Finance article

Deal or No Deal, That is the Question: The Impact of Increasing

Stakes and Framing Effects on Decision-Making under Risk

ROBERT BROOKS, ROBERT FAFF, DANIEL MULINO AND RICHARD SCHEELINGS

Department of Accounting and Finance Faculty of Business and Economics,

Monash University, Melbourne, Australia

ABSTRACT

In this paper, we utilize data from the Australian version of the TV game show, ‘Deal or No Deal’, to explore risk aversion in a high real stakes setting. An attractive feature of this version of the game is that supplementary rounds may occur which switch the decision frame of players. There are four main findings. First, we observe that the degree of risk aversion generally increases with stakes. Second, we observe considerable heterogeneity in people’s willingness to bear risk – even at very high stakes. Third, we find that age and gender are statistically significant determinants of risk aversion, while wealth is not. Fourth, we find that the reversal of framing does have a significant impact on people’s willingness to bear risk.

I. INTRODUCTION

The analysis of decisions under uncertainty is fundamental to modern economics and finance. This paper contributes to a recently developing empirical literature that adopts the central research question: How risk averse are individuals? Subsidiary questions regarding risk aversion that we address include its heterogeneity and how it varies with individual demographic characteristics (especially age, wealth and gender). While the theoretical literature on risk aversion and expected utility theory is large and long- standing, the literature explicitly testing for risk aversion is comparatively small. Such empirical tests as exist, either in laboratory or field experiments involving real stakes, have mostly been confined to small cash values. There has been a recent debate doubting the applicability of such estimates when extrapolated to high real stakes (see Rabin 2000). Our paper exploits an Australian game show dataset to explore the nature of risk aversion of contestants who face an environment of very high stakes.

r 2009 The Authors. Journal compilation r International Review of Finance Ltd. 2009. Published by Blackwell Publishing Ltd., 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

International Review of Finance, 9:1–2, 2009: pp. 27–50 DOI: 10.1111/j.1468-2443.2009.01084.x

‘Deal or No Deal’ is a half-hour TV game show in which contestants make a series of choices between a sure thing and a lottery.1 It is ideal for studying a range of issues relating to economic decision making. The show consists of a chosen contestant faced with 26 suitcases, randomly containing amounts ranging from 50 cents to US$200,000 dollars. There are up to nine ‘normal’ rounds in the main stage of the game. Unlike other versions of the show, the Australian version of ‘Deal or No Deal’ also involves the potential for one of two extra rounds – the Chance round and the SuperCase round.

First, when only two suitcases are left, the contestant may be offered a ‘Chance’ round, allowing them to exchange the certain amount that they’ve already won for a 55 lottery between the two remaining prizes. Second, when all suitcases have been revealed, the contestant may be given the option of swapping the certain amount that they have won for the ‘SuperCase’, which is a lottery in which one of eight prizes may be won. Both these possibilities are entirely at the discretion of the producers. These special rounds involve a reversal of the contestants’ frame of reference and, hence, are ideal for testing framing effects. Accordingly, we exploit this feature of our dataset.

Our paper investigates two fundamental issues. First, we explore the willingness of contestants to take risks with large monetary gambles. Second, we assess whether contestant decision-making reflects framing effects. Regard- ing the first issue, we find that, while on average most contestants on ‘Deal or No Deal’ are probably risk averse, their willingness to bear risk is greater than had previously been found in studies of US game shows. Moreover, many contestants are willing to take very risky gambles, even when the stakes are high. There is a high degree of heterogeneity among contestants. Our results also re-affirm the prior literature that people become more risk averse as stakes rise (Holt and Laury 2002).

The theoretical and scientific attraction of expected utility theory is that it posits a consistent preference relation regardless of changes in the ‘frame’ of the decision, especially with respect to changes in a decision-maker’s wealth. Prospect theory (which implies loss aversion2) is a well-known example of a theory of decision-making under uncertainty where that is not the case. The Australian version of the ‘Deal or No Deal’ game show is well-suited to test framing effects because some contestants face a reversal of the framing of their choice when they participate in either the Chance round or the SuperCase

1 We use data from the Australian version of Deal or No Deal, although the show has now been

syndicated in over 30 countries. It should be emphasized that the show, although franchised

from the same Dutch source (the Endemol TV entertainment company) is not identical across

all its franchises. Variations in the game show introduced by different countries leads to

different datasets. Confining our attention to a single version of Deal or No Deal has the

advantage of giving us a uniform experimental setting.

2 ‘Loss aversion’ describes how a person’s welfare will fall more as a result of losing a specified

amount of money than it rises when they win the same amount of money. People who are loss

averse will be willing to take large risks to avoid losses but will tend to be risk averse with

potential gains. See, for example, Kahneman and Tversky (1979).

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round described above. In the ‘normal’ rounds, contestants face the prospect of swapping their rights to the lottery for a sure amount of money. In contrast, in the Chance and SuperCase rounds, contestants face the prospect of exchanging a certain amount of money already won (via the ‘Deal’ agreed to earlier) for a gamble.

Approximately 40% of the contestants in our dataset participate in one of these ‘special’ rounds. We find that contestants exhibit a considerably higher level of risk aversion in both the Chance and SuperCase rounds than in the normal rounds. Assuming the validity of an underlying assumption that contestants are characterizable by some type of non-expected utility model, this appears to provide some support for a kind of preference reversal or framing effect. Notably, other game show studies in the literature, as well as versions of the ‘Deal or No Deal’ game show exhibited in other countries, do not involve such a reversal of the choice framework, and so were not able to test this behavioral effect.

On the important issue of the variation in risk aversion with agent characteristics, we find, consistent with much of the pre-existing literature, that attributes like age and gender have a statistically significant effect. While the evidence to date on this issue is mixed, where studies have found an impact, it is almost always that women are more risk averse than men. Our findings are consistent with Hartog et al. (2000) using survey data from the Netherlands, with Holt and Laury (2002), using experimental data, and with Cohen and Einav (2007), who utilize a large car insurance dataset to structurally estimate risk aversion and attributes long thought to influence risk aversion. A similar gender effect has also been found in several studies in the finance literature (see, e.g., Cohn et al. 1975; Lewellen et al. 1978).

