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Taking the temperature of the Columbia Card Task

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Taking the temperature of the Columbia Card Task

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Content Taking the Temperature of the Columbia Card Task
by
Kevin Kapadia
A Thesis Presented to the
FACULTY OF THE USC DORNSIFE COLLEGE OF LETTERS, ARTS, AND SCIENCES
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF ARTS
PSYCHOLOGY
May 2024
Copyright 2024 Kevin Kapadia

ii
TABLE OF CONTENTS
List of Tables……………..…………………………………………………………............……iv
List of Figures…………..…………...……………………………………………………….....…v
Abstract………………..……...…………………………………………………………………..vi
Introduction………..……………...……………………………………………….……..……..…1
Chapter One: Background…………...………………….…………………….……….…..……....3
Individual CCT Versions and Their Relationship to Outcome Variables…….…...….......3
General CCT Relationship to Outcome Variables………….………………..…….....…...4
Designs of CCT…………………………………………………………...…...…..……....4
Loss Card Position ………………………………………………..………….…...…........6
Research Questions and Hypotheses…………………………….…………..….....……...7
Chapter Two: Methods……………..…...…………………………………….………..…..…..10
Design Overview..…….…….…………………………………………….…………..…10
Participants……………………………..………………………………….…………..…10
Procedure………….………………….………………………………...……………..…12
CCT Versions…..…………………..……………………………………..…………..…12
Chapter Three: Results……………………....…..…………………………….………..……..…15
Overview of Analysis……………………...…………………………….…………....…15
General Participant Performance…………..…………………………….………..…..…15
Number of Cards Revealed………………...…………………………….…..………..…18
Loss Card Performance……………….…………………..…………….……………..…32

iii
Toasty Version Compared to Hot and Warm Versions ………………………..……..…35
Chapter Four: Discussion…………………….....……….…………………….………..……..…36
General Participant Performance…..…………………………………….……..……..…36
Number or Percent of Possible Cards Revealed……………………………..………..…36
Incentives…………………………………………………………….....……………..…37
Game Parameters………………………………………………..……….……..……..…38
Repetition of Game Parameters………………………………………….………..…..…38
Randomly Placed Loss Cards……………………………...…………….…………....…39
Toasty Version………………………………………..………………….………..…..…40
Limitations and Future Considerations…………….…………………….……..……..…40
Conclusions……………………………………...……………………….…………....…41
References…………………...…………………………………………………………..….....…42
Appendices……………………........………….…………………………………………………45
Appendix A: Parameter Combinations by Round………………....…………..………...45

iv
List of Tables
Table 1. Sample Demographic Information by Incentive Condition ……….....………………...10
Table 2. Optimal Number of Cards to Reveal by Parameters………………....………...….....…13
Table 3. Median Minutes (Interquartile Range) to complete CCT….…………….……….....…14
Table 4. Mean Total Scores over 24 Rounds ……………………….…………………..……….15
Table 5. Average Deviation Score……….................................................................................…16
Table 6. Cards Revealed by Version and Condition………......................................................…18
Table 7. Summary of ANOVA for Number of Cards Revealed…….………………..…….....…20
Table 8. Summary of ANOVA on Percentage of Possible Cards Revealed……….……….....…22
Table 9. Regression Coefficients for Cards Revealed by Round Number……………...….....…31
Table 10. Pairwise t-tests Comparing Mean Cards Revealed …………….…………………..…33

v
List of Figures
Figure 1. Interaction Between Version and Incentive Condition ……………………………….23
Figure 2. Interaction Between Version and Gain Amount……………….……………..……….24
Figure 3. Interaction Between Version and Loss Amount……………..………………..……….26
Figure 4. Interaction Between Version and Number of Loss Cards……………………………..27
Figure 5. Interaction Between Version and Repetition…………………………...……..……….28
Figure 6. Cards Revealed by Round Number in the Non-incentivized Condition………………29
Figure 7. Cards Revealed by Round Number in the Incentivized Condition……………………30
Figure 8. Mean Number of Loss Cards Revealed…………………………………….....……….32

vi
Abstract
The Columbia Card Task (CCT) is a behavioral measure of risk taking (BMRT), which has
been cited over 500 times (Google Scholar, 3/1/2024), and has seen widespread use since 2004
(Figner & Weber, 2011; Figner & Voelki, 2004). The original game had two versions (Hot and
Cold) measuring affective and deliberative decision making respectively. Each version included
54 scored rounds where the loss cards were placed at the end and nine unscored rounds where the
loss cards were placed randomly among the gain cards. Over time, the CCT has gone through
many iterations on critical components, such as the number of rounds, position of the loss cards,
and introduction of a new version (Warm). Despite this, there are several issues with the CCT,
notably a lack of convergent validity with other measures of risk taking. This paper reviews the
different iterations of the CCT, introduces a new (Toasty) version of the CCT that is a hybrid of
the hot and warm versions, explores the consequences of randomly placing the loss cards among
the gain cards consistent with instructions provided to participants, and examines the impact of
incentivizing participants based on their score. Results (N = 405) show that a new Toasty version
behaves similarly to the Warm but provides additional insights into risk taking behavior. When
loss cards are placed randomly, participants are still sensitive to the parameters of the game (gain
amount, loss amount, and number of loss cards), participants reveal the loss cards roughly half of
the time, and participants do not change the number of cards they reveal on rounds after they did
or did not reveal a loss card. Incentivizing participants in our study had no impact on the number
of cards revealed.
Keywords: behavioral measure of risk taking, incentives, sequential decision making, deliberative
decision making, affective decision making, deception, CCT

