cell phone airtime). To mimic the experience of playing the lottery, participants were asked to guess which six numbers between 1 and 49 were drawn at the national lottery at an undisclosed particular date over the past six months. The winning odds were randomly assigned within each group:<sup>15</sup> half of the participants were told they would win if they picked all six numbers correctly (odds 1:9,355,819), while the other half were told they would win if they picked at least four correct numbers (odds 1:800). These exact winning odds were not disclosed to participants. Overall, 26.6% of the participating sample chose to play the lottery, of which nobody won.

iii) Endline outcome: Between June and November 2012, approximately one year after the debiasing treatments were administered, an in-person endline survey was administered that collected data on gambling behavior of participants in the last six months. Information was also collected on a range of financial behaviors and attitudes. Note that although endline outcome measures are self reported, our empirical strategy exploits variation in the intensity of treatment rather than the binary effects of treatment. Since all respondents in this sample received the same treatment (but experienced different intensity due to the roll of dice) we are not concerned about reporting biases.

> 15Within the treatment group, random assignment was stratified along treatment intensity (above vs. below median number of rolls).

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# **3.3 Empirical Strategy and Identification**

The main empirical specification used in our analysis is straightforward because treatment was randomly assigned. In the spirit of Crepon, et al. (2013), this study employs two stages of exogenous variation. In the first stage, participants were randomly assigned to receive either the gambling debias or credit information treatment. In the second stage, the number of rolls it took treated participants to roll two sixes provided additional random variation in treatment intensity. For instance, participants who, by chance, rolled two sixes on the third try received a less intense debiasing treatment than participants who needed thirty rolls. We take advantage of this exogenous variation in treatment intensity to test the various theories of behavior change outlined in 2.3.2.

The control group received a treatment on credit to allay concerns of Hawthorne effects (see Appendix B for details). The two interventions were unrelated in content – the gambling intervention did not mention hire purchase credit, or even interest rates; and the credit intervention did not discuss lotteries, odds, or gambling.<sup>16</sup> However, since the unit of randomization was the individual rather than the village, there may be knowledge spillovers. Participants may have talked about their particular intervention with individuals in the same saving or borrowing group who were part of the control group. Any learning spillovers within a group would also lead to a downward bias of our results. Since we cannot rule this out, our results should be interpreted as a lower bound of the true effect.

In Table 2 we test for balance across the treatment groups and find that the random assignment at the two stages resulted in groups that were balanced across a range of observable baseline characteristics. The left panel in Table 2 reports the sample means and p-value of a test of equal means between the gambling debiasing group (T) and credit information participants who served as the control group (C). Of the 15 baseline characteristics tested, only one difference in means is (marginally) significant.

Figure 1 (Appendix) shows the distribution of number of rolls it took people in the sample to get two 6s. While the distribution is roughly normal, there are spikes at 15, 20, and 25 rolls. This resulted from field workers using different stopping rules, i.e. some stopped the demonstration after 15 or 20

> 16We designed the hire purchase intervention as a form of ’placebo treatment’. While it is theoretically possible that a better understanding of compound interest rates would also affect comprehension of low probabilities, this would only bias our treatment effects downwards. Another potential concern might be if the hire purchase debiasing intervention had a large effect on participants monthly expenditure: we may then observe increases or decreases in gambling due to wealth or liquidity effects. However, we do not observe changes in financial behavior or in discretionary income as a result of the hire purchase intervention.

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rolls if the participant had not rolled two sixes by then. We will therefore divide the sample into two treatment intensity groups depending on whether they needed more than the median (N=12) number of rolls. The rationale is that there are no clear excess mass in the distribution below the median, e.g. at 5 or 10 rolls. The assignment to the low vs. high intensity treatment group is therefore independent of the stoppage rule used by field workers. The key question for the identification strategy is whether the assignment to treatment intensity within the gambling debiasing group is orthogonal to the baseline characteristics.