The remainder of this paper is organized as follows. The next section briefly outlines the relevant literature. Section III outlines the ‘Deal or No Deal’ game show and describes the data it generates. Section IV presents and discusses our empirical results, and Section V concludes.

II. RELEVANT LITERATURE

Researchers have, to date, largely relied upon three methods to study the magnitude and variability (with stakes) of risk aversion. First, they have run experiments in which people face actual monetary gambles.3 Given the funding limits of such studies, many (though not all) were perforce small-stakes. The second method is to rely upon responses to surveys (see the discussion at the beginning of Camerer 1995). This permits the consideration of people’s attitudes to gambles involving much larger sums – but such studies are limited to hypothetical choices and there is no reason for thinking that what people say

3 See for example the survey of the laboratory auction literature by Bajari and Hortascu (2005),

and also Holt and Laury (2002), Harrison et al. (2003) and Goeree et al. (2000).

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they will do when faced with high stakes, is what they in fact will do (see Holt and Laury 2002, and the discussion in Hartog et al. 2000). Finally, there is the use of ‘field experiments,’ or situations of data-generation outside the direct control of the researcher in which people are faced with large gambles. This includes a game show literature as well as a small literature utilizing experiments conducted in developing countries. Collectively, these studies have found that people are generally (though only moderately) risk averse in high stakes environments, and that they become more risk averse as the stakes of the gamble increase (though, again, only mildly).

Most of the game show papers are limited in their direct comparability to our paper because they involve strategic interaction rather than, as is the case with ‘Deal or No Deal’, pure decision theoretic considerations. Papers concerning strategic game shows focus on the disjunction and possible means of reconciliation between actual play and the theoretically prescribed optimal play, an issue since resolved in laboratory experiments via the use of quantal response equilibrium models (see McKelvey and Palfrey 1995).4 A game show paper that focuses explicitly on measuring risk aversion is Gertner (1993). He utilizes data from the show ‘Card Sharks’. Gertner finds a very high coefficient of risk aversion. Further, Gertner finds that individual player-behavior is inconsistent with expected utility theory. Fullenkamp et al. (2003) consider lottery games and find risk aversion displayed and also that it varies with the size of the stakes. Hersch and McDougall (1997) consider the same type of data for lottery games and find that income is not a significant determinant, a finding replicated in the current paper. Beetsma and Schotman (2001) consider the show ‘Lingo’ and find evidence of risk aversion.

An advantage of the current paper compared with other game show papers is that ‘Deal or No Deal’ requires no special skills in order to succeed. This has been recognized as an important characteristic by researchers – so much so, that a rapidly expanding literature using ‘Deal of No Deal’ data has emerged contemporaneous with our work. Such studies are well represented by Bombardini and Trebbi (2005), Blavatskyy and Pogrebna (2006, 2008), Post et al. (2008), de Roos and Sarafidis (2006) and Andersen et al. (2006a, b and 2008).

Bombardini and Trebbi (2005), analyze the Italian version of the ‘Deal or No Deal’ global franchise and structurally estimate a sample average constant risk aversion parameter of about unity. Contrary to our work, they find no evidence for the dependence of risk aversion on agent characteristics like age and gender. In a finding relevant to our paper, they are unable to rule out that their dataset was generated via contestants possessing non-expected utility preferences. Two further papers utilizing the Italian version of the show are Blavatskyy and Pogrebna (2006, 2008). The main focus of the first of these is in confirming that contestant risk aversion is invariant under differing likelihoods of identical

4 Three papers consider the show ‘The Price is Right’: Bennett and Hickman (1993), Berk,

Hughson and Vandezande (1996) and Healy and Noussair (2004). A paper by Metrick (1995)

examines data from the game show ‘Jeopardy.’ None of them explicitly test for risk aversion.

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gains. In the second paper, the authors exploit a special suitcase-swapping feature of the Italian version of the game show to directly test for (and refute) contestant loss aversion. Andersen et al. (2006a, b) find evidence for probability weighting, but not for loss aversion. The paper by Post et al. (2008) uses combined data from the German, Dutch and Belgium franchises and they find that, independent of nationality, player behavior is both path-dependent and frame-dependent. Like us, de Roos and Sarafidis (2006) employ Australian data. They obtain (in a model which ignores the supplementary rounds) a structural estimate of risk aversion of one half (assuming zero initial wealth). They too are unable to rule out the hypothesis that their dataset was generated via contestants possessing non-expected utility preferences.

III. THE GAME SHOW

A. Description of the show

The TV game ‘Deal or No Deal’ is comprised of three stages. The first two involve the selection of a player (‘the contestant’) chosen to play the game (they reduce the contestant pool from 150 to one), and the third stage deals with the playing of the game proper.

In Stage 1, the 150 members of the studio audience are sorted into six groups of 25. One of these groups is chosen at random. An additional, 26th person is chosen at random from the remaining pool of 125. These 26 people progress to Stage 2. Stage 2 is a trivia contest based on three simple questions. Of the Stage 2 participants that answer the most questions correctly, the chosen contestant is the person with the fastest reaction time. The contestant then moves on to Stage 3, which is the segment of the game that is of interest for this paper.

Stage 3 constitutes the game proper, and is the part which generates the dataset used in this paper. It starts with 26 numbered suitcases, each of which contains a concealed, pre-determined monetary prize. The 26 unique money prizes range from 50 cents to a maximum of US$200,000, with most of the values falling below US$10,000. The schedule of prizes is contained in Appendix A. The schedule of prizes remains the same in each show, although the amount allocated to each numbered suitcase is determined randomly before the start of each show.

At the start of Stage 3, the contestant chooses one suitcase, which is set aside. If the contestant plays Stage 3 to its ultimate conclusion, the contestant will win the prize contained in that suitcase. The remaining 25 suitcases are given to the 25 unsuccessful participants in Stage 2 (‘the suitcase contestants’).

Next, in Round 1 of the game, the contestant chooses six suitcases, from the remaining 25, for removal. As the contestant nominates each suitcase for removal, the monetary prize contained in that suitcase is revealed by the suitcase contestant holding it. Once a money prize has been revealed, it is removed from the game and can no longer be won.