1
Taking the Temperature of the Columbia Card Task
The Columbia Card Task (CCT) is a prominent behavioral measure of risk taking (BMRT)
developed to mimic the parameters decision makers use in real life: possible gain amounts,
possible loss amounts, and probabilities of possible gains and losses (Figner & Voelki, 2004). Each
round of the CCT begins by providing the player with full information regarding the value of the
gain cards, the number of loss cards (out of 32), and the cost of revealing a loss card. Players decide
how many cards to reveal and are awarded the value of each gain card revealed until a loss card is
revealed. The round ends when the player chooses to stop and not reveal more cards or when a
loss card is revealed. The player is awarded the value of a gain card times the number of gain cards
revealed minus the value of a loss card if the round ended by revealing a loss card. The number of
cards revealed by the player is treated as a behavioral indicator of risk taking.
Originally, there were two versions of the game: Hot and Cold. In the Hot version, players
revealed one card at a time and received feedback immediately. However, to know how many
cards participants wanted to reveal, the loss cards were placed at the end, deceiving the
participants. This tactic provides the player with inaccurate feedback inconsistent with game
properties. In the Cold version, players chose the number of cards they would like to reveal based
on the round parameters and received no feedback until all rounds were completed. In contrast to
the Hot version, which measures affective (emotional) decision making, the Cold version measures
deliberative decision making and is unaffected by the loss cards' position.
Later, a hybrid version of the Hot and Cold called the Warm version was created in which
players choose the number of cards to reveal at the beginning of the round (similar to the Cold)

2
but also receive feedback at the end of the round (Huang et al., 2013). This modification solved
the problem of placing the loss cards at the end but did not allow participants to make card-bycard decisions as in the Hot version. However, the cards were still revealed one-by-one, providing
emotional suspense similar to the Hot version. Our study introduces the Toasty version, which is
identical to the Warm version, except that participants can continue to reveal cards after choosing
the initial number to reveal, maintaining the option to make multiple decisions in each round to
reveal cards as in the Hot version.
Since there is no reason to place the loss cards at the end in the Cold and Warm versions,
researchers have placed them randomly among the gain cards more frequently in recent years
(Dijkstra et al., 2022). However, there are no studies comparing all CCT versions when the loss
cards are placed randomly. In this paper, we review the evolution of the CCT and its various
versions, introduce a new version of the CCT called the Toasty version, explore the influence of
placing the loss cards randomly, and analyze the effects of incentivizing players based on their
score.

3
Chapter One: Background
Individual CCT Versions and Their Relationship to Outcome Variables
The original version of the CCT contained a Hot and a Cold version to measure deliberative
and affective decision making. In the Cold version, players chose the number of cards they would
like to reveal based on the game parameters and received no feedback until all rounds were
completed. In the Hot version, players revealed one card at a time and received feedback
immediately. According to the dual-system explanations of risk taking, decision making can either
be a deliberative thought process that evaluates the pros and cons before performing a decision
(Shafir et al., 1993) or an affective emotion-dominated decision-making process (Damasio, 1994;
Seguin et al., 2007).
For instance, a contributing factor to adolescents making risky decisions is an imbalance
between brain systems, in which the part of the brain responsible for affective decision making
tends to override the deliberative process (Casey et al., 2008; Steinberg, 2008). Figner et al. (2009)
showed that adolescents tend to take more risks when playing the Hot version but not the Cold
version, emphasizing the affective thinking pathway involved in the player’s mind. This study and
other studies (Holper & Murphy, 2014; Groot & Strien, 2019) all emphasize that the Hot version
primarily triggers affective decision-making strategies, whereas the Cold version primarily
triggers deliberative decision-making strategies. The Warm version was created to avoid
underestimating risk tolerance by randomly placing loss cards in the Hot version (Huang et al.,
2013). Recently, this version has gained popularity because it combines the advantages of both the
Cold and Hot versions into a single risk taking measure (Dijkstra et al., 2022).

4
General CCT Relationship to Outcome Variables
As a behavioral measure of risk taking, the CCT has many advantages. Unlike most other
current BMRTs, and as discussed previously, the CCT has different versions that measure an
individual’s risk taking pathways through different processes. In addition to multiple versions
specific to deliberative and affective decision making, the CCT can vary the game's risk properties
via the three parameters provided to the players (gain amount, loss amount, and the number of loss
cards). The structure of the CCT allows players to make judgments based on complete information
about the risk of each round, in contrast to ambiguous decision-making tasks such as the Balloon
Analog Risk Task (BART)) and the Iowa Gambling Task (IGT). The CCT design also enables the
researcher to distinguish how, when, and whether the game's components affect decision-making
(Figner & Weber, 2011; Groot & Strien, 2019).
The CCT is also correlated with certain personality traits. For instance, according to
Penolaszzi (2012), individuals with a high reward responsiveness trait exhibited sensitivity to
changes in gains and losses during the Hot version of the task. Other studies have shown CCT’s
correlation with impulsive sensation seeking, executive functions, behavior inhibition and
activation systems, age, temperature, narcissism, and alcohol use (Buelow, 2015; Brunell &
Buelow, 2017; Figner et al., 2009; Figner & Weber, 2011; Laliberte & Grekin, 2015). However,
the CCT has a low to moderate correlation with other risk taking measures (Buelow, 2015;
Markiewicz et al., 2020).
Designs of CCT
Early implementations of the CTT had 63 rounds, including all combinations of gain
amounts (10, 20, 30), loss amounts (250, 500, 750), and number of loss cards (1, 2, 3) to create a