The right panel of Table 2 reports a balance test of the randomization resulting from dice rolls. The first two columns report average baseline characteristics of the low intensity (below median rolls) and high intensity (above median) treatment groups. The last column reports p-values of a test of equal means between the control and two treatment groups. Similar to the previous test, only the difference in share of women between the different groups are statistically significant. When we simultaneously control for all covariates in a regression with the number of rolls to get two sixes or an indicator variable for high intensity as the dependent variable, none of the baseline characteristics are statistically significant.

While other differences in baseline characteristics are not statistically significant, some may still be economically meaningful. In particular, 14% of people in the high intensity treatment group had gambled before compared to 11% in the low intensity group. With a marginally higher share of gamblers in the high intensity group, a simple comparison of means may underestimate the true treatment effect. In the empirical analysis we therefore report results with and without controlling for these covariates.

Attrition was not an issue for the immediate outcome measure since it was captured immediately after the baseline survey. For the midline outcome data collection, we successfully reached 74% of the sample via phone, of which 78.4% agreed to participate. Results from a linear probability regression (Table 3, Columns 1-4) show that both the probability of reaching individuals and their decision to respond to the survey were not systematically correlated with treatment assignment, nor with the number of die rolls they required to obtain two sixes. As an additional test, we find that the decision to participate in the midline survey was not significantly correlated with the gambling decision in the immediate outcome measure. This supports the view that attrition does not bias results.

Overall attrition in the endline was 30.4%. This attrition rate is relatively high, however, it was primarily due to a hardware failure: all data from certain clusters was lost when the digital devices 15
used to conduct the surveys failed to synchronize. This reduces the precision with which we can estimate outcome measures collected at the endline. However, Table 3 shows that the attrition rates did not vary significantly between treatment and control groups (Column 5) or between the treatment intensity groups (Column 6).

## **3.4 Estimation**

Our main regression specification is as follows: _yi_ refers to the outcome of person _i_ . _Tlow_ and _Thigh_ are indicator variables for gambling debiasing participants that took below and above median number of rolls to get two 6s, respectively. Coefficient _β_ 1 and _β_ 2 estimate the average effect of being in the low and high intensity treatment group compared to the control group, respectively. _Xi_ is a vector of baseline covariates including gender, age, education levels, income level, and indicator variables for whether the person gambled before and uses formal financial services. We control for these covariates to increase the precision of treatment estimates. Regressions are estimated using robust standard errors _ei_ . We also report F-Test p-values of equality between _β_ 1and _β_ 2.

As discussed in Section 2.3.2, we test whether treated individuals became more sensitive to the small winning odds of a lottery. We do so by estimating the following specification: The variable _oddsg_ refers to the randomly assigned better winning odds in the midline outcome. Estimates of _δ_ 1 ( _δ_ 2) show how the odds sensitivity of the low (high) intensity treatment group compared to the control group. F-test p-values of equal coefficients ( _δ_ 1 = _δ_ 2) are also reported.

# **4 Results**

## **4.1 Gambling Behavior**

The analysis takes advantage of the fact that we have gambling outcome variables for individuals 16
at three points in time, as described in the previous section. Hence, to maximize statistical power, we aggregate outcomes for individuals across time and create an index of lottery outcomes, following Kling, et al. (2007).<sup>17</sup> Table 4 reports regression results using both the lottery index and individual survey measures as the dependent variables. Column 1 shows that the average treatment effect is close to zero and statistically insignificant. This suggests that in the aggregate, gambling behavior did not change in the treatment group. Columns 2 to 4 report results of regression model 1 that estimates differential treatment effects between the high and low treatment groups. Column 2 shows that results vary significantly between the two groups – the low intensity group, where individuals needed fewer attempts to get two sixes, gambled significantly _more_ than the control group, while the high intensity group gambled significantly _less_ . The treatment coefficients (compared to the control group) are statistically significant at the 5% and 10% level, respectively. The difference between the high and low treatment coefficients is also significant at the 1% level as indicated by the p-value of the F-test reported in the bottom row of Table 4. Results do not change in magnitude or statistical significance when we control for additional baseline covariates in columns 3 and 4.