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After the first six suitcases have been removed, the ‘Bank’ (i.e. the producers of the game show) makes an offer to the contestant via the host of the game show: the ‘Bank Offer’. The Bank Offer is a cash prize – determined, in part, by which money prizes remain available to be won in the 20 remaining unopened suitcases. The contestant can either accept this offer by choosing ‘Deal’, or continue to the next round of Stage 3 by choosing ‘No Deal’. When making this and all future decisions, the contestant is fully aware of which prizes remain available to be won.5

If ‘Deal’ is chosen, the contestant wins the money offered by the Bank but forfeits the right to continue playing Stage 3. If ‘No Deal’ is chosen, then the contestant moves to Round 2 of the game and must nominate a further five suitcases for removal from the 19 unopened cases still held by suitcase contestants. The contestant may not nominate the suitcase originally set aside. After the money prizes contained in these five suitcases are revealed, the contestant receives a second, revised Bank Offer. If, after the second Bank Offer, the contestant chooses ‘No Deal’, a further four suitcases must be removed (Round 3). The Bank then makes a third Bank Offer based on the remaining 11 suitcases.6

The contestant again chooses either ‘Deal’ or ‘No Deal’. If ‘No Deal’ is chosen, the contestant moves to a fourth Round and must nominate a further three suitcases for removal. After their removal, the Bank makes a fourth offer, based on the remaining eight unopened suitcases. The contestant again chooses ‘Deal’ or ‘No Deal’. If ‘No Deal’ is chosen, two more suitcases must be removed in Round 5, after which a fifth Bank Offer is made. If ‘No Deal’ is chosen after the fifth offer, the game enters a phase (Rounds 6–9) in which suitcases held by the suitcase contestants are removed one by one. After the removal of each suitcase, a new Bank Offer is made.

When only one unopened suitcase held by a suitcase contestant remains, the contestant must either accept the 9th Bank Offer or choose their own suitcase over the suitcase held by the single remaining suitcase contestant.

If at any time during the game the contestant has accepted a Bank Offer, s/he will continue to nominate suitcases for removal ‘as if’ s/he were still playing Stage 3. This heightens tension allowing TV viewers to imagine ‘what might have been.’ Finally, this counter-factual exercise allows for the possibility (since

5 One possible issue that could be raised concerning the mechanics of the bank’s offer is whether

it involves some strategic or informative element, transforming the environment of the field

experiment from a pure decision-theoretic to a game theoretic one. We found that the

correlation between, on the one hand, the ratio of the bank offer to the expected value of the

remaining suitcases, and, on the other, the ratio of the contestant’s initially chosen suitcase to

the expected value of the remaining suitcases, was 0.08 – a value sufficiently low to suggest

that strategic behavior is a non-issue. Moreover, this correlation falls in the final two rounds

and even turns slightly negative in round nine. Thus, our operating assumption in this paper –

that the contestants find themselves in a pure decision-theoretic environment – is justified.

6 That is, the suitcase originally chosen by the contestant and the 10 unopened cases still held

by suitcase contestants.

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this occurs at the discretion of the producers) of one of the two supplementary rounds (the Chance and SuperCase rounds) to be played. These rounds, unique to the Australian game show, are important for our test of framing effects. Appendix B contains a characterization of the rounds of play in the Australian version of ‘Deal or No Deal’. Appendix C summarizes the play in nine normal rounds and a Chance round from an illustrative actual game from our dataset in which the contestant wins US$100,000.

B. Description of the data

We have data for 102 episodes from the second and third series of the Australian version of the ‘Deal or No Deal’ game show. Table 1 displays descriptive statistics. The mean value of prizes won in these episodes is US$15,810 with a standard deviation of US$18,541.7 The minimum prize won was US$1 and the maximum US$105,000. Not surprisingly, the Bank Offers in the initial rounds were generally low relative to the expected value of the remaining suitcases. Given that there is only one contestant per show, the producers have a strong incentive to ensure that each contestant plays at least a few rounds. In our sample, no contestants accepted an offer in Rounds 1, 2 or 3, and only one contestant accepted in the fourth round. A total of 91 contestants played until at least Round 6.

However, these averages obscure interesting behavioral heterogeneity at the agent level. Perhaps most notably, 49 Bank Offers that were greater than the

Table 1 Basic descriptive statistics

Obs Mean SD Minimum Maximum

Prize Won 102 US$15, 810 US$18, 541 US$1 US$105, 000 OFFER 741 US$8, 717 US$9, 783 US$1 US$105, 000 MALE 728 0.48 0.49 0 1 AGE 728 32 years 9.7 years 18 years 66 years INCOME 720 US$421 US$86 US$250 US$650 HINCOME 720 US$920 US$200 US$450 US$1, 750 FINCOME 720 US$1, 089 US$256 US$550 US$1, 750

This table reports basic descriptive statistics for the full sample of rounds for the Australian version of the TV game show ‘Deal or No Deal’. The statistics shown are number of observations; mean; standard deviation; minimum value and maximum value. The variables are: Prize won; OFFER: the value of the bank offer; MALE: a dummy variable that takes the value of unity if the contestant is a male; AGE: the contestant’s age measured in years; INCOME: is individual income proxied by the average weekly income associated with the postcode (analogous to zip code) of the contestant based on data from the 2001 Australian Census; HINCOME: is household income proxied by the average weekly household income associated with the postcode of the contestant based on data from the 2001 Australian Census; FINCOME: is family income proxied by the average weekly family income associated with the postcode of the contestant based on data from the 2001 Australian Census.

7 For comparative purposes it should be noted that the 26 suitcases that are available to be won

at the beginning of each game have a mean of US$19,112 and standard deviation of

US$44,576.

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expected value of the remaining suitcases were rejected. Of these 49 rejected offers, 14 were 4US$8000, 10 were for 4US$10,000 and three exceeded US$20,000. The mean Bank Offer greater than expected value that is rejected is US$6000. Out of a sample of 102, eight different contestants rejected at least one offer greater than an expected value of more than US$10,000. As such, this represents a sizeable minority of the sample who exhibit risk-loving behavior with very large stakes.

We have data on three personal characteristics of each contestant: gender; age; and the postcode in which they reside.8 Forty-eight percent of contestants in the sample were male. The age of contestants varied from 18 to 66 years, with a mean of 32 and standard deviation of 10. For each postcode, we obtained average income data from the 2001 Australian Census, and used this as a proxy for individual wealth.

C. Strengths and limitations of the data

i. Strengths Two important advantages of our data are that they describe decisions with both high stakes and real financial consequences. Notably, Holt and Laury (2002) find evidence that people’s risk aversion is different when there are real stakes as opposed to hypothetical choices. Further, several studies (Binswanger 1980; Holt and Laury 2002) find that risk aversion increases along with the stakes of a gamble. It is important to stress that the stakes in ‘Deal or No Deal’ are higher than any feasible experiment and almost any other game shows. The mean prize won by contestants is almost US$16,000 with the highest prize being US$105,000.9

‘Deal or No Deal’ also offers contestants very simple, stark choices. Almost all other game shows that have been studied by economists involve some element of skill, whether it be knowledge of trivia, skill in word games or an ability to compute the odds in a game of chance involving cards. The only skill needed in ‘Deal or No Deal’ is the comparison of a gamble with a certain offer: precisely the computational capacity in which economists are interested when studying decision making under uncertainty.

Finally, the format of the Australian version of ‘Deal or No Deal’ (or, more precisely, the existence of the Chance and SuperCase rounds), is ideal for testing framing effects as many contestants face a change of framing in the final round of the game. This feature is not present in other game shows based on lottery choices, and is also not present in other franchises of the ‘Deal or No Deal’ paradigm shown in other countries.

8 Postcodes in Australia are analogous to Zip Codes in the United States.

9 Put another way, to perform this experiment from scratch would have required a total prize

pool of approximately US$1.6 million.

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ii. Limitations The possibility of selection bias in the contestant pool is an issue for this paper, as it is for all studies based upon game show data. The process of selecting the contestant in Stages 1 and 2 is likely to mitigate this problem.

As just explained above, there are two stages in the selection of the contestant. First, 26 people are randomly chosen from the audience. It is not clear that the people who volunteer for quiz show audiences are systematically more risk averse or more risk seeking than the broader population. Arguments might plausibly be made that, for example, they may be more extroverted, on average, than the general population, or that they may have more free time on average. But even if these conjectures are true, there can be no a priori supposition that these qualities are correlated with risk aversion, and certainly there is nothing in the existing literature to suggest that they are.

In the second stage, the 26 people randomly chosen from the audience compete to become the contestant by participating in a very simple trivia quiz in which the emphasis is on speed. There is no reason to think that there is any correlation between reaction time in a simple quiz and risk aversion.

The fact that the contestant is, in effect, randomly chosen from the audience via a two-stage process means that it is simply not possible for the producers of the show to engage in as much vetting of contestants as they would if contestants were chosen directly via an application process.

The artificial environment of the game show could potentially increase or decrease people’s risk aversion. On the one hand, the excitement of being on television, surrounded by lights and a screaming audience could make people more prone to risk taking or to errors of judgement. On the other hand, some people may become more risk averse when in front of a national audience and carefully avoid doing anything embarrassingly foolish. The possibility that these factors are roughly in balance, on average, is consistent with earlier studies of game shows which have found that contestants display levels of risk aversion broadly in line with participants in experimental studies.

IV. EMPIRICAL FINDINGS

A. Baseline analysis ignoring supplementary rounds

To explore our main research questions, we conduct probit regression modelling of the likelihood of accepting a bank offer against a number of factors related to the game and observable agent heterogeneity. Factors which raise the likelihood of accepting bank offers can be said to be covariates of risk aversion. Panel A of Table 2 shows both the chosen regressors and the results for the full dataset comprising Rounds 1–9 of such a probit regression (where the dependent variable is whether or not a Bank Offer is accepted). It is reported as model (1).

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Previous studies have found that risk aversion increases with rising stakes (see Binswanger 1980; Kachelmeier and Shehata 1992; and Holt and Laury 2002). Our results lend support to this. The higher is the Bank Offer relative to the expected value of the remaining suitcases, the more likely a person is to accept. The marginal effect of this ratio is 0.35. We also found a mild scale effect. The higher is the offer, the more likely is a person to accept. The marginal effect of a change in the offer of US$10,000 is 0.04. With respect to observable personal characteristics, only age was statistically significant.10 The model was better at approximating the effects of age when a quadratic, rather than linear, form was used. In unreported results, we also tested a model that included the standard deviation of the remaining prizes and various measures of regret.11 Neither of these variables was statistically significant.12

To check the robustness of our initial finding with respect to gender, we also included it as an interaction dummy. The results are contained in panel A of Table 2 as model (2). We interact gender with the offer and with the ratio of the offer to the expected value of the remaining suitcases. Males are more likely to have increasing risk aversion as the stakes of the gamble rise. They are also less likely than females to accept an offer for a given ratio between the offer and the expected value (i.e. to be less risk averse). The current consensus, in what is a still-developing literature, appears to be that when gender has been found to have a significant effect on the measurement of risk aversion (not all studies show an effect), the effect has been that women are more risk averse than men. Our results fit comfortably into this consensus.13

Panel B of Table 2 shows the hit-miss table for model (2) i.e. the likelihood of model (2) correctly predicting the decision for each observation when considering Rounds 1–9. Of the 728 offers made, 609 were rejected and 119 accepted. Our model correctly predicts 586 of the rejections (96%) and 49 of the acceptances (41%). This represents a 22% improvement over a baseline model that predicts rejection in all rounds. Notably, an alternative benchmark that separately predicts each round individually does no better than the benchmark

10 In supplementary analysis, we experimented with all three proxies for income for which we had

data: household income, family income and personal income. The results for household

income are shown. None of these measures of income was statistically significant.

11 To test regret, we included the ratio of the current Bank Offer to the immediately preceding

Bank Offer and, alternatively, the ratio of the current Bank Offer to the highest previous Bank

Offer made to the contestant. We also tested the difference between the current Bank Offer and

the immediately preceding/highest previous Bank Offer. None of these was statistically

significant. Results are not reported to conserve space.

12 For each of the models tested in the paper, we also estimated results for a panel specification

(fixed effects), grouping each agent’s sequence of decisions. Depending upon which variables

we included and the subset of our sample that we used (i.e. whether we included all rounds or

just Rounds 6–9), we found that the results either reverted to the non-panel specification or that

our estimates of the ratio of the variance of the individual effects to the total variance were not

statistically significant.

13 For a recent survey see Crossen and Gneezy (2004).

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used as there is a 450% chance of accepting in only Rounds 8 and 9 and it is only slightly higher than 50% in those rounds (51% and 52%, respectively).

Rounds 1–5 are relatively uninformative since the Bank Offers are typically set low enough to ensure rejection. Given that there is only one contestant per show, it is necessary for there to be at least five rounds to create a meaningful half an hour TV program. As a consequence, almost all of the interesting choices occur in Rounds 6–9. Accordingly, Table 3 shows the probit results and hit-miss table when the data for estimation is confined to Rounds 6–9. Note that focusing solely on later rounds reduces concern about the assumption of myopic decision-making made in this paper.

Focusing on Rounds 6–9 reduces the sample size to 233. Both the ratio of the Bank Offer to the expected value of the remaining suitcases and the size of the Bank Offer remain statistically significant in model (1) and the ratio is significant in model (2). Age is only statistically significant at the 10% level, which probably reflects the smaller sample size. Gender and income remain statistically insignificant.

The results for model (2) in panel A of Table 3 include interaction dummies with gender for Rounds 6–9. The interaction dummies remain statistically

Table 2 Probit model of accepting the bank offer in the TV game show ‘Deal or No Deal’ – all nine rounds

Panel A: Regression estimates

Model 1 Model 2

Coefficient (z-stat)

Marginal effect

Coefficient (z-stat)

Marginal effect

Constant �1.24 – �1.74n – (�1.66) (�2.56)

OFFER 0.294nn 0.04 0.223nn 0.03 (4.74) (3.31)

RATIO 2.40nn 0.35 2.57nn 0.37 (11.76) (10.94)

MALE �0.01 �0.001 – – (�0.04)

AGE �0.08n �0.01 �0.07 �0.01 (�2.23) (�1.79)

AGE2 0.83 0.12 0.63 0.09 (1.65) (1.23)

HINCOME �0.15 �0.02 – – (�0.43)

MALE�OFFER – – 0.37nn 0.05 (2.79)

MALE�RATIO – – �0.29 �0.04 (�1.46)

Number of Obs 720 728 Pseudo R2 0.371 0.381

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significant (although only at the 10% level for the interaction with the ratio) and once again indicate that males are more likely to become risk averse as the stakes increase but that males are also less likely than females to be swayed by a positive bank offer-expected value ratio.

As shown in panel B of Table 3, model (2) now correctly predicts 55% of acceptances, although the prediction rate for rejections falls to 83%. Overall, the model represents a 33% improvement over the baseline case in Rounds 6–9.

Panel B: Hit-miss tables for model 2

Estimated equation Constant probability

DV50 DV51 Total DV50 DV51 Total

P(DV51)�0.5 586 70 656 609 119 728 P(DV51)40.5 23 49 72 0 0 0 Total 609 119 728 609 119 728 Correct 586 49 635 609 0 609 %Correct 96.22 41.18 87.22 100.00 0.00 83.61 %Incorrect 3.78 58.82 12.78 0.00 100.00 16.39 Total Gain �3.78 41.18 3.61 – – – %Gain – 41.18 22.03 – – –

This table reports the results of two probit regression models of the probability of accepting the bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data used in this analysis are for the complete set of nine normal rounds of the game. Panel A shows the probit regressions results for model 1 – no interaction terms and model 2 – including interaction terms. The dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant and zero otherwise. The independent variables are defined as follows: OFFER is the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value of the gamble; MALE is a dummy variable that takes the value of unity if the contestant is a male; AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s age measured in years2; HINCOME is proxied by the average household income associated with the postcode (analogous to zip code) of the contestant based on data from the 2001 Australian Census. Immediately below each estimated coefficient in parentheses are the associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by 103 to enhance readability. nn and n Statistical significance at the 1% and 5% levels is indicated, respectively. Panel B shows hit-miss tables associated with Model 2 estimates reported in panel A. These contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand side of the panel (‘estimated equation’) the predicted probability of each observation is determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve prediction is made that all observations are equal to the most common case i.e. the offer is not accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified. The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage points and Percent Gain: as a percentage of the incorrect classifications in the constant probability model.

Table 2 (Continued)

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B. Extended analysis incorporating supplementary rounds

One of the most serious challenges to expected utility theory is the potential for preference reversals when the framing of a choice changes. Prospect theory is one example of a framing effect in which individuals will behave differently, depending upon their ‘reference point’. Prospect theory asserts that people will display an asymmetry in their attitude to risk delineated by gains versus losses. Specifically, prospect theory posits that people will generally be risk averse in lottery choices involving gains and risk seeking in lottery choices involving losses. In particular, prospect theory suggests a utility function that is (i) defined on deviations from the reference point (not on overall wealth); (ii) is concave for gains and convex for losses and (iii) is steeper for losses than gains. This results in the well known S-shaped utility function of Kahneman and Tversky (1979) and Tversky and Kahneman (1992).

It was mentioned in the section describing the rules of the game that, even once a contestant has accepted a Bank Offer, the game does not technically end. Rather, the contestant is required to engage in the counter-factual exercise of

Table 3 Probit model of accepting the bank offer in the TV game show ‘Deal or No Deal’ – rounds 6–9

Panel A: Regression estimates

Model 1 Model 2

Coefficient (z-stat)

Marginal effect

Coefficient (z-stat)

Marginal effect

Constant 0.70 – �0.17 – (0.65) (�0.17)

OFFER 0.16n 0.06 0.11 0.04 (2.40) (1.55)

RATIO 1.41nn 0.10 1.61nn 0.63 (5.49) (5.57)

MALE �0.12 �0.05 – – (�0.66)

AGE �0.10 �0.04 �0.09 �0.03 (�1.98) (�1.64)

AGE2 1.16 0.45 0.94 0.37 (1.65) (1.34)

HINCOME �0.42 �0.17 – – (�0.92)

MALE�OFFER – – 0.52nn 0.21 (2.73)

MALE�RATIO – – �0.39 �0.15 (�1.84)

Number of Obs 230 233 Pseudo R2 0.137 0.156

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continuing to remove suitcases from the remaining suitcases until only two remain, at which time the possibility (since this is entirely at the discretion of the producers) of playing a supplementary Chance or SuperCase round arises.

In the chance situation, the Bank Offers the contestant a chance to retract the ‘Deal’ they had accepted in an earlier round. If the contestant accepts the retraction, they swap all winnings from that previously made deal for a lottery. Since the Chance round only ever occurs in Round 9 when just two prize outcomes remain, the Chance round represents a choice between a 55

Panel B: Hit-Miss table for model 2

Estimated equation Constant probability

DV50 DV51 Total DV50 DV51 Total

P(DV51)�0.5 109 45 154 132 101 233 P(DV51)40.5 23 56 79 0 0 0 Total 132 101 233 132 101 233 Correct 109 56 165 132 0 132 %Correct 82.58 55.45 70.82 100.00 0.00 56.67 %Incorrect 17.42 44.55 29.18 0.00 100.00 43.33 Total Gain �17.42 55.45 14.15 – – – %Gain – 55.45 32.66 – – –

This table reports the results of two probit regression models of the probability of accepting the bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data used in this analysis are for rounds six to nine only. Panel A shows the probit regressions results for model 1 – no interaction terms and model 2 – including interaction terms. The dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant and zero otherwise. The independent variables are defined as follows: OFFER is the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value of the gamble; MALE is a dummy variable that takes the value of unity if the contestant is a male; AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s age measured in years2; HINCOME is proxied by the average household income associated with the postcode (analogous to zip code) of the contestant based on data from the 2001 Australian Census. Immediately below each estimated coefficient in parentheses are the associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by 103 to enhance readability. nn and n Statistical significance at the 1% and 5% levels is indicated, respectively. Panel B shows hit-miss tables associated with Model 2 estimates reported in panel A. These contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand side of the panel (‘estimated equation’) the predicted probability of each observation is determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve prediction is made that all observations are equal to the most common case i.e. the offer is not accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified. The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage points and Percent Gain: as a percentage of the incorrect classifications in the constant probability model.

Table 3 (Continued)

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gamble between two prizes versus the amount already won in a previous round when the bank offer had been accepted. It is important to note that the Chance round is only ever offered when the two remaining prizes differ by a large magnitude, highlighting the contrast between the risky and the safe options. For example, in one actual game, the contestant faced a choice between a certain offer of US$15,100 and a gamble between US$10 and US$75,000. The person chose the sure amount of money. Accepting the ‘Chance’ offer is not compulsory. In our sample, the Chance option was offered 20 times, with the mean value of the two cases being US$18,229 compared with the considerably lower mean value of already accepted deals of US$9824. Notwithstanding this, in only seven Chance rounds was the suitcase gamble accepted, suggestive of loss aversion at work.

The SuperCase round is played after all suitcases have been opened. If the contestant elects to take the SuperCase option, they will win whatever cash amount is revealed to be inside the SuperCase, and forfeit their previously struck deal. In each game where it is offered, one of the following cash values will be selected at random, and placed inside the SuperCase: US$0.50; US$100; US$1000; US$2000; US$5000; US$10,000; US$20,000 or US$30,000. The mean and standard deviation of the SuperCase option are US$8510 and US$11,000, respectively. In our sample, the SuperCase was offered 24 times, with the contestants having previously accepted deals ranging from US$2100 to US$17,800. The mean of previously accepted deals was US$8750. For example, in one game, the contestant had previously accepted a Deal of US$6350. After all suitcases had been revealed, the contestant was offered the SuperCase option. The contestant accepted, and won US$20,000. In only eight SuperCase rounds was the SuperCase chosen.

It can be seen from this description of the two supplementary rounds that they involve a change in the framing of the choice faced by the contestant. On the one hand, in Rounds 1–9, the contestant chooses whether or not to swap his/her right to a lottery for a sure amount of money. The choices involve only possible gains, not possible losses. The contestant ‘owns’ the right to keep removing suitcases until only the suitcase initially nominated remains and to receive Bank Offers after each round of this process. Each time a Bank Offer is made, the contestant is being asked to sell this lottery. On the other hand, in the Chance and SuperCase rounds, the choice is reversed, and the possibility of making a loss is introduced. Specifically, the contestant has already accepted a Deal and is being asked to swap his/her sure winnings for a gamble. In other words, the contestant is now being asked to buy a new lottery. If the contestant’s current winnings become the new reference point (as suggested by prospect theory), then accepting either the Chance or SuperCase deals will mean accepting a positive probability of suffering a loss relative to the reference point and a positive probability of enjoying a gain relative to the reference point. Specifically, consider the Chance round in which a person will face a choice between the two remaining suitcases or a sure amount of money. Thus, in the Chance round, the contestant chooses between a 50–50 chance of losing

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or gaining relative to the reference position or status quo. A person with an S-shaped utility function which is steeper for losses than gains will be less likely to accept a Chance (or SuperCase) round gamble.

To explore the issue of loss aversion, we again re-estimate the probit regression but this time include the impact of the Chance and SuperCase rounds on the willingness of a contestant to accept an offer. While the offer is usually the Bank Offer, in the Chance and SuperCase rounds, the offer represents the status quo. The results of this new probit regression are shown in Table 4.

Panel A of Table 4 contains the results of a Probit for Rounds 1–9 that includes dummies for whether the decision is made during a Chance or SuperCase round. A further variable, ‘high cases remaining’ is also included. The highcase variable is the proportion of remaining suitcases that are higher than that round’s Bank Offer. We include it to capture the possible heuristic

Table 4 Probit model of accepting the bank offer in the TV game show ‘Deal or No Deal’ incorporating the chance and SuperCase rounds – all nine rounds

Panel A: Regression estimates

Coefficient (z-stat) Marginal effect

Constant �1.69n – (�2.16)

OFFER 0.375nn 0.04 (4.42)

RATIO 3.13nn 0.31 (9.91)

CHANCE 2.77nn 0.81 (5.37)

SUPERCASE 4.07nn 0.95 (4.19)

HIGHCASE �2.56nn �0.25 (�2.86)

AGE �0.08 �0.01 (�1.78)

AGE2 0.70 0.07 (1.20)

MALE�OFFER 0.274 0.03 (1.81)

MALE�RATIO �0.65n �0.06 (�2.04)

MALE�CHANCE �1.63n �0.05 (�2.41)

MALE�SUPERCASE �1.97 �0.05 (�1.65)

MALE�HIGHCASE 1.77 0.18 (1.76)

Number of Obs 728 Pseudo R2 0.485

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behavior by contestants – that the contestant takes account of how many remaining suitcases are above the Bank Offer for that round.

The Chance and SuperCase dummy variables and the highcase variable are all statistically significant at the 1% level. Further, the Chance and SuperCase dummies have a high marginal effect. Males are less likely to accept the Bank Offer in the Chance and SuperCase rounds (i.e. they are more likely to take the

Panel B: Hit-miss table

Estimated Equation Constant probability

DV50 DV51 Total DV50 DV51 Total

P(DV51)�0.5 586 59 645 609 119 728 P(DV51)40.5 23 60 83 0 0 0 Total 609 119 728 609 118 728 Correct 586 60 646 609 0 609 %Correct 96.22 50.42 88.74 100.00 0.00 83.61 %Incorrect 3.78 49.58 11.26 0.00 100.00 16.39 Total Gain �3.78 50.42 5.13 – – – %Gain – 50.42 31.30 – – –

This table reports the results of a probit regression model of the probability of accepting the bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data used in this analysis incorporates all nine normal rounds of the game, as well as the supplementary ‘Chance’ and ‘SuperCase’ rounds. Panel A shows the probit regressions results. The dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant (or, in the case of the Chance and SuperCase rounds, the contestant opts for the previously accepted Bank Offer) and zero otherwise. The independent variables are defined as follows: OFFER is the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value of the gamble; CHANCE is a dummy variable that takes the value of unity if the round is a chance round; SUPERCASE is a dummy variable that takes the value of unity if the round is a SuperCase round; HIGHCASE is the proportion of remaining suitcases that are higher than that of the bank’s current offer; AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s age measured in years2; MALE is a dummy variable that takes the value of unity if the contestant is a male. Immediately below each estimated coefficient in parentheses are the associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by 103 to enhance readability. nn and n Statistical significance at the 1% and 5% levels is indicated, respectively. Panel B shows hit-miss tables associated with the model estimates reported in panel A. These contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand side of the panel (‘estimated equation’) the predicted probability of each observation is determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve prediction is made that all observations are equal to the most common case i.e. the offer is not accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified. The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage points and Percent Gain: as a percentage of the incorrect classifications in the constant probability model.

Table 4 (Continued)

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gamble by giving up their already won prize) and are also less likely to be affected by the high case rule of thumb. The statistical significance and high marginal effect of the dummies for the Chance and SuperCase rounds in these probit regressions is suggestive of a reference point switching explanation for any greater reluctance to accept risk in the Chance or SuperCase rounds compared with the scenario faced in earlier rounds.

Panel B of Table 4 repeats the earlier exercise of comparing the predictive power of the model against the benchmark. The model performs considerably better than the model in the previous section, correctly predicting 50% of acceptances and representing an overall 31% improvement on the benchmark model.

Table 5 tests the same model as outlined in Table 4, but using data only from Rounds 6 to 9. As discussed, almost all of the difficult choices faced by

Table 5 Probit model of accepting the bank offer in the TV game show ‘Deal or No Deal’ incorporating the chance and SuperCase rounds – Rounds 6–9

Panel A: Regression estimates

Coefficient (z-stat) Marginal effect

Constant �0.80 – (�0.76)

OFFER 0.247nn 0.01 (2.85)

RATIO 2.32nn 0.92 (6.08)

CHANCE 2.17nn 0.60 (4.17)

SUPERCASE 3.01nn 0.66 (3.02)

HIGHCASE �2.06n �0.81 (�2.12)

AGE �0.08 �0.03 (�1.34)

AGE2 0.78 0.31 (1.02)

MALE�OFFER 0.419n 0.17 (2.04)

MALE�RATIO �0.69n �0.27 (�2.01)

MALE�CHANCE �1.59n �0.42 (�2.36)

MALE�SUPERCASE �1.78 �0.44 (�1.44)

MALE�HIGHCASE 1.64 0.64 (1.50)

Number of Obs 233 Pseudo R2 0.256

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contestants are in Rounds 6–9. Once again, most variables are statistically significant at the 1% level and the Chance and SuperCase dummies have a high marginal effect. Once more, the highcase variable is statistically significant and, as expected, its marginal effect is much higher for these later rounds than it was for the entire sample. Despite a small loss of accuracy on the rejections, we see a 44% overall improvement on the benchmark.

Panel B: Hit-miss table

Estimated equation Constant probability

DV50 DV51 Total DV50 DV51 Total

P(DV51)�0.5 111 21 132 132 101 233 P(DV51)40.5 36 65 101 0 0 0 Total 147 86 233 132 101 233 Correct 111 65 176 132 0 132 %Correct 75.51 75.58 75.54 100.00 0.00 56.67 %Incorrect 24.49 24.42 24.46 0.00 100.00 43.33 Total Gain �24.49 75.58 18.87 – – – %Gain – 75.58 43.55 – – –

This table reports the results of a probit regression model of the probability of accepting the bank offer in a given round of the Australian version of the TV game show ‘Deal or No Deal’. The data used in this analysis incorporates data for rounds six to nine, as well as the supplementary ‘Chance’ and ‘SuperCase’ rounds. Panel A shows the probit regressions results. The dependent variable (DV) takes a value of unity if the bank offer is accepted by the contestant (or, in the case of the Chance and SuperCase rounds, the contestant opts for the previously accepted Bank Offer) and zero otherwise. The independent variables are defined as follows: OFFER is the value of the bank offer measured in US$10,000 units; RATIO is the ratio of the bank offer to the expected value of the gamble; CHANCE is a dummy variable that takes the value of unity if the round is a chance round; SUPERCASE is a dummy variable that takes the value of unity if the round is a SuperCase round; HIGHCASE is the proportion of remaining suitcases that are higher than that of the bank’s current offer; AGE is the contestant’s age measured in years; AGE2 is the square of the contestant’s age measured in years2; MALE is a dummy variable that takes the value of unity if the contestant is a male. Immediately below each estimated coefficient in parentheses are the associated z-statistics. The reported coefficient on and marginal effect of AGE2 are both scaled by 103 to enhance readability. nn and n Statistical significance at the 1% and 5% levels is indicated, respectively. Panel B shows hit-miss tables associated with the model estimates reported in panel A. These contingency tables show a 2�2 scheme of correct and incorrect classifications. In the left hand side of the panel (‘estimated equation’) the predicted probability of each observation is determined relative to a 0.5 probability cut-off value. In this case a correct classification occurs when the predicted probability �0.5 (40.5) coincides with an actual value for the dependent variable equal to 0 (1). In the right hand side of the panel (‘constant probability’) a naı̈ve prediction is made that all observations are equal to the most common case i.e. the offer is not accepted (DV50). In this case all DV50 (DV51) observations are correctly (incorrectly) classified. The ‘predictive ability’ of the model is gauged by a measure of the gain achieved from applying the probit specification relative to the naı̈ve case, and is recorded as the Total Gain: in percentage points and Percent Gain: as a percentage of the incorrect classifications in the constant probability model.

Table 5 (Continued)

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V. CONCLUSION

In this paper, we analyze a simple lottery-choice setting within the Australian version of the TV game show, ‘Deal or No Deal’, that allows us to explore a range of issues related to risk aversion in the context of both very high and wide- ranging (possible) payoffs. Notably, a feature of the game is especially convenient for testing non-expected utility theories relating to the effects of changes in reference points.

The main findings of our analysis are easily summarized. First, we generally observe that as the stakes of this lottery game increase, so to does the degree of risk aversion (similar to Holt and Laury 2002). Having said that however, we observe considerable heterogeneity in people’s willingness to bear risk – indeed, a sizeable proportion of contestants in our sample appear to be risk-loving. Moreover, such risk loving behavior is sometimes evident with decisions involving very high stakes. We also find heterogeneity with respect to observable agent characteristics, with age and gender being statistically significant determinants of risk aversion, while wealth is not.

Second, we are able to exploit a special feature of the game show that sometimes appears at the final decision-stage and which reverses the choice faced by contestants up till that time. Specifically, instead of being offered a sure-thing in exchange for a lottery, contestants who are entitled to end the show with money already secured, are offered a lottery in exchange for that sure-thing. In this context, we find that the reversal of framing has a significant impact on people’s willingness to bear risk, and that their high level of risk aversion during the Chance and SuperCase rounds is consistent with the existence of framing effects.

Robert Faff Department of Accounting and Finance Faculty of Business and Economics Monash University Victoria 3800 Australia [email protected]

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APPENDIX A

Table A1 Schedule of prizes in ‘Deal or No Deal’ TV game show

US$0.50 US$1000 US$1 US$1500 US$2 US$2000 US$5 US$3000 US$10 US$5000 US$25 US$7500 US$50 US$10,000 US$75 US$15,000 US$100 US$25,000n

US$150 US$50,000 US$250 US$75,000 US$500 US$100,000 US$750 US$200,000

nIn 41 of the 102 episodes of the game show for which we have data, a new car was substituted as the prize in place of the US$25,000 amount. The car was worth approximately US$25,000 and, therefore, for convenience, we used the monetary value of US$25,000 for that suitcase in all instances.

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APPENDIX B

Table B1 Characterization of the rounds of play in the ‘Deal or No Deal’ TV game show

Round #

# of beginning

cases

# of cases

removed

# of ending cases

Bank offer

Decision Outcome

1 26 6 20 US$BO1 Reject Play next round Accept Take US$BO1 (denote as

US$WIN)1

2 20 5 15 US$BO2 Reject Play next round Accept Take US$BO2 (US$WIN)1

3 15 4 11 US$BO3 Reject Play next round Accept Take US$BO3 (US$WIN)1

4 11 3 8 US$BO4 Reject Play next round Accept Take US$BO4 (US$WIN)1

5 8 2 6 US$BO5 Reject Play next round Accept Take US$BO5 (US$WIN)1

6 6 1 5 US$BO6 Reject Play next round Accept Take US$BO6 (US$WIN)1

7 5 1 4 US$BO7 Reject Play next round Accept Take US$BO7 (US$WIN)1

8 4 1 3 US$BO8 Reject Play next round Accept Take US$BO8 (US$WIN)1

9 3 1 2 US$BO9 Reject Win US$prize in own case (US$WIN)1

Accept Take US$BO9 (US$WIN)1

Chance2 – – – Lottery: Case A or

Reject Retain US$WIN

Case B Accept Win US$A or US$B Super- Case3

– – – Lottery: SC1 or SC2 or SC3 or SC4 or . . . SC8

Reject Retain US$WIN

Accept Win US$0.50 or US$100 or US$1000 or . . . . US$30,000

1This may not be the final outcome of the game – the contestant may be invited to partake in the Chance or SuperCase round, after Round #9. 2In the Chance round the bank offers the (uncertain) lottery choice involving the two cases remaining in Round #9: Case A or Case B. 3In the SuperCase round the bank offers the (uncertain) lottery choice involving eight different super case values – denoted SC1, SC2, . . ., SC8. The possible values contained in the super case are: US$0.50; US$100; US$1000; US$2000; US$5000; US$10,000; US$20,000 and US$30,000.

Deal or No Deal, That is the Question

r 2009 The Authors Journal compilation r International Review of Finance Ltd. 2009 49

APPENDIX C

Table C1 Illustration of the rounds of play in an actual episode of the ‘Deal or No Deal’ TV game show

Round #

# of beg cases

Cases removed # of end cases

Bank offer

Decision Outcome

1 26 6 cases: US$75,000; US$750; US$50; US$25; US$25,000; US$50,000

20 US$9100 Reject Play next round

2 20 5 cases: US$200,000; US$0.50; US$2; US$3,000; US$100

15 US$3800 Reject Play next round

3 15 4 cases: US$500; US$5; US$1000; US$10

11 US$6910 Reject Play next round

4 11 3 cases: US$2000; US$1; US$250

8 US$8450 Reject Play next round

5 8 2 cases: US$7500; US$15,000

6 US$7400 Reject Play next round

6 6 US$10,000 5 US$9900 Reject Play next round

7 5 US$75 4 US$12,250 Reject Play next round

8 4 US$150 3 US$17,700 Accept Take US$11,400

9 3 US$1500 2 NA NA NA Chance – – – Lottery:

US$5000 or US$100,000

Accept Win US$100,000

International Review of Finance

r 2009 The Authors Journal compilation r International Review of Finance Ltd. 200950