5
3x3x3 design. All 27 combinations were repeated twice for a total of 54 scored rounds. In these
scored rounds, the loss cards were always placed at the end so researchers could determine how
many cards each participant wanted to reveal in a given round. The other nine rounds were not
scored, and the loss card was placed at an early position to diminish the chances of players learning
of the deception that the CCT deck was stacked with loss cards placed at the end.
Researchers have introduced a shortened version of CCT using only the maximum and
minimum value of each of the three game parameters in the original version (Penolazzi et al., 2012;
Huang et al., 2013; Panno et al., 2013; Pripfl et al., 2013; Holper & Murphy, 2014; Buelow, 2015;
Brunell & Buelow, 2017; Schumpe et al., 2017). In the shortened version, each round has a
combination of gain amounts (10 or 30), loss amounts (250 or 750), and some number of loss cards
(1 or 3) to create a 2x2x2 design. Traditionally, this design is repeated three times, resulting in 24
rounds, but researchers have repeated it anywhere from 2 to 6 times, resulting in 16 to 48 rounds
(Groot & Strien, 2019; Dijkstra et al., 2020).
Most of these 2x2x2 designs were conducted without any unscored rounds (Huang et al.,
2013; Panno et al., 2013; Chen et al., 2020; Dijkstra et al., 2022; de Groot & van Strien, 2019;
Buelow, 2015; Holper & Murphy, 2014; Pripfl et al., 2013). In contrast, some researchers chose
to run the study with unscored rounds (Markiewicz et al., 2015a; Markiewicz et al., 2015b; Dijkstra
et al., 2020; Figner et al., 2009a; Markiewicz et al., 2020; Figner et al., 2009b). One explanation
for this difference, discussed later, is the default settings of the platform many researchers use to
administer the CCT. Other studies have used different combinations of parameters in unique ways,
but the two most common designs are the 3x3x3 and 2x2x2 described above (Markiewicz &
Kubińska, 2015; Markiewicz et al., 2020).

6
Loss Card Position
In Figner’s original paper (Figner & Voelki, 2004), they explain that the loss cards were
placed at the end so the measure of risk taking (number of cards chosen) in the Hot version would
not be truncated. However, this decision has not been unanimously adopted by other researchers.
Many studies have placed the loss cards randomly among the gain cards, consistent with the
instructions provided to players (Dijkstra et al., 2022; Kluwe-Schiavon et al., 2015; Holper &
Murphy, 2014; Pripfl et al., 2013; Jamieson et al., 2012; de Groot & van Strien, 2019; Dijkstra et
al., 2022; Chen et al., 2020). Since this truncates the results of the Hot version, researchers have
taken different approaches to mediate this issue. Dijkstra and colleagues (2022) placed the loss
cards throughout to create a model to estimate the number of cards participants would have
revealed in the Hot version had their results not been cut short.
Other researchers, de Groot & van Strien (2019), only used the rounds where participants
did not reveal a loss card. However, this approach is particularly troublesome because it biases the
presented data since, on average, the excluded rounds will have more cards revealed than the not
excluded rounds (Huang et al., 2013). The remaining studies reported the truncated results for the
Hot version (Kluwe-Schiavon et al., 2015; Holper & Murphy, 2014; Pripfl et al., 2013; Jamieson
et al., 2012; Dijkstra et al., 2022; Chen et al., 2020). Only two of these papers report the average
number of cards revealed for the truncated Hot version (Kluwe-Schiavon et al., 2015; Chen et al.,
2020)). Other studies placed the loss cards at the end with the use of unscored rounds to mitigate
player suspicions that the CCT deck was stacked (Markiewicz & Kubińska, 2015; Markiewicz et
al., 2020; Figner et al., 2009; Markiewicz et al., 2015).

7
One possible explanation for placing the loss cards at the end vs. randomly appears to be
the default settings of the software used to administer the CCT. The E-prime software (Chen et al.,
2020; Dijkstra et al., 2022) and “columbiacardtask.org” (not available at this time) (Huang et al.,
2013) both place the loss cards randomly. The Inquisit software places them at the end
(Markiewicz & Kubińska, 2015; Markiewicz et al., 2020; Markiewicz et al., 2015).
Research Questions and Hypotheses
In order to explore differences between and within the CCT versions, we pose several
empirical questions. Questions 1 - 3 address which features of the CCT design influence the
number and percent of possible cards revealed. Question 4 entails analysis regarding participant
performance related to loss cards. Question 6 is exploratory regarding the new Toasty version. We
also report information related to the completion time, final score, number of loss cards revealed,
and cards revealed relative to the optimal between each version to elicit a better understanding of
participant performance between each version.
An essential aspect of this study is that the loss cards were placed consistent with
instructions provided to participants. As described in the background, there is no consensus on
whether deceiving participants by placing all loss cards at the end is necessary. Furthermore, the
deception provides false feedback and participants who “learn” loss cards are hard to reveal will
reveal more cards in later rounds. This provides an overall bias to the number of cards revealed
and confounds the construct of risk taking with learning. If deception is not necessary (participants
are sensitive to the same features) it would not be justified under the IRB common rule. This study
aims to present the results of honest CCT designs and whether participants are still sensitive to the
same features as the original version.

8
Q1: How does the CCT version, whether participants are incentivized or not, and the
interaction between the two impact the number and percent of possible cards revealed?
H1: We hypothesize that participants will reveal fewer cards in the incentivized condition
and that this will be dependent on the CCT version. Specifically, the effect will be stronger in
versions with feedback than without because participants will not realize they are taking more
cards than optimal.
Q2: How do the game parameters (gain amount, loss amount, number of loss cards), the
CCT version, and the interaction between the game version and each game parameter impact the
number and percent of possible cards revealed?
H2: We hypothesize that participants will reveal more cards when the gain amount
increases, the loss amount decreases, and the number of loss cards decreases. We also hypothesize
that these effects will depend on the CCT version. Specifically, versions that rely on more
deliberative decision making processes will show a stronger effect compared to versions that rely
on more affective processes because participants will pay more attention to the round parameters.
Q3: How do the CCT version, repetitions of parameter combination, and the interaction
between the two impact the number and percent of possible cards revealed?
H3: We hypothesize that the number of cards revealed will decrease each time a parameter
combination is repeated, and these effects will depend on the CCT version. Specifically, this effect
will be stronger in versions with feedback than without because participants will realize they are
taking more cards than optimal.

9
Q4: How does the number of cards revealed change on rounds after participants revealed
a loss card or did not?
H4: We hypothesize that participants will reveal fewer cards on rounds following a round
where they revealed a loss card because their affective decision making processes will lead to more
conservative play following a loss.
Q5: Does the new Toasty version result in a unique measure of risk taking, or do
participants play the new Toasty version similar to either the Warm or Hot version of the CCT?