Table 4 also reports results of the same regression specification estimated separately for the three gambling outcomes that comprise the lottery index. All gambling outcomes show a consistent picture: the high treatment intensity group gambled less and the low treatment group gambled more relative to the control group. Estimated effects are large in magnitude. Individuals in the high treatment group gambled 29% less in a lottery offered after the debiasing intervention while the low treatment intensity group gambled 19% more compared to the control group in a lottery offered immediately after the intervention. It is noteworthy that the effects persist one year after the intervention – in the final follow-up, 10.7% of people in the low treatment intensity group reported playing the lottery compared to 7.4% in the control group. The equivalent figure for the high treatment intensity group was 4.7%. The p-values on the F-tests are statistically significant, hence showing that the differences between high and low intensity groups are significantly different from each other.

As discussed earlier, our main specification divides the treatment intensity into above and below median, because of differential stoppage rules. We can nevertheless examine how decisions vary when

> 17The index is created by adding values for the two indicator outcomes (midline, endline) and a standardized measure of the number of rounds played (immediate).

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using all available variation in treatment intensity. Figure 2 shows the relationship between the full distribution of treatment intensity and the lottery index non-parametrically. Fitting a local polynomial function using a Epanechikov kernel confirms a relatively monotonous negative relationship between the number of rolls and gambling behavior.

# **4.2 Odds Sensitivity**

Next we explore whether the debiasing treatment led to a change in the sensitivity to winning odds. As described in Section 2, our study design randomly varied the winning odds of gambles offered to the sample at midline. Figure 2 shows the effect of improving the winning odds (from having to get all six numbers right to having to get at least four right) on the probability that a participant chose the lottery over a certain amount, separately for the high and low treatment intensity groups. Improving winning odds induced individuals in the high intensity group to increase the take-up of the lottery from 13% to 30% (middle panel), whereas there was no such change for the low intensity group (right panel).

Table 5 reports these results in a regression framework. Column 1 shows that when we pool winning probabilities in the full sample, higher winning odds are associated with a higher probability of choosing the lottery. As shown in the graph, the low intensity group was more likely and the high intensity group was less likely to choose the gamble compared to the control group. However, these estimates are not significant at conventional levels. The p-value of a test of equal coefficients between the two treatment groups is 0.15. The specification in Column 2 includes interaction terms between the treatment groups and the better odds dummy. The coefficients on these interaction terms confirm that the low intensity group was less sensitive and the high intensity group was more sensitive to changing winning odds than the control group. However, the test of equal coefficients of these interaction terms ( _δ_ 1 and _δ_ 2) cannot be rejected at conventional significant levels (p-value=0.2). While we lack the statistical power to provide conclusive evidence, these results provide suggestive evidence that at the change in gambling behavior can at least partly be explained by a change in sensitivity to winning odds.

# **4.3 Discussion of Mechanisms**

Taken together, our regression analysis points to changes in risk _beliefs_ rather than risk _preferences_ 18
as the mechanism of impact on gambling outcomes. Specifically, the strong treatment heterogeneity based on intensity of treatment provides evidence against entertainment utility or a general change in risk _preference_ as the driving mechanism for behavior change.

As a final test of mechanisms, we can directly observe whether there was substitution to other forms of gambling as a result of the debiasing treatment, with the hypothesis that lowering the entertainment utility of gambling would likely not lead to such substitutions. Conversely, if individuals updated beliefs on lotteries through a new heuristic or better odds sensitivity, then they may substitute to other forms of gambling that do not deal with lottery odds. Fortunately, we observe spending on such an alternative form of gambling – scratch cards. Functionally, scratch cards are quite different from lottery tickets as the former does not involve choosing winning numbers and hence had very little similarity with our debiasing treatment.

Results reported in Table 1 show that individuals indeed substituted between different types of gambling based on treatment intensity. The low intensity treatment group was more likely than the control group to play the lottery but less likely to play scratch cards while the high intensity treatment group was significantly more likely to switch and play scratch cards instead of the lottery. This substitution between different forms of gambling further corroborates that the intervention changed beliefs of winning odds (albeit narrowly for the national lottery) rather than affecting entertainment utility people derive from gambling.