10
Chapter 2: Methods
Design Overview
Data for this study was collected in a mixed 4x2 between and 3x2x2x2 within-subject
design. The between-design consisted of 4 CCT versions (Cold, Hot, Warm, and Toasty) and two
incentive conditions (incentivized and non-incentivized) for each CCT version. Each subject then
played 24 rounds of the CCT with the lowest and highest values for gain amount (10 or 30), loss
amount (250 or 750), and number of loss cards (1 or 3) crossed and repeated three times for a
3x2x2x2 within-subject design.
Participants
Data for all samples was collected on Prolific, a well-validated (Douglas et al., 2023)
source of online participants for behavioral research. All participants were based in the United
States and self-reported to be fluent in English. Participants in both incentive conditions were paid
at a fixed rate depending on which version they took. The fixed rate was calculated from pretesting
data to compensate participants at a rate of $12 per hour, giving them generous time to finish.
Participants who completed the Cold version received $2.00, participants who completed the Hot
version received $2.25, and participants who completed the Warm or Toasty version received
$2.50. Non-incentivized participants received only the fixed payment, whereas incentivized
participants also received a bonus of $1 for every 100 points they scored. Participants received no
bonus if their score was negative and were not penalized. The median bonus received was $5.85,
and the maximum bonus received was $20.60. If participants played each round optimally, their
expected bonus would be $26.10. Participants played only one version, either incentivized or not.

11
Table 1 displays demographic information indicating that the samples for the two incentive
conditions are comparable.
Table 1
Sample Demographic Information by Incentive Condition
Non-Incentivized Incentivized
Sample Size N 198 207
Gender Female
Male
Other
53.37%
44.38%
2.25%
47.54%
49.18%
3.28%
Race Caucasian
Asian or Pacific
Islander
Black or African
American
Other
71.67%
8.33%
8.89%
11.11%
77.22%
10.56%
7.77%
4.44%
Ethnicity Latino/a or Hispanic 9.44% 6.52%
Age Mean Age in Years
(SD)
37.16 (12.64) 36.29 (12.49)

12
Procedure
The procedure for all samples was identical. All participants were recruited through
Prolific, and no identifiable information was recorded. The University IRB approved the study as
Exempt. Participants began the survey by completing their demographic information and were
then directed to a link to download the CCT through the program Inquisit (Version 6). The Inquisit
software allows researchers to choose and edit hundreds of popular psychological tests and
interventions. Our Inquisit code was modified to place the loss cards randomly among the gain
cards. Participants were assigned to one of the four versions of the CCT and either an incentivized
or non-incentivized condition. Each version of the CCT is described in a later section. Upon
completing the CCT, participants entered a completion code in Qualtrics and completed openended feedback questions.
CCT Versions
Four different versions of the CCT were compared in the study. In the Cold version,
participants made only one decision each round: the number of cards they wanted to reveal. They
selected a number at the top of the screen from 0 to 32 and then proceeded to the next round
without any feedback. Their decision of how many cards to reveal is based only on the gain
amount, loss amount, and number of loss cards. In the Hot version, participants made multiple
decisions because they decided whether to reveal another card after every card they received
feedback. In the Warm version, participants select how many cards they wish to reveal by clicking
on them and then receive feedback on those cards one by one. In the Toasty version, participants
clicked on the number of cards they wanted to reveal and then saw the feedback for those cards
one-by-one. They can then continue to reveal cards or end the round. The Hot and Warm versions

13
can be considered extreme cases of the Toasty version. A player who commits to reveal only one
card at a time in the Toasty version would play the same way as in the Hot version. Likewise, a
player who reveals only the cards committed at the beginning of the round would be playing the
same way as in the Warm version.
In all four versions, participants were provided the gain amount, loss amount, and number
of loss cards for each round. In all versions except the Cold, participants received feedback by the
end of the round. For our study, a 2x2x2 design was employed with 10 or 30 gain points, 250 or
750 loss points, and one or three loss cards. This 8-round block was then repeated three times for
a total of 24 rounds. The parameters within each 8-round block were randomized but were the
same for all four versions. For example, for all versions, the first round had a gain amount of 30,
a loss amount of 250, and one loss card. The position of the loss card(s) was randomized within
each round. The parameter combinations and the optimal number of cards to reveal for each
parameter combination are presented in Table 2. The complete list of parameter combinations by
round is displayed in Table A.1.

14
Table 2
Optimal Number of Cards to Reveal by Parameters
1 Loss Card 10 Gain Amount 30 Gain Amount
250 Loss Amount 6 23
750 Loss Amount 0 6
3 Loss Cards 10 Gain Amount 30 Gain Amount
250 Loss Amount 0 4
750 Loss Amount 0 0

15
Chapter 3: Results
Overview of Analysis
In order to answer the research questions proposed earlier, we present a series of analyses
following the order of the questions. We begin by comparing the completion time, the final score
of participants, and cards revealed relative to the optimal to provide background for participant
performance. Next, we evaluate the number of cards and percent of possible cards revealed in a
mixed design ANOVA to evaluate differences between versions, incentive conditions, round
parameters, and repetitions of round parameters. Afterward, we present a between-subjects
ANOVA regarding the number of loss cards participants revealed, followed by an analysis
regarding their behavior (number of cards revealed) on rounds after revealing or not revealing a
loss card. Finally, we evaluate whether participants play the Toasty version more similar to the
Warm or Hot version.
General Participant Performance
Completion Time
Table 3 shows the median minutes required to complete each version. Note that for the
Cold version, each round required one action (clicking a number from 0 to 32). Each card required
a separate click for the Hot, Warm, and Toasty versions, and the card animation for the Warm and
Toasty is much slower than the Hot. The Warm and Toasty versions also require participants to
select some number of cards at the beginning of the round, similar to the Cold version.

16
Table 3
Median Minutes (InterQuartile Range) to complete CCT
Version Non-incentivized Incentivized
Cold 3.62 (1.97) 4.10 (2.09)
Warm 8.02 (2.44) 9.00 (3.63)
Toasty 10.84 (3.79) 11.18 (4.34)
Hot 6.47 2.66) 5.93 (2.36)
Final Score
Table 4 shows the mean total score and percentage of participants with a positive score by
version and condition. As mentioned, participants were not penalized for having a negative score
in the incentivized condition. A two-way ANOVA was conducted to analyze the effect of the CCT
version and incentive condition on the final score. There was a significant main effect of CCT
version (F(3,397)=3.386, p=.018, η2 = 0.03), no significant main effect for incentive condition
(F(1,397)=3.163, p=.076, η2 = 0.01), and no significant interaction effect (F(3,397)=.621, p=.602,
η2 = 0.00). Pairwise t-tests using Holm’s correction (ɑ = 0.05) method found a significant
difference between Warm (M = -1864.14, SD = 1751.81) and Hot (M = -2693.07, SD = 1970.18).
The results of Fisher’s exact test (p = .219) do not indicate a significant association between the
percentage of participants with a positive score and either the CCT version or the incentive
condition.

17
Table 4
Mean Total Scores over 24 Rounds and Percentage of Participants with Positive Scores
Version Non-incentivized Incentivized
Mean Score
Percentage of
Participants
with a
Positive
Score
Mean Score
Percentage of
Participants
with a
Positive Score
Cold -2287.96 10.20% -1960.00 19.64%
Hot -3088.37 4.08% -2320.58 15.38%
Warm -1913.40 18.00% -1813.88 18.37%
Toasty -2258.20 16.00% -2088.00 12.00%
Cards Revealed Relative to Optimal Amount
Table 5 presents the average deviation score for each version of the CCT in the nonincentivized and incentivized conditions. Each deviation score was calculated by subtracting the
optimal (highest expected value) number of cards to reveal for that set of parameters from the
average number of cards revealed for that set of parameters. For example, for a gain amount of 10,
a loss amount of 250, and 1 loss card, the optimal number of cards to reveal is six. If participants
revealed an average of 12.3 cards, the deviation score would be +6.3 (indicating that participants
are revealing 6.3 more cards than they should be). The optimal number of cards to reveal for each
combination of parameters can be found in Table 2. It should be noted that in four of the eight
combinations of parameters, the optimal number of cards to reveal is zero.

18
Table 5
Average Deviation Score
Version Non-incentivized Incentivized
Cold +8.15 +8.70
Hot +3.45 +2.36
Warm +4.25 +3.80
Toasty +4.29 +4.70
Note. The positive signs refer to participants revealing more cards on average than optimal if
maximizing the expected value.
Number of Cards Revealed
The primary variable of interest in the CCT is the number of cards the participant reveals.
This variable serves as a behavioral measure of risk taking or risk tolerance. Revealing more cards
per round indicates greater risk taking behavior, and revealing fewer cards per round indicates less
risk taking behavior. Table 6 presents the mean and standard deviation of the number of cards
revealed in each version and the percentage of cards possible to reveal relative to the position of
the loss card. For example, if the loss card was the 10th and the participant revealed eight cards in
the round, the percentage would be 80. In the Cold, Warm, and Toasty versions, if the participant
revealed more cards than the index of the loss card, the percentage was rounded down to 100
(indicating they revealed the loss card). The percentages are included because, in the Hot version
(and occasionally in the Toasty), participants could not reveal more cards than the index of the loss
card, so the number of cards is biased downward.

19
Table 6
Cards Revealed by Version and Condition
Version Mean Number of Cards
Revealed per Round
Standard Deviation of Cards
Revealed per Round
Percentages of Possible Cards
that could be Revealed per
Round
Nonincentivized
Incentivized Nonincentivized
Incentivized Nonincentivized
Incentivized
Cold 12.85 13.29 5.20 5.25 73.50% 69.39%
Warm 9.06 8.67 4.64 4.08 64.00% 63.58%
Toasty 9.16 9.54 3.03 3.93 70.52% 70.26%
Hot 8.26 7.24 2.36 2.78 79.87% 69.44%
The following ANOVA models include only the main effects and the two-way interaction
effects between version and the other design factors to align with the research questions. A
summary of the 4 (version) x 2 (incentive condition) x 3 (repetition) x 2 (gain amount) x 2 (loss
amount) x 2 (number of loss cards) mixed model ANOVA for the number of cards revealed is
presented in Table 7. Five of the six main effects were significant, including version, while four
of the five 2-way interactions with version were significant.
For the marginal means of cards revealed, pairwise t-tests using Holm’s correction (ɑ =
0.05) method comparing CCT versions found participants revealed more cards in the Cold version
(M = 13.09, SD = 10.03) compared to the Hot (M = 7.74, SD = 6.30), Warm (M = 8.87, SD =
7.42), and Toasty (M = 9.35, SD = 6.58) versions. Participants also revealed more cards in the

20
Warm and Toasty versions compared to the Hot. Pairwise t-tests using Holm’s correction (ɑ =
0.05) method comparing repetition blocks found that participants revealed more cards in the
second block (M = 10.15, SD = 8.16) than in the first (M = 9.58, SD = 7.78) or the third (M = 9.67,
SD = 8.10).

21
Table 7
Summary of ANOVA for Number of Cards Revealed
Term df
numerator
df
denominator
F Statistic P value Eta Squared
Value
Version 3 397 33.84 <.001 .20
Incentive Condition 1 397 0.13 0.72 .00
Repetition 2 802 8.52 <.001 .02
Gain Amount 1 401 146.60 <.001 .25
Loss Amount 1 401 77.10 <.001 .14
Number of Loss
Cards
1 401 595.13 <.001 .58
Version*Incentive
Condition
3 397 0.75 0.53 .00
Version*Repetition 6 802 9.25 <.001 .06
Version*Gain
Amount
3 401 17.04 <.001 .09
Version*Loss
Amount
3 401 28.44 <.001 .15
Version*Number of
Loss Cards
3 401 7.66 <.001 .02
The same ANOVA (4 (version) x 2 (incentive condition) x 3 (repetition) x 2 (gain amount)
x 2 (loss amount) x 2 (number of loss cards) mixed model) conducted on the number of cards