# **4.4 What Can Explain the Large Effects?**

Given that most previous studies in the financial education and debiasing literature have found modest results, it may be surprising that a simple experiential debiasing treatment that did not take more than ten minutes led to large and persistent treatment effects. The gambling treatment may have been more effective in changing beliefs on gambling winning odds for at least three reasons. First, as pointed out by Heath et al. (1998), while debiasing techniques that build on preexisting knowledge make behavior changes less costly, they also do not create much enthusiasm and are more likely to get ignored. Our study implemented debiasing techniques through experiential learning combining both novel and familiar elements: while participants were generally familiar with the concept of rolling dice, they were likely to be unfamiliar with the link to winning probabilities of the lottery. This explanation 19
is supported by experiences from field workers who reported that most participants were intrigued by the dice game. As discussed in Section 2, the intervention may have thus activated more stages of the learning cycle.

Second, we may observe large effects because the treatment had elements of a ‘counter-biasing’ strategy (Jolls and Sunstein 2006). The experience of getting all sixes in both the one die and two dice round with only few rolls combined with information that the chances of winning the lottery jackpot are equivalent to adding ‘only’ seven additional dice may have caused a strong emotional reaction. This memorable event may have become the basis of a new availability bias: study participants that needed many rolls and thus memorize the difficulty of winning gamble less than the control group, while low treatment intensity participants remember the ease of winning and gamble more.<sup>18</sup> Along similar lines, Griffin and Tversky (1992) and Fischhoff and Hall (1992) show that people are imperfect when updating their beliefs with new evidence: the strength of the evidence tends to dominate its weight compared to predictions of a Bayesian model. Kahneman (1998) dubbed this phenomenon the ‘ _power of the particular_ ’. For example, when testing the bias of a coin, people make their judgment primarily by the proportion of tails and heads in the sample with insufficient consideration of the sample size (Slavic and Lichtenstein 1971; Rabin 2002). Consequently, people are overconfident in evidence generated by small samples.

Third, our study sample is very different from those of previous studies, which in most cases conducted lab experiments in developed countries. Our sample of women in rural South Africa with relatively little formal education may have been particularly receptive to the interactive and intuitive nature of learning about probabilities. This explanation is supported by earlier research showing that debiasing techniques tend to be more effective if they are simple as they do not tax cognitive resources like memory or attention (Bell et al. 1988).

Next, we discuss whether there are reasons to believe that our results translate to other populations or whether there was something particular about our sample that made participants particularly receptive to the debiasing intervention.

> 18Finding of earlier research showing that emotional events are particularly effective in creating cognitive biases (Nisbet and Ross 1980), is supported by the fact that the effects of the low intensity treatment (which may have led to an overestimation of the jackpot winning odds) are consistently larger in magnitude than effects of high treatment intensity.

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# **4.5 External Validity: How Did Individuals Learn?**

A natural question that arises is whether our intervention would yield similar effects among other samples and in different setting. The education literature indeed finds that individuals have different optimal learning styles and a teaching method that worked well in rural South Africa may not be effective in a different environment. Specifically, learning styles can be categorized along two dimensions: (i) modes of grasping experience and (ii) modes of processing experience. In grasping experience, some learn new information best through “ _experiencing the concrete, tangible, felt qualities of the world, relying on our sense_ ” whereas others absorb new information through abstract conceptualization that includes contemplating and analyzing experiences (Kolb and Kolb 2005). Similarly, individuals differ in how they process experience: some favor reflective observations that include careful observation of peers while others prefer active experimentation.

While optimal learning styles were initially believed to be individual specific and fixed, recent studies have argued that they are instead dynamic and depend on the environment and past life experiences. It seems likely that the environment poor individuals in developing countries face would favor a learning style that focuses on concrete experiencing and active experimentation. First, there is less division of labor so individuals observe the relationship between actions and outcomes without needing to reason about the underlying mechanism or complexity.<sup>19</sup> For example, observing the behavior of seaweed farmers in Indonesia, Hanna et al. (2014) note that farmers unintentionally experiment in the production process by varying pod sizes. Second, individuals with less schooling may be less likely to develop analytical skills needed for abstract conceptualization and reflective observations. Hence, experiential learning interventions may be particularly relevant for individuals with such accommodating learning styles who primarily learn from ‘hands-on’ experience and tend to act on ‘gut’ feelings instead of logical analysis (Boyatzis et al. 1999: 6).

The data in our study allows us to shed some light on how individuals learn, which helps address the external validity question. We are particularly interested in whether participants with little formal education gained an intuitive understanding of the relatively sophisticated debiasing concept that rolling additional sixes gets _exponentially_ more difficult with each die added. We take advantage of the fact that we have two independent treatment indicators for each participant: the number of times

> 19Studies have shown individuals in executive jobs that require focus on decision making and task accomplishment require accommodating learning styles (KK).

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to get a six with one die (round 1) and the number of times to get all sixes with two dice (round 2). To provide intuition for our test of learning mechanisms, imagine two participants who both needed 15 rolls to get both sixes in round two. Person A took ten times to get the six in round 1 whereas it took Person B only two times. In theory, the overall treatment could be more effective for either person. For person A, both rounds convey the same message that it is very difficult to get sixes. For person B, the treatment may be more effective because the larger difference in number of attempts in the two rounds better conveys the message that getting all sixes becomes increasingly difficult with each additional die. This is particularly relevant because our treatment message, comparing the odds of winning the lottery jackpot to the odds of rolling all sixes with nine dice, is based on the concept of this exponential increase in difficulty as dice are added.

To distinguish between these two possible learning mechanisms, we divide the sample in each round along the median number of rolls and compare the four possible combinations of treatments. Table 6 shows the results of this analysis. Column (2) reports results of the previous analysis of round two (two dice). Column (1) shows results of the same econometric specification using only the information of round 1 (one die). The coefficients are of the same sign as for round 2 but not statistically significant. It is also reassuring that the coefficient is much smaller as the treatment is weaker compared to rolling two dice. Column (3) reports results of the previously discussed analysis with the treatment groups divided into four groups depending on whether participants needed above or below median number of rolls in the two rounds. The only significant coefficients are for people that had the same outcome in both rounds ( _<_ / _<_ and _>_ / _>_ ) which provides evidence in support of the theory that reinforcement is more effective. Comparing participants in our motivating example corroborates this conclusion. Person B ( _>_ / _>_ ) gambles less than person A ( _<_ / _>_ ). The difference in coefficient is statistically significant at the 10 percent level as reported in an F-test in the last row.

Overall, these results suggest that reinforcement of the same lesson in both rounds is the most effective treatment. Taken at face value, this finding confirms that experiential learning may be most effective for people without strong abstract reasoning skills as the concept of an exponential increase in difficulty is more sophisticated than the concept of reinforcement.

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# **5 Concluding Remarks**

In this paper, we test whether experiential learning about lottery odds through a simple and interactive dice game can lead to meaningful impacts on gambling behavior. We find significant heterogeneity in impacts based on the intensity of treatment with the high intensity treatment group exhibiting reductions in gambling behavior and the low intensity group exhibiting the opposite. These results are consistent with a model where individuals update their beliefs about lottery winning odds through the experience of the game – those who experience poor odds in the game end up being effectively debiased whereas those who by chance experience good odds in the game end up with reinforced biases about the lottery.

Our study is one of the first pieces of field research that shows experiential learning in general and experiential debiasing in particular have the potential to be a promising alternative to the traditional method of conveying information, especially for people with little formal education. Yet, the perverse results for the low intensity treatment group serve as a caution that debiasing instruments can potentially backfire. Future programs should be designed to take into account and minimize this risk. In our specific game design, this perverse outcome could easily have been avoided, for instance by adding a third die to the game. Future research should also explore whether similar interventions prove to be effective in changing behavior in domains like technology adoption or financial decision making in which lecture-based provision of information has been shown to be ineffective.

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