22
revealed was also conducted on the percent of possible cards revealed with a modified empirical
logit transformation. The transformation (half of the lowest observed value) replaces values of 0
with and 1 with 1- so that a logit transformation can be conducted on values of 0 and 1 without
changing the shape of the distribution of the values as much as a typical logit transformation
(Stevens et al., 2016). The summary for the ANOVA on the percent of possible cards revealed is
presented in Table 8. All six main effects were significant, including version, while four of the five
2-way interactions with version were significant.
For the marginal means of percent of possible cards revealed, pairwise t-tests using Holm’s
correction (ɑ = 0.05) method comparing CCT versions found participants revealed a higher
percentage of possible cards in the Hot version (M = 74.5, SD = 33.95) compared to the Cold (M
= 71.31, SD = 37.30), Warm (M = 63.79, SD = 36.75), and Toasty (M = 70.39, SD = 34.11)
versions, more in the Cold version compared to the Warm, and more in the Toasty version
compared to the Warm. Pairwise t-tests using Holm’s correction method (ɑ = 0.05) comparing
repetition blocks found that participants revealed more possible cards in the first block (M = 73.91,
SD = 34.37) than in the second (M =68.16, SD = 36.05) or the third (M = 68.04, SD = 36.57).

23
Table 8
Summary of ANOVA on Percentage of Possible Cards Revealed
Term df
numerator
df
denominator
F Statistic P value Eta Squared
Value
Version 3 397 4.87 0.002 .03
Incentive Condition 1 397 4.08 0.04 .01
Repetition 2 802 40.87 p<.001 .09
Gain Amount 1 401 103.83 p<.001 .20
Loss Amount 1 401 188.67 p<.001 .31
Number of Loss
Cards
1 401 41.88 p<.001 .09
Version*Incentive
Condition
3 397 1.53 0.21 .01
Version*Repetition 6 802 6.79 p<.001 .04
Version*Gain
Amount
3 401 5.55 p<.001 .03
Version*Loss
Amount
3 401 7.16 p<.001 .04
Version*Number of
Loss Cards
3 401 4.14 0.007 .03

24
Version and Incentive Condition
There was a significant main effect for version for both the number and percent of possible
cards revealed. Incentives only had a significant effect on the percentage of possible cards
revealed. The interaction between version and incentive condition was not significant for either
dependent variable. Figure 1 plots the interaction between version and incentive condition for both
dependent variables. For the number of cards revealed, participants revealed significantly more in
the Cold version, and all but the Hot version revealed more in the incentivized condition. In
contrast, for the percentage of possible cards revealed, participants revealed significantly more in
the Hot version and the non-incentivized condition.
Figure 1
Interaction Between Version and Incentive Condition for Number and Percent of Possible Cards
Revealed

25
Version and Gain Amount
For both the number and percentage of possible cards revealed, there was a significant
main effect for gain amount and the interaction between gain amount and version. Figure 2 plots
the interaction between version and gain amount for both dependent variables. All versions showed
an increase in the number and percent of possible cards revealed when the gain amount increased
from 10 to 30. However, this effect was strongest in the Cold version, which relies on more
deliberative processes. For the number of cards revealed, the Warm version (which relies on more
deliberative processes than the Hot) also showed a stronger effect than the Hot version.
Figure 2
Interaction Between Version and Gain Amount for Number and Percent of Possible Cards
Revealed

26
Version and Loss Amount
For both the number and percentage of possible cards revealed, there was a significant
main effect for loss amount and the interaction between loss amount and version. Figure 3 plots
the interaction between version and loss amount for both dependent variables. For the number of
cards revealed, all versions except the Hot showed a decrease in the number revealed when the
loss amount increased from 250 to 750. This effect was the strongest for the Cold version, while
the Warm and Toasty versions showed minor effects. For the percent of possible cards revealed,
all versions showed a decrease in the percentage revealed when the loss amount increased. The
Cold version had the strongest effect, while the effects for the Warm, Toasty, and Hot versions
were similar to each other.

27
Figure 3
Interaction Between Version and Loss Amount for Number and Percent of Possible Cards
Revealed
Version and Number of Loss Cards
For both the number and percentage of possible cards revealed, there was a significant
main effect for the number of loss cards and the interaction between the number of loss cards and
version. Figure 4 plots the interaction between version and the number of loss cards for both
dependent variables. For the number of cards revealed all versions showed a decrease in the
number revealed when the number of loss cards increased from 1 to 3. There was no significant
difference between the effect in the Cold and other versions. In contrast, for the percent of possible
cards revealed all versions showed an increase in the percentage revealed when the number of loss
cards increased from 1 to 3. This effect was the weakest for the Cold version, while the other three

28
versions had a similar effect. It should be acknowledged that the change in direction is most likely
because the number of possible cards a participant could reveal decreases considerably when the
number of loss cards increases.
Figure 4
Interaction Between Version and Number of Loss Cards for Number and Percent of Possible Cards
Revealed
Version and Repetition of Parameters
For both the number and percentage of possible cards revealed, there was a significant
main effect for the repetition of parameters and the interaction between repetition and version.
Figure 5 plots the interaction between version and the repetition for both dependent variables. For
the number of cards revealed, the Cold and Hot versions showed an increase in cards from the first
to second repetition and a decrease from the second to third repetition. The Warm and Toasty

29
versions showed a decrease as the repetition number increased. There is little change between the
repetition for the Cold version for the percent of possible cards revealed. In the other versions
(where participants receive feedback), there is a decrease in the percentage of possible cards
revealed as the repetition number increases.
Figure 5
Interaction Between Version and Repetition for Number and Percent of Possible Cards Revealed
Viewed as a function of round, Figures 6 and 7 present the mean number of cards revealed
in all four versions for each incentive condition. Table 9 shows the coefficients for the regression
lines fitted with the intercept, slope, and p-value for the slope. Both the Warm incentivized, R2 =
0.33, F(1, 22) = 11.00, p = .003 and Toasty non-incentivized R2 = 0.27, F(1, 22) = 8.06, p = .010,
participants significantly decreased the number of cards revealed over rounds. The Cold and Hot
versions had no significant changes in the number of cards revealed over rounds.

30
Figure 6
Mean Number of Cards Revealed by Round Number in the Non-incentivized Condition
Note: The dashed lines are linear models fitted on the data for each version. The intercept and
slope for each line can be found in Table 9.

31
Figure 7
Mean Number of Cards Revealed by Round Number in the Incentivized Condition
Note: The dashed lines are linear models fitted on the data for each version. The intercept and
slope for each line can be found in Table 9.

32
Table 9
Regression Coefficients for Cards Revealed by Round Number
Version Intercept Slope P-value of Slope
Nonincentivized
Incentivized Nonincentivized
Incentivized Nonincentivized
Incentivized
Cold 13.90 13.62 -0.08 -0.03 0.47 0.87
Hot 8.49 8.79 -0.02 -0.12 0.85 0.15
Warm 10.47 11.50 -0.11 -0.23 0.10* 0.00***
Toasty 11.54 11.20 -0.19 -0.13 0.00*** 0.09*
*p<.10, ***p <.01
Loss Card Performance
Number of Loss Cards Revealed
Figure 8 displays the mean number of times in 24 rounds that participants revealed a loss
card with 95% confidence intervals. In the Cold version, participants had no feedback on whether
they revealed a loss card. A 4 (version) x 2 (condition) between-subjects ANOVA for number of
loss cards revealed indicated a significant main effect of version (F(3,397)=8.89, p<.001, partial
η
2=.07), no main effect for incentive condition (F(1,397)=2.187, p=.14, partial η
2=.01), and no
interaction effect (F(3,397)=.759, p=.518, partial η
2=.01). Follow-up pairwise t-tests using Holm’s
p-value correction (ɑ = 0.05) for version found participants revealed more loss cards in the Hot
version (M = 13.07, SD = 4.91) compared to the Warm (M = 10.07, SD = 4.53) and Toasty versions

33
(M = 11.3, SD = 4.43) and revealed more loss cards in the Cold version (M = 12.77, SD = 4.74)
compared to the Warm version.
Figure 8
Mean Number of Loss Cards Revealed (out of 24 rounds) by CCT Version and Incentive Condition
Note: The black error bars represent 95% confidence intervals.
Behavior After Revealing or Not Revealing a Loss Card
Table 10 displays the results of paired t-tests comparing the number of cards revealed on
rounds after a participant revealed a loss card (“Loss”) and rounds after which they did NOT reveal
a loss card (“Gain”). The Cold version was excluded because participants received no feedback
and would not know whether they revealed a loss card on the previous round. No comparison had
a significant difference at ɑ = 0.05, and effect sizes for the differences were small

34
Table 10
Pairwise t-tests Comparing Mean Cards Revealed After “Gain” and “Loss” Rounds
Version &
Condition
Mean Cards
Revealed
After “Gain”
Rounds
Mean Cards
Revealed
After “Loss”
Rounds
Pairwise t-test
statistic
P value Cohen’s D
effect size
Hot
Nonincentivized
8.76 8.35 0.64 0.52 0.13
Hot
Incentivized
7.70 7.21 0.65 0.52 0.13
Warm
Nonincentivized
8.46 9.94 -1.55 0.12 0.31
Warm
Incentivized
8.43 9.57 -1.29 0.20 0.26
Toasty
Nonincentivized
8.87 9.65 -1.21 0.23 0.24
Toasty
Incentivized
9.92 10.46 -0.71 0.48 0.15

35
Toasty Version Compared to Hot and Warm Versions
As described earlier, the Hot and Warm versions can be considered limiting cases of the
Toasty version. However, results indicate that participants play the Toasty version more like the
Warm version than the Hot. In the non-incentivized condition, participants asked for feedback only
once in 76.56% of rounds (playing the same way as the Warm version). In the incentivized
condition, participants asked for feedback only once in 76.72% of rounds. No participant in the
Toasty version revealed cards one-by-one (equivalent to the Hot version) for more than one round.

36
Chapter 4: Discussion
General Participant Performance
Despite relatively large incentives, participants overall performed poorly on all versions of
the CCT. In no version or incentive condition did more than 20% of participants receive a positive
score. The results indicated that participants were sensitive to the parameters of the game.
However, the large number of cards revealed over the optimal suggests they did not understand
the large penalty of revealing a loss card or chose to ignore it. Since the optimal number of cards
to reveal is so low, virtually every participant is considered risk seeking because they are revealing
more cards than the optimal, even if they reveal 1 card in some instances. This problem is most
likely further compounded by deceptive feedback in other studies in which the loss cards are placed
at the end. Without the penalty for revealing loss cards participants would reveal even more cards
than the optimal compared to our results. Thus, participants’ scores may be systematically inflated,
diminishing the effectiveness of the CCT as a measure of risk taking. Possible solutions are to
lower the loss amounts or raise the gain amounts to produce more parameter combinations where
the optimal number of cards to reveal is not zero.
Number or Percent of Possible Cards Revealed
When viewing only the number of cards revealed with the loss card(s) placed randomly,
participants revealed the most cards in the Cold version. This result likely follows because, in the
Cold version, participants receive no feedback until the end of the study. Lacking feedback
throughout the game, they do not realize they are revealing more than eight cards over the optimal
number each round on average compared to only 3-4 more in the other versions. Interestingly,
when looking at the percentage of possible cards to reveal, we see that the Hot version has the

37
highest percentage of cards revealed. This result matches other studies where the loss cards were
placed at the end (Markiewicz & Kubińska, 2015; Figner et al., 2009).
Participants are still sensitive to all game parameters when looking at the percentage of
possible cards revealed; however, the direction of the effect for the number of loss cards changes
compared to the number of cards revealed. Alternative analyses, such as the percentage of possible
cards revealed, provide additional insights when loss card(s) are placed randomly but require the
data to be transformed and are impacted by the number of loss card(s).
Incentives
We did not observe any significant differences between the incentivized and nonincentivized conditions except for participants revealing a higher percentage of possible cards in
the non-incentivized condition. There are several possible explanations for this. Less likely is that
incentives were not great enough to matter to participants. Past research on incentivizing
participants primarily compares participants who are given a monetary incentive and those who
voluntarily opt into the study (Shamon & Berning, 2020). In our study, the non-incentivized
version compensated the participants approximately $12 per hour. The incentivized participants
could win an additional dollar for every 100 points at the end of the game. If a participant played
to maximize the expected value, their expected bonus would be $26.10, over ten times the base
rate in any version of the CCT.
Participants may likely be incentivized and want to perform better in the incentivized
version. Still, they do not know how to play optimally and receive more points, as reflected by the
large percentage of negative total scores over all 24 rounds. The fact that the majority of the
participants had a negative score and revealed several cards above the optimal amount, with or

38
without incentives, raises the question of whether the parameters of the game are set to an
appropriate level for when the game is played honestly (loss cards placed randomly).
Game Parameters
While previous studies have found that participants are more sensitive to the parameters in
the Cold version because of the deliberative nature of the task (Figner et al., 2009; Markiewicz &
Kubińska, 2015), no study has corroborated this when the loss cards are randomly placed. When
looking at the number of cards revealed, participants in the Cold version were the most sensitive
to the parameters of the game. Participants were overall the most sensitive to the number of loss
cards, indicating they cared the most about their probability of being penalized and not what they
could potentially gain or lose. When looking at the percent of possible cards revealed, participants
in the Cold version were still the most sensitive to the parameters of the game. The percentage of
possible cards revealed analysis indicates that the effects of all three game parameters are equal in
determining the number of cards participants chose to reveal.
Repetition of Game Parameters
Despite the large penalty for revealing a loss card, participants revealed a similar number
of cards the first time a parameter combination was presented as the second and third time. For the
number of cards revealed in the Hot version participants revealed more cards the second and third
time a parameter combination was repeated despite receiving feedback. Although the Warm and
Toasty versions showed a gradual decline in the number of cards revealed, these versions also took
the longest to complete. They were also the only versions to significantly decrease the number of
cards revealed as a function of the round number, suggesting participants may have become bored,
fatigued, or, if penalized severely enough in the beginning, have lost interest in the game. In the

39
three versions where participants received feedback, the percentage of possible cards revealed
decreased from the first and second repetitions. However, this decrease did not occur during the
third repetition despite participants revealing more cards than optimal.
Randomly Placed Loss Cards
Participants revealed loss cards in approximately half of the rounds they played. However,
this was higher in the Cold and Hot versions than the Warm and Toasty versions. One possible
explanation is that in the Cold version, participants revealed more loss cards due to a lack of
feedback, while in the Hot version, participants revealed more loss cards because of the increase
in affective decision making. Affective decision making would increase the number of loss cards
revealed since participants focus less on round parameters and more on previous performance.
Participants revealing loss cards approximately half the time is surprising because the loss amount
is so high compared to the gain amount and occurs even when participants were incentivized.
We found no differences in the number of cards participants revealed on rounds after they
revealed a loss card or did not reveal one. There is a small effect for the Warm version (regardless
of incentives) and the non-incentivized condition of the Toasty version. Surprisingly, participants
revealed more cards on rounds after they revealed a loss card than after they did not. Additionally,
there is no effect using Cohen’s D for either incentive condition in the Hot version, where we
expect increased affective decision making. Since the strongest effect from the interaction graphs
between game parameters and version was the number of loss cards for the Hot version,
participants appear to care most about the probability of revealing a loss card but understand that
rounds are independent, i.e., cards have no memory of previous rounds.

40
Toasty Version
While the Toasty version of the CCT we introduced performed similarly to the Warm
version, it gave some interesting insights into how participants make decisions. Even when
presented with the option of revealing cards after every card, participants still chose to reveal cards
only at the end of the round in over 75% of cases. Additionally, most participants revealed cards
three or fewer times in each round played. One possible explanation for this result is the additional
time required to reveal cards in the Toasty version, which was the longest of the 4 CCT versions
because of the slow card animation. However, similar results were produced even when offered
generous incentives for good performance. Having to confirm they were ready to reveal cards
instead of receiving instant feedback may have also resulted in participants using more deliberative
decision-making processes instead of affective ones and led to results more similar to the Warm
version than the Hot.
Limitations and Future Considerations
While our study provided a general overview of the CCT and introduced a new version,
several improvements or additions could have been made. The order of parameters within rounds
was the same for all participants in all four versions, which produced similar card patterns revealed
over time in Figures 6 and 7. This design was utilized to compare results across the four versions.
However, future studies should aim to randomize the order of the parameters in case the order of
round parameters being presented impacts results. Additionally, future studies should explore
alternative parameter selections for the CCT to evaluate participant performance for cases in which
the optimal number of cards to reveal is greater, with fewer cases in which the best option is to
reveal no cards.

41
Conclusions
Based on the results, there is no reason to place the loss cards at the end and deceive
participants playing the CCT. We observed that participants were still sensitive to the game's
parameters, albeit to varying degrees across versions. While randomly placing the loss cards does
not deceive participants, it does prevent fair comparisons across versions. Alternative analyses,
such as the percentage of possible cards revealed, should be used when comparing the Hot and
Toasty versions to any other version. The game's parameters should also be reevaluated, as most
participants had a negative score and revealed the loss card in approximately half of the rounds.
Incentivizing participants also had little impact on performance.

42
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45
Appendix
Table A.1
Parameter Combinations by Round
Round Number Gain Amount Loss Amount Number of Loss Cards
1 30 250 3
2 30 750 1
3 10 250 1
4 30 750 3
5 10 750 1
6 30 250 1
7 10 750 3
8 10 250 3
9 30 250 3
10 30 250 1
11 30 750 3
12 10 750 3
13 10 250 3
14 10 750 1
15 30 750 1
16 10 250 1

46
17 10 250 3
18 30 750 1
19 30 250 1
20 10 250 1
21 10 750 1
22 30 750 3
23 30 250 3
24 10 750 3

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Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu