Computers in Human Behavior 142 (2023) 107657

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Computers in Human Behavior
journal homepage: www.elsevier.com/locate/comphumbeh

A large-scale prospective study of big wins and their relationship with
future involvement and risk among actual online sports bettors☆
Timothy C. Edson a, b, *, Eric R. Louderback a, b, Matthew A. Tom a, b, Kahlil S. Philander c, d,
John M. Slabczynski a, Taylor G. Lee a, Debi A. LaPlante a, b
a

Cambridge Health Alliance, a Harvard Medical School teaching hospital, Malden, MA, USA
Harvard Medical School, Boston, MA, USA
Washington State University, Pullman, WA, USA
d
University of Sydney, NSW, Australia
b
c

A R T I C L E I N F O

A B S T R A C T

Handling Editor: Nicolae Nistor

Clinicians have proposed that big wins early in a gambler’s betting experience can lead to increased involvement,
and eventually problematic gambling. Understanding how this effect manifests in online sports betting is
important, as this form of gambling has grown increasingly popular worldwide and continues to expand.
Methods: Using matched pair analysis and other methods (e.g., survival analysis, fixed effects regression), we
examined big wins’ ability to predict future gambling involvement and behavior using bet level data from 36,328
sports gamblers who subscribed to a large, European online gambling operator. Big wins were defined two ways.
Results: Big wins in sports betting were associated with increased engagement, losses, and risk in the following
weeks, with the impact declining over time. The exact timing of when a big win occurs after subscribing does not
appear to have a major effect on subsequent behaviors. These findings held for both definitions of big wins.
Implications: This study supports the existence of a big win effect in online sports betting, but more research is
needed to determine whether there is an “early” big win effect, and whether big wins are indeed associated with
problematic gambling.

Keywords:
Gambling
Online gambling
Big wins
Sports betting
Matched pair analysis
Survival analysis

1. Introduction
1.1. The early big win effect and general big win effect
Although our understanding of disordered gambling and gambling
behavior in general has evolved and become more nuanced, there are
still important and influential theories with limited support. One of
these is the notion that a large win early in one’s gambling career will
lead to future problem gambling: the big win effect (Custer, 1984; Custer
& Milt, 1985; Davies, 2022). Specifically, in widely-cited clinical re­
ports, Custer described the early winning phase, where the individual
who will later experience problem gambling begins gambling with a
significant stroke of luck. Eventually, winning comes to an end and shifts
to a losing phase where the individual begins to lose control over their
gambling. After the gambler depletes all of their winnings, and then
their bankroll (i.e., money available for gambling), debts begin to mount
and the individual begins to display behavior emblematic of what was

referred to as compulsive gambling at the time. Custer argued, drawing
from his clinical experience, that the notable shift was due to a big win
that occurred early in the gamblers’ gambling careers (Custer, 1984).
Thus, early big wins are defined as subjectively large prizes (typically
worth around a month’s salary) won by gamblers during an initial and
formative period of their gambling experience (Custer & Milt, 1985),
that have the potential to promote excessive and even problematic
gambling.
While these clinical observations clearly highlight the importance of
early gambling big wins, it remains unclear whether early big wins are
only important in the context of an individual’s entire gambling expe­
rience (regardless of gambling product or service), or whether early big
win effects can also be unique for specific gambling products or operator
experiences (e.g., individual early big win effects for: brick-and-mortar
gambling, online gambling, sports gambling at a specific operator,
etc.). It is also unclear whether there is simply a general big win effect –
does any substantially large win influence future gambling behavior,

This study was preregistered on the Open Science Framework (https://osf.io/efc4d).
* Corresponding author. Division on Addiction, Suite 630, Cambridge Health Alliance, Malden, MA, 02148, USA.
E-mail address: tedson@cha.harvard.edu (T.C. Edson).

☆

https://doi.org/10.1016/j.chb.2023.107657
Received 16 August 2022; Received in revised form 5 January 2023; Accepted 9 January 2023
Available online 10 January 2023
0747-5632/© 2023 Elsevier Ltd. All rights reserved.

Computers in Human Behavior 142 (2023) 107657

regardless of when it occurs? Outside of retrospective self-report studies,
researchers are better equipped to test a general big win effect, or
product/operator-specific early big effects, than they are an early big
win effect that occurs early on in an individual’s gambling experience.
The potential psychological mechanisms behind the big win effect
are numerous. Illusion of Control (Stefan & David, 2013), or the idea
that someone’s big win is the direct result of their keen skill and mastery
of the craft (and therefore future big wins will inevitably follow) rep­
resents one potentially important mechanism. Operant conditioning
(Skinner, 1963), or reinforcement of behavior through reward schedule,
is another. Still other explanations come from behavioral economics,
such as the availability heuristic (Tversky & Kahneman, 1973), whereby
meaningful amounts of winnings are more likely to stick in one’s head
than more modest winnings. The representative heuristic (Tversky &
Kahneman, 1971), could also explain the effects of early big wins that
happen after only limited amounts of play, which can lead one to believe
that these are common occurrences. Relatedly, the “hot hand” effect
(Gilovich, Vallone, & Tversky, 1985) suggests that big wins might occur
in streaks, and that subsequent big wins are likely to follow an initial big
win. Finally, there is the house money effect (Thaler & Johnson, 1990),
where a gambler might more freely gamble away a big win believing it
to be the house’s money they are risking, rather than their own. It should
also be noted that while some of these psychological mechanisms could
underlie both early and general big win effects, a few might be particular
to just one type. For example, illusion of control, hot hand, and house
money effects could apply to any big win, with less relevance for
formative big wins early in the career, whereas the representative
heuristic is clearly more likely to speak to early big wins specifically.
Furthermore, while all of these mechanisms are quite different from one
another, there is one potential common thread throughout all of them:
as time goes on following the big win without a repeat big win, the effect
of the big win on behavior would presumably be expected to diminish or
even deteriorate over time.

reported significantly larger first wins than those who were non-problem
gamblers (Turner, 2006). One study suggested that the early big win
effect is not only present but has a larger effect compared to other
variables commonly associated with problem gambling such as impul­
sivity and erroneous beliefs (Turner, 2008). However, at least two
studies assessing early big wins have reported null results (Edgerton,
2015; Kassinove & Schare, 2001), one of which was a longitudinal study
that assessed the role of early big wins in later development of Gambling
Disorder (Edgerton, 2015).
As previously noted, the vast majority of research assessing the big
win effect has been laboratory-based or relied on self-report. Though
these designs certainly have merit, they also present some methodo­
logical issues when trying to accurately measure certain constructs such
as gambling behavior. Turner (2006), for instance, asked respondents to
retrospectively self-report an event that might have happened 30 years
previously, which presents significant risk for recall bias. Self-report of
gambling expenditure, more generally, has been shown to be unreliable
(Braverman, Tom, & Shaffer, 2014; Heirene, Wang, & Gainsbury, 2021).
For example, Braverman and colleagues noted that 34%–40% of par­
ticipants self-reported favorable distortions of their gambling gain­
s/losses relative to their actual performance. Even more importantly,
they report that the size of the discrepancy between reported perfor­
mance and actual performance was correlated with self-reported prob­
lem gambling symptoms.
Many lab and self-report study designs also rely on samples of small
groups of university students, who might have limited generalizability
to the broader population of gamblers (Gainsbury & Blaszczynski,
2011). Other studies rely on online convenience samples. However,
these samples too face similar issues in terms of data integrity and val­
idity (Pickering & Blaszczynski, 2021). Experimental studies’ limited
time horizons are also not ideal for assessing longer-term changes in
gambling behavior or the later development of disordered gambling in
the real world. In addition, laboratory studies do not (and to stay in
compliance with contemporary research ethics commissions, probably
cannot) have participants wager their own money, nor truly receive
large sums of actual money in the form of big wins. In some cases,
participants wager “lab points” whose utility might not be 100% (i.e.,
not r = 1) correlated with the size of participants’ rewards for joining the
study. The inability to gamble with one’s own money in these scenarios
can lead to strategies and behaviors different from what occurs in
real-life gambling environments (Weatherly & Phelps, 2006). These
complications with lab research are in addition to the typical biases in
lab studies such as the Hawthorne effect, or behavioral changes in
response to being observed in an experimental setting (Landsberger,
1958; Merrett, 2006; Roethlisberger & Dickson, 1939). Thus, while the
big win effect has been evaluated empirically, there are still substantial
questions that remain unanswered, including whether it manifests in
actual gambling behavior.

1.2. Assessing the big win effect: laboratory and self-report studies
Although foundational research by Custer (1984) first advanced the
notion of the early big win effect, more recent clinical evidence is also
supportive of it. For example, the majority of individuals receiving
treatment from the National Gambling Treatment Service in the United
Kingdom (i.e., England, Scotland, Wales, and Northern Ireland) reported
having an early big win (National Gambling Treatment Service, 2021).
These types of clinical reports have helped to emphasize the idea of early
big wins as a major catalyst to the development of problem gambling.
Moreover, while at least some discussions of the big win effect more
generally have focused on specific products, such as jackpots in elec­
tronic gambling machines (EGMs; e.g., Donaldson, Langham, Rockloff,
& Browne, 2016; Rockloff & Hing, 2013), the potential for big wins and
big win effects does not appear to be confined any one product.
Multi-game parlays in sports betting, for instance, have the potential to
turn small stake sizes into enormously large prizes. Even games where
players can at most double their stake (e.g., Blackjack) have the po­
tential for large payoffs at higher stakes.
Consistent with Custer’s initial observations, most previous litera­
ture has focused on the effects of early big wins rather than big wins
more generally. Researchers empirically testing the early big win effect
have either confined their tests to laboratory settings ( Kassinove &
Schare, 2001; Weatherly, Sauter, & King, 2004) or relied on self-report
data (Edgerton, 2015; Turner, 2006). Among these studies, evidence of
an early big win effect has been fairly mixed, with potentially greater
evidence for a lifetime early big win effect and less evidence for a
product-specific early big win effect. For example, participants in a
simulated slot experiment who experienced a big win on their 5th spin
played longer than those who experienced a big win on their first spin as
well as those who never experienced a big win (Weatherly et al., 2004).
In a self-report study, individuals with disordered gambling on average

1.3. Assessing the big win effect: actual user record data
A more contemporary research approach has used actual gambling
record data to assess traditional theories. We are aware of only two
studies that assessed the big win effect using actual user record data
(Edson, Tom, Philander, Louderback, & LaPlante, 2021; Smith, Levere,
& Kurtzman, 2009). Both of these studies used $1000 as their threshold
for “big win”. Edson & colleagues also used a separate definition that
defined big wins as multiplications of wager size (see discussion of Prize
Ratio, below). Smith and colleagues examined big wins (and losses)
among 356 poker players, finding that players tended to play less
aggressively following a big win. Edson and colleagues conducted a
more focused analysis on big wins specifically, analyzing a prospective
dataset of 34,596 Daily Fantasy Sports (DFS) subscribers from a major
DFS provider, DraftKings, which was based on over 18 million entries
into DFS contests. Their findings showed that experiencing a big win in
DFS significantly predicted future increased DFS engagement (i.e.,

Computers in Human Behavior 142 (2023) 107657

increased contest entry fees and more contest entries) and losses (i.e.,
higher net loss), yet also showed that the relationship between a big win
and engagement and losses decays over time. They also observed that
later big wins had a slightly stronger, albeit very small, effect compared
to earlier big wins on future DFS engagement, which led them to
conclude that timing of big wins in DFS is likely of little importance.
However, both poker and DFS are considered to be more “skilled”
forms of gambling with unique player pools, and the findings from these
studies regarding the effects of big wins on player behavior might not be
generalizable to other products. DFS also is not legally recognized as a
form of gambling by some jurisdictions (Weston, 2021). Importantly, we
are not aware of any research on the big win effect using actual gambling
records for online sports gambling, which remains one of the most
popular forms of online gambling in Europe (European Gaming &
Betting, 2019), and whose popularity in the ripe U.S. gambling market is
likely to increase following a 2018 U.S. Supreme Court ruling that ended
Federal restrictions on sports wagering (Legal Sports Report, 2020).
Hence, examining big wins in gambling formats such as sports betting
remains important.

online sports betting and online gambling operator based in Europe,
during February 2015. Bet-by-bet sports gambling data were delivered
to us by bwin, with all datetimes for each bet in GMT (Greenwich Mean
Time). The datetimes for all other data (i.e., bettor data, deposit and
withdrawal data) were in CET (Central European Time) and did NOT
switch to CEST during daylight savings. We converted the date-times in
all files to each bettor’s local date and time based on their country of
record (i.e., the country in which they subscribed to bwin). We only had
access to the bettors’ country of record and no smaller geographic unit.
The vast majority of these bettors were from member countries of the
European Union (McAuliffe, Louderback, Edson, LaPlante, & Nelson,
2022; Nelson et al., 2021). For bettors who reside in countries with
multiple time zones, we utilized the time zone of the most populous city
in that country.
Measures included number of selections/propositions, amount spent
on stake, and amount won in prizes for each bet placed from each bet­
tor’s initial February 2015 subscription date through July 16, 2020 (i.e.,
the latest date a bet was placed in the data). In all, the data comprised
bet-level information for a total of n =36,328 individual bettors. For
each bettor, we generated weekly aggregates of their engagement be­
haviors and losses (i.e., total stake, number of bets, and net loss for each
week they played) and calculated the median values of wager size and
betting odds for each week they played, to assess riskiness of betting.
Here, we define a “week” as a seven-day period beginning on a Sunday at
midnight (e.g., 2021-02-21 00:00:00). We considered the bettors’ “first
week” as the week they subscribed to bwin. Bettors who signed up
earlier during the recruitment period had more available weeks than
bettors who signed up later.

2. The present study
The current study expands our knowledge of the big win effect by
examining big wins evident in actual gambling records for sports bet­
tors. Guided by prior research assessing the big win effect among DFS
players (Edson et al., 2021), this study used matched pair analysis,
survival models, and several robustness tests to empirically assess the
big win effect among all individuals who subscribed to a major European
online sports gambling website during February 2015. Lacking
self-report data (and thus a viable clinical measure of problem
gambling), we use actual gambling records to assess the big effect in
terms of its association with excessive engagement. Specifically, we
focus on the extent to which big wins promote increased betting
engagement (i.e., total stake, number of bets), risk (i.e., increased odds
and stake size), and losses (i.e., net loss) (Research Question 1). Given
that many of the psychological mechanisms for the big win effect (e.g.,
illusion of control, availability heuristic) are predicated on its weak­
ening over time, we also assessed this possibility: whether the big win
effect weakens, or disappears entirely, over time (Research Question 2).
Finally, in addition to testing the big win effect more generally, we also
sought to conduct a limited test of the early big win effect hypothesis –
specifically, are earlier wins within a single gambling operator and
product more meaningful, in terms of increased risk and engagement,
than later ones (Research Question 3). We call this test “limited” because
Custer considered early big wins in the context of a gambler’s entire life.
Here, our examination of temporality is limited to the gambler’s expe­
rience with a single product and operator.
More specifically, the present study assessed:

3.2. Study design
We employed a longitudinal prospective cohort design with repeated
time points and preregistered our study on the Open Science Framework
prior to conducting any analyses. Each time point comprises weekly
aggregates of bettor-level sports gambling engagement and performance
on the bwin website . Time points are repeated for each bettor for each
week since they subscribed, starting with the week of subscription (week
1) and the last available full week the bettor was eligible to play when
the data the were delivered to us in July 2020 (i.e., between week 281
and week 284, depending on the week the bettor subscribed during
February 2015). We used matched pair analysis to match each big
winner with a sports bettor exhibiting similar engagement and risk
profiles during the week of the big win, but who did not experience a big
win that week, and compared both individuals on subsequent week
engagement, risk, and loss metrics.
3.3. Measures
3.3.1. Identifying and demographic variables
Identifying and demographic variables in the data included bettor
ID, gender, age, and week number (see Table 1 for descriptions).

(1) How big wins in actual online sports betting are associated with
future sports betting engagement/risk/loss metrics among all
online sports bettors who subscribed to a sports betting website
during February 2015;
(2) Whether the empirical relationship between a big win and sports
betting engagement metrics changes depending on how many
weeks have elapsed since the big win; and,
(3) Whether the effects of having a big win vary depending on the
amount of time between someone’s entrance onto a sports betting
website and their big win (i.e., is there an early big win effect, at
least within a single product domain)?

Table 1
Identifying and demographic variables.
Bettor ID:
Gender
Age
Week number t

3. Method
3.1. Data and participants
Participants included all individuals who subscribed to bwin, a large

Identification numbers used to distinguish one bettor from another.
Each bettor’s self-reported gender at registration (only male or
female was available)
Each bettor’s self-reported age, in whole years, at registration
Given a Bettor ID, a week number of 1 means the week that the
bettor subscribed to bwin. A week number of 2 means the week after
the week of subscription. For example, if an individual subscribed
on Wednesday, 2019-11-06, then the start and end times for that
person’s week 1 would be Sunday 2019-11-03 00:00:00 and
Saturday 2019-11-09 23:59:59, respectively, and the corresponding
week 4 would start at Sunday 2019-11-24 00:00:00. The exact
number of days represented in week 1 vary from bettor to bettor,
depending on the date of subscription.

Computers in Human Behavior 142 (2023) 107657

3.3.2. Dependent variables
Edson et al. (2021) examined the effects of big wins on engagement
outcomes (i.e., total entry fees, number of entries), and losses (i.e., net
loss). We used analogous outcome measures for sports betting (Table 2).
In addition, we extended the original analyses by also examining the
effects of big wins on the “riskiness of betting” outcomes (i.e., stake size
and betting odds).

Table 3
Independent variables.
Big win measure 1
(Custer’s definition)

3.3.3. Independent variables
Our main independent variable of interest was experiencing a big
win. We defined the term “big win” in two different ways (Table 3).

Big win measure 2 (Prize
Ratio definition)

3.3.4. Covariates and transformations
We matched big winners and matched (i.e., non-big winner) controls
on five variables. These included measures tapping prior engagement,
prior riskiness of betting, and previous losses (Table 4).
3.4. Inference criteria
We used a statistical significance level of α = 0.05. All reported pvalues rely on two-tailed tests of significance.

Table 4
Matching covariates.
Prior week’s engagement (total
stake and number of bets

3.4.1. Hypotheses and analytic plan
Prior to testing our hypotheses, we first conducted a brief census of
big win events among our sample of sports bettors during the study
period, specifically noting how many bettors experienced at least one
big win based on just Custer’s definition, how many bettors experienced
at least one big win based on just the Prize Ratio definition, how many
bettors experienced at least one big win based on both definitions, and
how many bettors did not have a big win.
We also calculated a similar census of big wins themselves during the
study period, noting how many big wins that met just Custer’s definition
occurred, how many big wins that met just the Prize Ratio definition
occurred, and how many big wins that met both definitions occurred.

Prior week’s riskiness of betting
(stake size and odds)
Cumulative net loss

Hypothesis 1. Online sports bettors who experience a big win will
exhibit more sportsbook engagement (i.e., higher total stake and a
greater number of bets placed), greater losses, and more risky engage­
ment (i.e., higher median stake size and higher median betting odds) in
the following week when compared with bettors who do not experience

Current week’s number
of bets
Current week’s median
stake size
Current week’s median
odds

Persistence

Frequency of play

We matched bettors based on prior sports betting
engagement in terms of total stake and total
number of bets during the week prior to the week
of the big win.
We matched bettors based on prior sports betting
riskiness in terms of median stake size and median
betting odds during the week prior to the week of
the big win.
Because past success rates might inform future
betting behaviors, we matched bettors based on
their cumulative net loss (i.e., running net loss
since they first deposited) as of the end of the
week prior to the week of the big win. Sports bets
made during this period that did not resolve until
the week of the big win, or later, did not count
towards this calculation.

a big win.
Our primary interest in Hypothesis 1 is to test how big wins imme­
diately influence subsequent engagement, risk, and loss outcomes. We
specifically seek to assess how these outcomes differ for people who
experience a big win with those who do not, yet the use of observational
data prevents random assignment (Shah, Laupacis, Hux, & Austin, 2005)
of the treatment variable (i.e., experiencing a big win). To remedy these
issues, we followed a matched pair approach. Matched pair analysis is an
appropriate way to simulate experimental designs with observational
data, and has gained a significant amount of traction in addiction
research specifically and public health research more generally (Chan
et al., 2022). Examples in the gambling literature include: Auer, Hopf­
gartner, & Griffiths, 2018; Braverman, LaPlante, Nelson, & Shaffer,
2013; Edson et al., 2021; Gray, LaPlante & Shaffer, 2012; Madden,
Petry, & Johnson, 2009). We used Mahalanobis distance matching (King
& Nielsen, 2019; Stuart, King, Imai, & Ho, 2011) to pair big winners with
matching controls. In their study of big wins in DFS, Edson et al. (2021)
found that Mahalanobis distance substantially outperformed similar
distance methods such as propensity score, in terms of accurately
matching big winners and matched controls.
Our matching procedure involved first identifying all big winners for
each week of the study period, starting at Week 1. For Week 1 big
winners, we picked matched controls randomly because all matching
covariates are equal to zero. For the remaining weeks, we used the
matchit() function from the MatchIt package in R v. 4.1.1 (Ho, Imai,
King, & Stuart., 2011; R Core Team, 2022) to match each big winner
with another bettor who played that same week but did not experience a
big win, using the five aforementioned covariates (i.e., number of bets,

Table 2
Dependent variables.
Current week’s total
stake
Current week’s net loss

Our first measure of “big win” is derived from the
clinical observations of Custer (1984), later Custer and
Milt (1985), and finally an adaptation of those
conceptualizations proposed by Edson et al. (2021),
which is any single prize that is greater than or equal to
€1000. For a given bettor/week, this variable takes a
value of 1 if the bettor experienced at least one Custer
Big Win that week, otherwise 0.
Our second measure of “big win” is Prize Ratio (Edson
et al., 2021), which is the size of a prize divided by the
largest wager on a single bet the bettor had ever made
up to and including that bet. Among all winning bets, we
considered those that fell in the top 1% of prize ratios to
meet the criteria for Prize Ratio big win (i.e., we ordered
all winning bets by prize ratio and took the top 1%,
which might have included some instances of multiple
big wins from the same bettor). For a given bettor/week,
this variable takes a value of 1 if the bettor experienced
at least one Prize Ratio Big Win that week, otherwise 0.

The total amount a bettor spent on sports betting wagers in
week t
The sum of all stakes minus the sum of all winnings across
the sports bets the bettor made in week t. Sports bets made
during week t but resolved after week t still count towards
this measure’s calculation
The total number of sports bets submitted in week t
The median of stake for sports bets submitted during week
t. We used the median instead of mean to partially mitigate
the outsized effects of outliers.
The median of calculated odds (e.g., calculated odds for an
even money bet is 2.0 [i.e., the bet returns double the
amount of the stake]) for sports bets submitted during
week t. We used the median instead of mean to partially
mitigate the outsized effects of outliers.
Among big winners, the number of consecutive
prototypical “months” (i.e., 4-week periods) they play (i.e.,
in which they made at least one sports bet on bwin)
following the week of the big win. We tracked persistence
for a total of six 4-week periods.
Among big winners, the number of active days on bwin
sportsbook during the 24 weeks (i.e., six prototypical
months) following their big win divided by their total
active duration (i.e., number of days, inclusive, between
first active day and last active day) during this same 24week period, and multiplied by 100.

Computers in Human Behavior 142 (2023) 107657

total stake, median stake size, median odds, and cumulative net loss)
based on Mahalanobis distance. We set the parameter ratio equal to 1 so
that each treatment case is matched to only one control case. If there
were multiple viable matching candidates (i.e., multiple matches),
matchit() chose one randomly. The MatchIt package includes several
methods for matching that are applicable for the present dataset: exact,
subclassification, nearest neighbor, optimal, and coarsened exact. We
compared each of these methods and used the optimal matching
method, which resulted in the lowest mean difference between the big
winners and corresponding matching controls. A summary of the bal­
ance table (see supplementary materials), shows that, for each matching
covariate, the mean difference between the big winners and their
matched controls was less than the corresponding mean difference be­
tween the big winners and the rest of the unmatched sample of bettors.
After conducting the matching procedure, we tested Hypothesis 1
using a matched pair t-test (see Moore, McCabe, & Craig, 2009, p. 428)
with Welch’s approximation for degrees of freedom to assess mean
differences between the big winners and their matching controls on (1)
total stake, (2) number of bets, (3) net loss, (4) median stake size, and (5)
median odds during their week after the big win (e.g., if the big win
occurred in Week 1, then we compared the big winner and his matched
control on Week 2 results; if the big win occurred in Week 48, then we
compare the two bettors on their Week 49 results).

big win), month 3 (i.e., weeks 9–12 after the week of the big win), month
4 (i.e., weeks 13–16 after the week of the big win), month 5 (i.e., weeks
17–20 after the week of the big win) and month 6 (i.e., weeks 21–24
after the week of the big win). Each month variable was set to 1 if the
bettor placed one or more bets during that month and 0 if the bettor did
not place a bet.
The resultant variable, Persistence, is a time-based dropout variable,
which is well suited for survival analysis. We created a survival curve
based on the non-parametric Kaplan-Meier estimator (Efron, 1988) with
months on the x-axis and the probability of persistence on the y-axis.
Then, to empirically assess how the week of the big win affects persis­
tence, we estimated two Cox Proportional Hazards models: (1) a model
with just the independent variable (week of big win) predicting the
hazard function, and (2) a second model with added controls for a
bettor’s age, gender, frequency of play and stake per day (i.e., total stake
divided by number of active days) in all available weeks leading up to,
and including, and the week of the big win event. This second model
controls for potentially confounding effects of time and financial
engagement across the sample of big winners and any potential effects of
gender and age as covariates.
3.6. Frequency of play
For both sub-samples of big winners, to test how bettors’ general
engagement in sports betting may vary depending on how early in their
sports betting experience the big win occurred, we employed ordinary
least squares (OLS) linear regression to model the frequency of days
bettors are active during the 24-week period following the big win, with
week of big win as the sole independent variable. Next, we estimated the
same regression model with added controls for age, gender, frequency of
play, and stake per day (i.e., total stake divided by number of active
days) in all available weeks leading up to, and including, the week of the
big win. We chose OLS regression for this analysis as the outcome of
interest, Frequency, was amenable to this type of analysis, and most
researchers have familiarity with it. We conducted the necessary tests (e.
g., residual plots, qq plots) to ensure that all major assumptions of OLS
were satisfied (e.g., homoscedasticity, no autocorrelation, normality in
the distribution of residuals), which are available in the online supple­
ment. These tests indicated no major violations of regression
assumptions.

Hypothesis 2. For bettors who experience a big win, its effect on
sports betting engagement/risk/losses will tend to diminish and/or
dissipate over time.
To test Hypothesis 2, we assessed trend differences on the five
outcome variables in the weeks beyond the subsequent weeks following
the early big win. Specifically, in addition to testing mean differences of
outcomes between big winners and their matched pairs in the week
following the big win, we used a matched pair t-test to assess mean
differences of outcomes between big winners and their matched pairs in
the second week following the big win, and repeating this up to the 24th
week (i.e., approximately 6 prototypical months) following the big win.
We graphed the Cohen’s d effect sizes (Cohen, 1988) derived from these
analyses, where the x-axis reflects the week number (starting with week
1 after the week of the big win and ending with week 24 after the week
of the big win) and the y-axis shows the Cohen’s d value for that week
number. We also indicated the weeks where the associated t-value for
each Cohen’s d was significantly greater than 0. We then examined this
graph to determine whether, for each outcome, the big win effect di­
minishes (i.e., decreased size of Cohen’s d over time) and/or dissipates
(i.e., increased likelihood of non-significant corresponding t-values over
time).

3.7. Matching filters
For conducting a census of big wins and big winners, we considered
all big wins that met the aforementioned Custer & Prize Ratio defini­
tions. For the subsequent analyses that test hypotheses, we considered:
(a) the presence of a sufficient follow-up period; and (b) the potential for
previously experienced big wins to affect one’s eligibility as a matching
control. As such, for the purpose of hypothesis testing, we considered
bettors eligible as big winners if: (a) they experienced their first big win
by the respective definition for the given week (i.e., for repeat big
winners, we only counted their first big win) and (b) they have at least
24 following weeks where they are eligible to play. We considered
bettors eligible as matched controls if: (a) they had not experienced an
initial big win by the respective definition before and during the given
week, and (b) have at least 24 following weeks where they are eligible to
play.

Hypothesis 3. Among big winners, shorter time to a big win (within a
single product domain) will be associated with more persistence (i.e.,
more months gambling consecutively during active duration) and
greater frequency (i.e., percentage of active days during active duration)
following the big win.
3.5. Persistence
To test how persistence may vary depending on how early in a bet­
tor’s experience on bwin’s sports betting platform the big win occurred,
we first constructed two new datasets. Dataset 1 comprised the subgroup
of bettors who won over €1000 in a single contest (i.e., Custer’s defi­
nition) and Dataset 2 comprised the subgroup of bettors who experi­
enced a big win based on prize ratio (i.e., Prize Ratio definition). To
measure when the big win occurred, we created a new variable in each
of the two datasets that is assigned a numeric value based on the week
number in which the big win event occurred for each respective bettor.
We then created six new variables for each bettor that correspond to
each prototypical month (i.e., four-week period) following their per­
sonal big win event. These variables were: month 1 (i.e., weeks 1–4 after
the week of the big win), month 2 (i.e., weeks 5–8 after the week of the

3.8. Sensitivity analyses
Testing for Confounding Bias. Although matched pair analysis is
intended to reduce confounding by effectively simulating a randomized
control trial, there is still potential for confounding bias because the
variables on which we match big winners to controls might not represent
all the factors that confound the relationship between experiencing a big
win and our outcome variables. Therefore, as an initial sensitivity

Computers in Human Behavior 142 (2023) 107657

analysis, we computed e-values (Haneuse, VanderWeele, & Arterburn,
2019) for each of the Cohen’s d’s we calculated for testing Hypotheses 1
and 2 in matched pair analysis. E-values help to address the concern that
observational studies cannot foreseeably control for all unmeasured
confounders. Using the effect size of interest, e-values provide a theo­
retical estimate of the amount of unmeasured residual confounding that
would be necessary to nullify said effect size of interest (Basham &
Karim, 2002). We used the R package ‘EValue’ to compute e-values,
specifically using the function evalues.MD().
In addition to e-values, we also re-ran the matched pair analysis
testing Hypothesis 2 (i.e., graphing Cohen’s d of outcome variables for
the 24 weeks following the big win), after dropping specific matched
pairs from each re-run. First, we dropped any matched pairs that con­
tained either a repeat big winner (i.e., the big winner experienced one or
more big wins of the respective definition during the 24 weeks following
the big win) OR a matched control big winner (i.e., the matched control
experienced an initial or several big wins of the respective definition
during the 24-week follow up period). Then we dropped ONLY matched
pairs that involved a repeat big winner of the respective definition.
Finally, we dropped ONLY matched pairs that involved a matched
control big winner of the respective definition. We visually compared
the revised figures from these sensitivity analyses with the main figure to
determine whether repeat big winners or matched control big winners
individually or collectively confounded the main results.
Assessing the Percentage of Matched Pairs That Support Hypotheses 1
and 2. For each of the paired t-tests we calculated for the 24 weeks
following a big win, we calculated: (1) the percentage of matched pairs
that support the hypothesis (i.e., the big winner has a higher value on the
metric than the matched control), (2) the percentage of matched pairs
that tie (i.e., the big winner has the same value on the metric as the
matched control, including zero values for weeks that neither made a
bet), and (3) the percentage of matched pairs that do not support the
hypothesis (i.e., the matched control has a higher value on the metric
than the big winner).
Fixed Effects Panel Models. Consistent with sensitivity analyses
employed by Edson et al. (2021), we estimated a set of complementary
fixed effects regression models that test the overall robustness of the
matched pair analyses (i.e., Hypotheses 1 & 2), as well as derivations of
survival analyses (Hypothesis 3) that assess the effects of grouped time
intervals (i.e., experiencing a big win either within or after a 4-week
period), with a 16-week follow up period. We estimated two deriva­
tions of the fixed effects models. As Edson et al. (2021) describe: “the
fixed effect model design allows for the removal of potential
individual-level endogenous error that is constant over time.
Fixed-effect models are commonly used in panel data sets [e.g.,
bet-by-bet gambling record data] when there is an immeasurable un­
observed effect in each individual … unlike matching, then, the fixed
effects model is still valid even if we did not measure all person-level
variables that predict having a big win” (pg. 7). First, we estimated
the fixed effects models including big winners who experienced subse­
quent big wins during the 24 weeks following the initial big win event.
Next, to assess the potential effects that multiple big winners might have
had on the overall results, we re-estimated the fixed effects models
excluding big winners who experience subsequent big wins (i.e., big
wins that occur during the 24 weeks following their initial big win). All
fixed effect models were estimated using Stata 15.
Incorporating All Gambling Activity. In addition to bet-by-bet level
sports data, for this sample of bettors we also have data for their activity
on other gambling products on bwin (i.e., casino games, poker, and
bingo) at the daily aggregate level. For our final sensitivity analysis, we
substituted pertinent outcome variables (i.e., total stake, net loss with
regards to sports betting engagement) with corresponding metrics that
account for all gambling activity available in the matched pair analyses.
Additionally, in the fixed effects analyses and survival analysis deriva­
tions, we substituted pertinent outcome and control variables (i.e., total
stake, net loss) with the weekly aggregates of these same metrics for all

gambling activity available for each bettor. We limited these analyses to
total stake and net loss outcomes because these outcomes are not specific
to sports betting (e.g., as opposed to median odds) and their values are
not dependent on product mechanics (e.g., casino betting is faster paced
than sports betting, thus bettors can rack up more bets in less time).
These revised analyses helped us to determine whether any big win ef­
fects we identified in the main analysis were attenuated or enhanced by
activity on other products outside of sports betting.
3.9. Planned exploratory analyses
Assessing the Prevalence and Effects of No Immediate Withdrawal
Following the Big Win. One of the major concerns surrounding big wins is
the tendency for bettors to continue gambling with those winnings in
order to repeat the big win experience, rather than partially re-allocating
at least some of the winnings to other activities or to one’s personal
savings (Edson et al., 2021). It follows that gamblers who intend to
continue gambling with all of their winnings would choose not to
withdraw any money immediately following the big win. Therefore, as
an added exploratory analysis, we examined the prevalence and effects
of big wins that are followed by a withdrawal soon after (i.e., within 24
hours following the win) AND in which the withdrawal is not reversed
(see Parke & Parke [2019] for more information on reverse with­
drawals) AND where the withdrawal is not accompanied by a deposit or
deposits greater than or equal to the withdrawal, within that same
24-hour period. We first calculated the count and percentage of all big
wins that occur during the study period that are followed by a with­
drawal soon after. Then, among the subsets of big winners we used for
examining Hypothesis 3, we assessed the count and prevalence of big
winners who withdrew soon after their big win. Using this same sample,
we coded “withdrew soon after” as a dummy variable and substituted
this predictor for “week of big win” into the analyses we specified for
predicting persistence and frequency outcomes for testing Hypothesis 3.
Assessing Gender and Age Effects. We ran an alternative specification
of the matched pair analyses testing Hypothesis 1 to account for the
potential interaction effects of gender and age on the big win effect. For
these analyses, we estimated a log-transformed linear regression model
with robust standard errors on the following main outcomes: total stake,
number of bets, median stake size, and median odds during the subse­
quent week. The main independent variable was big winner status
(versus matched control), and we controlled for bettor age (as of initial
registration with bwin) and gender (male vs. female). We then added
two interaction terms to each of these models: age with big winner status
and gender with big winner status.
4. Human subjects
The Cambridge Health Alliance Institutional Review Board deter­
mined that this study was exempt from IRB review because it uses sec­
ondary data.
5. Results
5.1. Descriptive analyses
A total of 27,926 big wins occurred during the approximately fiveyear study period. There were 22,688 (81.2% of all big wins) that met
only the Prize Ratio criterion, 514 (1.8%) that met both criteria, and
4724 (16.9%) that met only Custer’s criterion. Out of the 36,328 bettors
in our analytic sample, 9393 (25.9%) experienced at least one big win by
either definition. The vast majority of the big winners (9105 bettors,
97.0% of big winners, 25.1% of all players) experienced at least one
Prize Ratio big win. Bettors who experienced at least one Custer big win
were rare (709 bettors, 7.5% of big winners, 2.0% of all players).
In all, 5238 big wins met the Custer definition (prize of 1000 euros or
more). Of these, 1663 (31.7%) were associated with combo bets (bets

Computers in Human Behavior 142 (2023) 107657

median odds of bets associated with Custer big wins was 2.0 (i.e., pays
even money, that is, winnings include both the stake size and the
refunded stake itself), and the median stake size was 800 euros.
In all, 23,202 big wins met the Prize Ratio definition (top 1% of Prize
Ratio among all bets placed). Of these, the vast majority (16,322, 70.3%)
were associated with combo bets or system bets, and a minority (5,581,
24.1%) were associated with an in-game bet. The median odds of bets
associated with Prize Ratio big wins was 10.88 (i.e., pays approximately
11:1), and the median stake size was 5 euros.

associated with multiple propositions, where all propositions need to
win in order to win the bet, also known as parlays) or system bets (i.e.,
bets associated with multiple propositions, where only some proposi­
tions, or specific combinations, need to win in order to win the bet). The
remainder were associated with single bets. The majority of Custer big
wins (3,619, 69.1%) were associated with an in-game (a.k.a., liveaction) bet, where a proposition can only be selected once a contest
begins and whose odds can change throughout the contest. The
remainder were associated with pre-match (aka, fixed-odds) bets. The

Fig. 1. Cohen’s d standardized effect sizes (bets, total stake, net loss, median stake size) for the 24 weeks following a big win for both big win definitions (notes:
Cohen’s d’s with corresponding t-values that are non-significant (i.e., p greater than or equal to 0.05) are censored from these trendlines and thus are not displayed;
graphing lines denote adjacent time points that are both significant, to further illustrate any instances of robustness to deterioration effects; median odds was
excluded because subsequent week analyses [Hypothesis 1] were not supported for this outcome).

Computers in Human Behavior 142 (2023) 107657

The minimum qualifying Prize Ratio threshold (as a reminder, unlike
betting odds, this is based on the largest wager placed up to that bet, not
the wager of the bet) was 3.7 X the wager (25%: 4.3X, Median: 5.5X,
75%: 8.2X, Max: 2912.9X). Considering only Prize Ratio big wins
experienced by Prize Ratio big winners in the matched sample, the fivenumber summary of Prize Ratio for these wins is as follows: (Min: 3.7X,
25%: 4.3X, Median: 5.5X, 75%: 8.2X, Max: 635.9X). To put these
numbers in perspective, the five number summary of Prize Ratio for all
winning bets that occurred during the two-year study period is as fol­
lows: (Min: 0.00001X, 25%: .1X, Median: .2X, 75%: .6X, Max: 2912.9X).

0.36). As with Custer big winners, Prize ratio big winners did not
significantly differ from matched controls on median odds (Mean
[SD]BW = 70.72297.5]; Mean [SD]MC = 102.1 [2652.4]; t [692] = 1.3, p
= .20) during the week following the big win event.
5.2.2. Assessing the diminishing/deterioration effect of big wins in sports
betting over time
Fig. 1 contains plots of Cohen’s d’s derived from each of the matched
pairs t-tests between big winners and matched controls for the four
outcomes that were significant in subsequent week analysis (i.e., we
excluded the median odds outcome due to the absence of an initial Big
Win effect), across the 24 weeks following the big win event. For number
of bets across Prize Ratio matched pairs, we observed just a diminishing
effect (i.e., long-term decreasing value of Cohen’s d over time). For
number of bets and net loss across Custer matched pairs, we observed
just a deterioration effect (i.e., increased likelihood/frequency of nonsignificant underlying t-tests over time). For the remaining outcomes
for both matched pair groups (Custer and Prize Ratio), we observed both
a diminishing and deterioration effect. Notably, Custer big wins elicited
the strongest overall effect size (for median stake size during week 1)
whereas Prize Ratio big wins had the most consistent significant effect (i.
e., longest tail; for number of bets).

5.2. Confirmatory analyses
5.2.1. Examining the effects of big wins on immediate subsequent sports
betting engagement and risky behavior
During the week following the big win, compared to matched con­
trols, Custer big winners in the matched sample (N = 693) placed more
bets (Mean [SD]BW = 33.8 [115.6]; Mean [SD]MC = 18.5 [54.8]; t [692]
= 3.3, p < .05; Cohend = 0.40), staked more money (Mean [SD]BW =
2211.8 [5444.7]; Mean [SD]MC = 451.5 [1434.3]; t [692] = 8.6, p < .05;
Cohend = 0.47), experienced greater net loss (Mean [SD]BW = 159.0
[1064.5]; Mean [SD]MC = 35.4 [211.1]; t [692] = 3.0, p < .05; Cohend =
0.17) and had a higher median stake size (Mean [SD]BW = 71.4 [156.2];
Mean [SD]MC = 18.0 [37.0]; t [692] = 8.9, p < .05; Cohend = 0.53).
Custer big winners did not significantly differ from matched controls on
median betting odds (Mean [SD]BW = 100.2 [779.0]; Mean [SD]MC =
121.6 [1633.1]; t [692] = 0.3, p = .75) during the week following the big
win event.
Compared to matched controls during the week following the big
win, Prize Ratio big winners in the matched sample (N = 9024) placed
more bets (Mean [SD]BW = 20.1 [51.7]; Mean [SD]MC = 8.5 [25.4]; t
[692] = 19.9, p < .05; Cohend = 0.47), staked more money (Mean
[SD]BW = 166.0 [976.0]; Mean [SD]MC = 85.7 [699.6]; t [692] = 6.7, p
< .05; Cohend = 0.21), experienced greater net loss (Mean [SD]BW =
22.1 [333.7]; Mean [SD]MC = 7.7 [103.6]; t [692] = 4.0, p < .05;
Cohend = 0.08) and had a higher median stake size (Mean [SD]BW = 6.5
[21.8]; Mean [SD]MC = 5.3 [21.4]; t [692] = 3.7, p < .05; Cohend =

5.2.3. Assessing the relevance of the timing of big wins on subsequent sports
betting engagement
Custer big winners (n = 693) and Prize Ratio big winners (n = 9074)
had similar rates of persistence during the 6 months following the big
win event (Fig. 2). Compared to their matched controls, Custer big
winners had elevated persistence during only month two, while Prize
Ratio big winners had elevated persistence compared to matched con­
trols for all six months. In a Cox Proportional Hazard analysis modeling
persistence, the week of a big win had an extremely small, albeit sig­
nificant, negative effect on the hazard function for both Custer big
winners (Hazard Ratio [HR] = 0.996, 95% CI = [0.995, 0.997]) and
Prize Ratio big winners (HR = 0.9988, 95% CI = [0.9983, 0.9992]).
These significant effects remain after controlling for players’ frequency
of play and stake per day in the weeks leading up to, and including the

Fig. 2. Kaplan–Meier survival curve of persistence among Custer big winners (n = 693), Custer matched controls (n = 693), Prize Ratio big winners (n = 9074), and
Prize Ratio matched controls (n = 9074).

Computers in Human Behavior 142 (2023) 107657

week of the big win, as well as bettor gender and age, for both Custer big
winners (HR = 0.997, 95% CI = [0.995, 0.998]) and Prize Ratio big
winners (HR = 0.9993, 95% CI = [0.9988, 0.9998]).
Similarly, linear regression models indicated that week of the big win
had a small negative effect on frequency of play for Prize Ratio big
winners (b = − 0.06, β = − 0.10, SE = 0.007, p < .05). The effect of week
on the big win on frequency of play for Custer big winners was not
significant (b = − 0.00, β = − 0.10, SE = 0.015, p = .932). Moreover, the
effect of week of the big win on frequency of play for Prize Ratio big
winners became non-significant after accounting for frequency of play
and stake per day in the weeks leading up to and including the week of
the big win, as well as bettor gender and age (b = − 0.01, β = − 0.01, SE
= 0.008, p = .27).

models also control for cumulative net loss. A Custer big win is associ­
ated with a $4866 increase in the next week’s stakes, a $387 increase in
net loss, and a 31 unit increase in the number of bets. A Prize Ratio big
win is associated with a $176 increase in stakes, a $27 increase in net
loss, and a 22 unit increase in bets. We find similar effects on median
stake size and weak effects of big wins on median odds levels. The Custer
big win is statistically significant at the α = 0.05 level, but the model
shows poor goodness-of-fit. The Prize Ratio big win has no statistically
significant effect on median odds.
To validate our findings related to Hypothesis 2, we fit fixed-effect
regression models similar to those above but added lagged big win
variables of up to 16 weeks. We find that effects generally are statisti­
cally significant throughout the period, but the size of the coefficients
and the standard errors generally appear to decay over time. The only
persistent effect is the impact of Prize Ratio big wins on number of bets,
which shows a statistically significant effect in all 16-week lag effects.
To test the robustness of our findings related to Hypothesis 3, we
estimated a set of Kaplan-Meier survivor functions and a set of Cox
Proportional Hazard Models that differ from our main analyses specif­
ically in terms of how the timing of early/late big wins is measured.
Instead of a numeric “week number” predictor, these analyses collapse it
into two categories of “early” (within four weeks) and “later” (after four
weeks). The Kaplan-Meier survivor functions estimate the likelihood
that an individual account would become dormant. In these analyses, we
find that big wins extend the survival function, but that early big wins
(within the first four weeks of account opening) have smaller impacts
than later big wins, which contrasts with our main survival analyses.
Unlike the matched pair analysis, the fixed-effect analysis cannot correct
for survivorship bias in comparing early big wins to later big wins.
Similar to our Kaplan-Meier modeling, we regress our big win vari­
ables on the length of account activity in weeks. We find evidence
supporting the impact of big wins on activity length. For example, in one
model a big win at some point in the player’s experience on the site is
related to a 60% reduction in the probability of observing a final week of
activity in any given period. Again, we observe that the net effect size is
larger for big wins occurring after the first four weeks of play, rather
than during that period.

5.2.4. Planned sensitivity analyses
The full results of the sensitivity analyses, including all graphs and
tables, are available in the online supplement. Here we provide a sum­
mary of each:
The median e-values for Custer big matched pairs during the 24week follow-up period were 1.7 for Custer matched pairs and 1.3 for
Prize Ratio matched pairs. The maximum e-values (2.6 and 2.4 for
Custer and Prize Ratio big winners respectively) both fell on Week 1. The
consistently high e-values we observed suggest that our matched pairs
test results were robust.
Upon examination of the revised Cohen’s d graphs, after removing
matching cases where either big winner or matched control experienced
an additional/initial big win, we observed that the big win effect (Week
1) gets stronger for the net loss outcome, for both Prize Ratio and Custer
matched pairs. In contrast, for total stake, the big win effect during Week
1 disappears for Prize Ratio matched pairs and becomes weaker for
Custer matched pairs. After removing matching cases where just big
winners experience another big win, the big win effect disappears for the
number of bets outcome for Custer matched pairs, while the big win
effect becomes slightly stronger for the net loss outcome for both Custer
and Prize Ratio matched pairs, and for all outcomes the dissipation effect
happens more quickly. Finally, after removing matching cases where
just matched pairs experienced an initial big win during the 24-week
follow-up period, there appears to be little change in the results, with
a single exception: the dissipation effect of prize ratio big wins on me­
dian stake size does not happen as quickly among Prize Ratio matched
pairs.
An examination of the percentage of matched pairs that support
Hypotheses 1 and 2 revealed some unique insights on the potential
timings for how long the big win effect tends to last (see Supplementary
Materials). For all outcomes, the point of convergence (i.e., the point
where the percentage of cases in which big winners and matched con­
trols are equal (i.e., tie) on the raw metric begins to exceed the per­
centage of cases in which big winners are greater than matched controls
on the raw metric) is at approximately Week 4 for Prize Ratio matched
pairs and somewhere between Week 6 or 7 for Custer matched pairs.
Finally, after re-running confirmatory hypothesis tests for the total
stake and net loss outcomes, and taking into account the effects of big
wins on all gambling activity (casino games, poker, and bingo, in
addition to sportsbook) related to these outcomes, we observed that the
big win effect on total stake disappears during Week 1 for Prize Ratio
matched pairs, and becomes noticeably weaker for Custer matched pairs
(in terms of size of Cohen’s d). However, for net loss, the big win effect
on Week 1 remains and becomes noticeably stronger for both big win
definitions on the net loss outcome, although its effect appears to
dissipate and/or deteriorate more quickly afterward.
We estimated a set of fixed-effect and random-effect models that
assess the impact of the Custer and Prize Ratio big wins on our outcome
variables. As in our matched pair analysis, we use weeks since the first
bet as our unit of time and account IDs as our panel variable. In all our
models, we find statistically significant and economically meaningful
effect sizes from big wins on weekly stakes, net loss, and bets. Our

5.2.5. Planned exploratory analyses
Out of the 5238 Custer big wins that occurred during the study
period, 1004 of them (19.2%) involved the big winner net withdrawing
(i.e., withdrawal[s] exceeds deposit[s]) within 24 hours. Out of the
23,202 Prize Ratio big wins that occurred during the study period, 447
of them (1.9%) involved the big winner net withdrawing within 24
hours. Among the matched pair sample of Custer big winners (n = 693),
200 of them (28.8%) net withdrew within 24 hours of the big win.
Among the matched pair sample of Prize Ratio big winners (n = 9074),
88 of them (0.97%) net withdrew within 24 hours of the big win. Ac­
counting for frequency of play and stake per day in the weeks leading up
to, and including the week of the big win, as well as bettor gender and
age, net withdrawing after the big win had a substantial negative effect
on persistence for Prize Ratio big wins (HR = 0.57, 95% CI = [0.46,
0.70]) but no significant effect on persistence for Custer big wins (HR =
1.00, 95% CI = [0.85, 1.18]). Accounting for frequency of play and stake
per day in the weeks leading up to, and including the week of the big
win, as well as bettor gender and age, net withdrawing did not have a
statistically significant effect on frequency of play for either Custer big
winners (b = − 0.95, β = − 0.01, SE = 2.48, p = .703) or Prize Ratio big
winners (b = 3.6, β = 0.10, SE = 3.34, p = .279).
Finally, upon estimating log transformed linear regression models
with robust standard errors on each of the main outcomes (excluding net
loss) during Week 1, we did not detect any interaction effects between
big winner status and age or between big winner status and gender that
were significant at p < .05.

Computers in Human Behavior 142 (2023) 107657

6. Discussion

handful of potential cognitive mechanisms and social/behavioral ef­
fects. One of these is that, following a big win, bettors now have more
money with which to gamble, and consumption generally increases with
gains in wealth, consistent with the wealth effect (Mehra, 2001). Several
explanations from cognitive and behavioral psychology might also
explain increased engagement following a big win. Specifically, big win
effects could result from several cognitive biases or distortions (Granero
et al., 2020; Ledgerwood et al., 2020) experienced by players such as the
availability heuristic (Fortune & Goodie, 2012), representative heuristic
(Tversky & Kahneman, 1971), house money effect (Thaler & Johnson,
1990), “hot hand” effect (Gilovich, Vallone, & Tversky, 1985), and
insensitivity to small sample sizes (Leonard & Williams, 2016), which
make the odds of experiencing a big win seem far better than they
actually are and also could lead to big winners to attribute their big win
to skill over luck. Sports betting contains some degree of skill (Trippiedi,
2014); however, the scant probability of consistently winning and an
even lower probability of winning big suggests that luck plays a more
dominant role. Yet, studies have shown that gambling winners often
attribute their success to their own skill or ability (i.e., the illusion of
control), instead of chance (Myrseth, Brunborg, & Eidem, 2010; Zhou
et al., 2012).
A second explanation, drawn from behavioral psychology, is focused
on the operant conditioning (Skinner, 1963) process that occurs when a
gambler experiences winning, leading to reinforcement of betting
behavior, and thus more sustained or persistent gambling to seek
another win. Although much of the literature on operant conditioning
has focused on within-session behavior with well-documented effects of
wins on future reinforcement of gambling behavior in experimental
studies (see Barton et al., 2017; Leino et al., 2016), discussion of
between-session or longer-term reinforcement processes in the litera­
ture, like we see here, is comparably rare (e.g., Redish, Jensen, Johnson,
& Kurth-Nelson, 2007).
Given that we do not have access to psychometric measures on
participant cognitive distortions or biases, or the extent of operant
conditioning, we cannot directly test these potential explanations for big
wins effects empirically, other than to suggest that they could be playing
a role in explaining the effects of big wins on future online sports betting
engagement.

Using actual digital betting record data from a large sample of online
sports bettors (N = 36,328) from a large European gambling operator,
we assessed the effects of big wins on future sports betting engagement,
losses, and risk. In addition to replicating Edson and colleagues’ (2021)
original analyses of big wins in DFS, we also expanded upon their work
by examining additional outcomes (i.e., risk metrics — median betting
odds and median stake size) as well as conducting additional novel
exploratory analyses (e.g., assessing the prevalence/effects of big wins
followed by a withdrawal soon after) and sensitivity analyses (e.g.,
calculating e-values). The present study represents an important
extension of this original work and is one of the first to assess the big win
effect among actual online sports gamblers with prospective gambling
record data.
6.1. Key findings
We found that experiencing a big win was associated with increased
engagement initially, with little impact beyond an approximately fourweek period. These results were robust in both the main matched pair
analyses and fixed effects sensitivity analyses, suggesting that our results
are not contingent on the modeling approach. Additional sensitivity
analyses that excluded matched pairs involving multiple big winners
and incorporated betting activity from other products (i.e., casino,
poker, and bingo) also revealed very similar findings, again strength­
ening the evidence for the presence of a big win effect in the domain of
sports betting based on actual behavioral data. Moreover, we saw sig­
nificant effects for both definitions of big win (Custer and Prize Ratio).
Here we reiterate Edson et al.’s (2021) conclusion that the two defini­
tions “are likely tapping different dimensions of ‘big.’ Specifically,
whereas the Custer definition might represent an absolute or objective
measure of ‘big,’ the Prize Ratio definition could represent a measure of
‘big’ that is more subjective and relative to an individual’s traditional
wager size” (p. 10). In sports betting, we find that different betting be­
haviors might lead a bettor to one definition. Specifically, large stake
bettors who play short odds are more likely to experience a Custer big
win, while low-stakes long-odds bettors are more likely to experience a
Prize Ratio big win.
However, although the pathways to these definitions of big win
might differ, their effects on future engagement and losses remain
similar. There were some notable differences. Custer big wins exhibited
greater magnitude of effects on absolute stake and net loss (see Fig. 1),
which is likely the result of individuals who experience Custer big wins
already betting at greater magnitudes of play. Prize ratio big wins, on the
other hand, appear to have a longer lasting effect on general engagement
behaviors, namely number of bets (see Fig. 1) and persistence (see
Fig. 2). On the whole, we believe both of these definitions hold unique
value, and deserve consideration from stakeholders and in future in­
vestigations of big wins.
These findings on big wins and subsequent increased engagement
generally replicate those found for big wins in DFS by Edson et al.
(2021), which suggests the big win effect is not particular to any one
form of wagering. Overall, we interpret these similarities as resulting
from product features inherent in DFS and online sports betting, as well
as potential cognitive states and traits of the players themselves (e.g.,
perceived knowledge about sporting outcomes) that are similar in these
gaming formats. DFS and online sports betting both have a wide variety
of sporting contests to bet on each day at a variety of levels of stakes, so
big winners have a wide variety of betting opportunities to wager on
following their big win. Both products also use a built-in withdrawal and
deposit account that displays individuals’ overall funds available for
gambling, so a large influx of money from the big win would be clearly
visible to them, making them aware of their larger bankroll, and the bets
that they could place with it.
That big win effects appear to decline over time gives credence to a

6.2. Differences between online sports betting and DFS
We observed three important differences between our findings and
the DFS findings reported in Edson et al. (2021). First, while we found
weak evidence for an early big win effect in the matched pair analyses of
this study, Edson and colleagues (in their matched pair analyses)
observed weak evidence for a late big win effect. That is, big wins that
happen later on in DFS, within a single product domain, tended to have a
stronger effect on increased engagement compared to earlier wins,
although like this study the effect size they observed was very small. The
fixed effect sensitivity analyses we conducted in this study also suggest
that earlier big wins (i.e., within the first 4 weeks) elicit a weaker effect
than later big wins (i.e., after 4 weeks) on continued engagement. We
have no clear explanation for these differences between the matched
pair and fixed effect sensitivity analyses in this area, although slight
differences in methodology (e.g., week number was treated as a numeric
predictor in matched pair analysis, while the fixed effect analyses
treated “early” and “later” big wins as categorical predictors separated
by a slightly arbitrary four-week threshold) could explain the conflicting
results. Overall, we interpret this inconsistency as a potential sign that
the effect of the timing of big wins (at least within a single product
domain) is probably of lesser importance. Future research should focus
on the timing of big wins over an individual’s entire life course, in
addition to within-product timing.
Second, Custer big wins were rarer in this study (i.e., 7.5% of big
winners experienced at least one Custer big win) than Edson and col­
league’s DFS study (i.e., 44.2% of DFS big winners experienced a Custer

Computers in Human Behavior 142 (2023) 107657

big win). On a similar note, prize ratios in Edson et al.’s DFS study
tended to be much higher (median of 20X) than the ratios of Prize Ratio
big wins in this study (median of 5.5X). We attribute both of these dif­
ferences to the differential play mechanics of DFS and sports betting. In
DFS, the headliner contests that tend to yield extremely large prizes are
always guaranteed to have a (big) winner. In sports betting, big wins
result only from short-odds/large stake bets or long odds bets (e.g.,
multi-prop parlays and large system bets such as “goliaths”), with none
of these bets guaranteed to win. On one hand, we expect most in­
dividuals to either be hesitant or flat out not have the ability to risk 800
euros (the median stake size of a Custer big win) on a single bet. On the
other hand, bets with long odds (e.g., multi-prop parlays, large system
bets such as “goliaths”) are extremely unlikely to pay off. Between the
two sides, compared to DFS, we can expect a lower prevalence of Custer
big wins and a lower threshold for what constitutes a Prize Ratio big win
in online sports betting.
Third and finally, the effects of big wins on net loss slightly differed
between the two products. In Edson et al.’s DFS study, while big wins
had a positive effect on net loss among all matched pairs (main analyses)
and all big winners (fixed-effects analyses), this effect disappeared when
repeat big winners (presumed to be more professional players) and their
matched pairs were removed from those analyses. This suggests that a
big win’s effect on subsequent losses in DFS was only confined to players
for whom the big win was not a sign of greater skill. In this study, the
positive effect of big wins on net losses in sports betting remained even
though we initially included matched pairs and big winners who expe­
rienced several big wins. The effect of big wins on net loss became
stronger when we removed matched pairs where the big winner had
subsequent big wins during the 24-week follow-up period, suggesting
that the inclusion of skilled players had some effect on the main results.
Even still, their inclusion did not remove the significant effect of big
wins on net loss. This difference suggests that, compared with DFS, for
which big wins in many cases might be a sign of actual skill, big wins in
sports betting could be more so related to luck. If this is the case, it could
potentially lead sports bettors, in particular, to misattribute their win­
nings to perceived skill and bet more money in order to replicate their
past results, which could in more cases than not lead to mounting
demoralizing losses. It should be noted in this study we did not fully test
the latter assertion – whether big winners, more often than not, expe­
rience net losses that deplete their initial big win and lead them deeper
into a state of net loss – future research can and should test this assertion.

bet on sports alike. First, operators should consider tools to promote
responsible gambling (RG) and player safety that are deployed after a
player experiences a big win by either definition. This proactive RG
approach might include emails, push notifications and/or site pop ups
that inform the player of their big win with links to RG resources, a
recommendation to withdraw at least some of their winnings to their
bank account, and/or personalized normative messaging (e.g., “Most
people who win big save some of it for later, have you considered saving
or investing your winnings?“), which has been shown to be effective in
curbing excessive gambling (Celio & Lisman, 2014; see a review on
normative messaging in Saxton, Rodda, Booth, Merkouris, & Dowling,
2021). Recommendations to withdraw at least some of the big win could
be particularly effective for promoting responsible gambling, given ev­
idence from the present study, which shows that: (1) most big winners,
left to their own devices, choose not to immediately withdraw their big
win, (2) continued engagement following a big win tends to result in net
losses, and (3) immediate withdrawals following a prize ratio big win
tends to lead to less persistent play. Future research should consider
testing the efficacy of this type of messaging, and its effects on with­
drawal behavior and engagement following a big win.
Second, additional steps that operators could take after a player gets
a big win might include advising players of the actual odds of winning
(e.g., see Gainsbury, Abarbanel, Philander, & Butler, 2018) and making
it clear that luck plays a large role in determining winning (even in
skill-based products), and especially in winning big. Such an approach
would help to clarify the role that chance plays in big wins, thus
potentially reducing false confidence or cognitive distortions regarding
the outsized role of skill in determining sports betting outcomes.
6.4. Study limitations
Our study is not without limitations. First, to be consistent with longstanding clinical observations about the magnitude of big wins (Custer,
1984; Custer & Milt, 1985; Kassinove & Schare, 2001) and recent
empirical research on big wins (e.g., Edson et al., 2021), we selected the
1000 euro threshold for the Custer definition and the top 1% of prize
ratios for the prize ratio definition. Other researchers might identify or
select different big win thresholds, and therefore might reach different
conclusions than those we arrived at in this study.
Second, the intent of this study was to test the popular assertion that
there exists an arbitrary threshold by which a sports gambling win is
large enough to have a large effect on subsequent behavior. However,
there exists the possibility that wins, more generally, have a linear effect
on subsequent behavior that is roughly proportional to their size. More
research is needed to test this assertion, which would call into question
whether there truly is a “big win” effect, rather than just a “win effect”.
Third, our basic description of the median stakes and median odds of
both Custer and Prize Ratio big wins (see beginning of the Results sec­
tion) indicates that big wins of both definitions derive from only certain
types of bets (i.e., high stakes bets for Custer big wins and long odds bets
for Prize Ratio big wins). Unlike gambling products where single actions
have multiple possible payout-to-stake ratios (e.g., lotteries and scratch
tickets, EGMs, poker tournaments), sports bets typically have only two:
zero and the one where the gambler wins. In order for a typical sports
bettor to have a chance of a big win, they either have to bet a large
amount or pick a bet with long odds. In this study, although we matched
big winners with controls with similar median stake sizes and betting
odds, and controlled for these variables in fixed-effects analysis, in at
least some cases it is possible that we could have been comparing people
with big wins to people who never gave themselves a chance to have a
big win. At the very least, our matched pairs analyses in particular might
have systematically excluded individuals who play at low stakes and
betting odds — meaning the results of this study could potentially
represent the big win effect on future engagement among sports bettors
trying for big wins, rather than sports bettors more generally.
Fourth, our betting account data are from only one online sports

6.3. Theoretical and practical implications
Early evidence from clinicians such as Custer (1984) and contem­
porary clinical reports (Davies, 2022) suggest that big wins, particularly
those that occur early on in the gambling experience, serve as precursors
to increased gambling and the development of gambling problems. This
study was supportive of the first part of this assertion, namely that big
wins have an effect on future engagement, losses, and risk in online
sports betting. This study—like a previous study of big wins in DFS by
Edson et al. (2021)—did not find strong evidence for an early big win
effect, insofar as early big wins kept bettors active, but for no more
weeks than it would have at any other point in time. A potential reason
we, along with the previous DFS study, observed these null findings
could be due to design limitations inherent to both – specifically, only
being able to examine the timing of big wins within the confines of single
product and operator domains. The combined findings of that study, and
our own, suggests that any early big win effects within single product
and operator domains are either weak or non-existent. It remains
possible that early big wins (i.e., true early and formative gambling
experiences) are more meaningful than later ones, however without
access to an individual’s entire gambling history, this will be difficult to
tease out and assess.
Our findings can help to inform evidence-based recommendations
and have practical implications for gambling operators and people who

Computers in Human Behavior 142 (2023) 107657

betting provider, so it is possible that the players in our sample also had
accounts and/or played with other operators. This might have limited
our ability to potentially capture “early” big wins for individuals who
had been gambling extensively before engaging in online sports betting
on bwin, or who might have experienced a big win on another operator’s
website during the study period. Bettors also could have changed their
level of engagement with other Internet and land-based gambling op­
erators. However, we were only able to monitor changes in playing
behavior with the single operator described here. Although it would be
very difficult to coordinate with multiple gambling operators to obtain
betting account data for the same individuals, future studies should seek
to obtain account data from more than one operator to assess big wins
and engagement on more than one gambling platform.
Finally, this study did not include a measure of problem gambling to
assess the relationship between experiencing a big win and problem
gambling, which represents an important direction for future research
on big wins in sports betting, as well as big wins in gambling more
generally. Because bettors generally cannot easily recall gambling ex­
penditures (Braverman et al., 2014; Heirene et al., 2021), we strongly
recommend the continued use of actual gambling data based on betting
records to examine big wins — however, we also recommend that this
future research consider linking gambling data to self-report outcomes
that include a problem gambling measure.

This research was supported by a research contract between the
Division on Addiction and Entain, PLC (Entain). Entain is a major Eu­
ropean provider of online and land-based gambling products, inlcuding
bwin. Entain had no involvement with the development of our research
questions or protocol. They did not see any associated materials while
the study was in progress or do not have any editorial rights to any
resulting manuscripts. Entain communication about this work requires
approval by the Division on Addiction.

receiving funding from DraftKings, Inc., a sports betting and gaming
company; Entain PLC (formally GVC Holdings PLC), a sports betting and
gambling company; EPIC Risk Management; Foundation for Advancing
Alcohol Responsibility, a not-for-profit organization founded and fun­
ded by a group of distillers; Massachusetts Department of Public Health,
Office of Problem Gambling Services via Health Resources in Action;
National Institutes of Health (National Institute of General Medical
Sciences and National Institute on Drug Abuse) via The Healing Lodge of
the Seven Nations; and Substance Abuse and Mental Health Services
Administration via the Addiction Treatment Center of New England.
During the past five years, the Division on Addiction has also
received funding from the David H. Bor Library Fund, Cambridge Health
Alliance; Fenway Community Health Center, Inc.; Greater Boston
Council on Alcoholism; Integrated Center on Addiction Prevention and
Treatment of the Tung Wah Group of Hospitals, Hong Kong; Massa­
chusetts Department of Public Health, Bureau of Substance Addiction
Services; Massachusetts Department of Public Health, Bureau of Sub­
stance Addiction Services via St. Francis House; the Massachusetts
Gaming Commission, Commonwealth of Massachusetts; MGM Resorts
International via the University of Nevada, Las Vegas; and Substance
Abuse and Mental Health Services Administration via the Gavin
Foundation.
During the past five years, Timothy C. Edson has provided paid
consulting services on responsible gambling programs for Premier Lot­
teries Ireland, the operator of the National Lottery of the Republic of
Ireland.
During the past five years, Eric R. Louderback has received research
funding from a grant issued by the National Science Foundation (NSF), a
government agency based in the United States. His research has been
financially supported by a Dean’s Research Fellowship from the Uni­
versity of Miami College of Arts & Sciences, who also provided funds to
present at academic conferences. He has received travel support funds
from the Hebrew University of Jerusalem to present research findings
and has also provided paid consulting services on responsible gambling
programs for Premier Lotteries Ireland, the operator of the National
Lottery of the Republic of Ireland.
During the past five years, Matthew A. Tom received an honorarium
and travel funds from the International Center for Responsible Gambling
(ICRG).
During the past five years, Kahlil S. Philander has received research
funds from the Washington State Gaming Commission, Manitoba
Gambling Research Program, UNLV International Center for Gaming
Regulation, U.S.-Japan Business Council, Wynn Resorts, Board of Re­
gents of the Nevada System of Higher Education. He has received
consulting payments from British Columbia Lottery Corporation, Eilers
& Krejcik Gaming, Seminole Hard Rock Entertainment Inc., Responsible
Gambling Council of Canada, the Commonwealth of The Bahamas, West
Virginia Lottery, Indiana Gaming Commission, Intralot, and iDevelop­
ment and Economic Association. He has received expert witness pay­
ments from Crown Resorts Ltd, Jones Ward PLC, and Scientific Games
Corp.
John M. Slabczynski has no financial disclosures or conflicts of in­
terest to declare.
Taylor G. Lee has no financial disclosures or conflicts of interest to
declare.
During the past five years, Debi A. LaPlante has received speaker
honoraria and travel support from the National Center for Responsible
Gaming (NCRG) and the National Collegiate Athletic Association. She
has served as a paid grant reviewer for NCRG and received honoraria
funds for preparation of a book chapter from Universitée Laval. She is a
non-paid board member of the New Hampshire Council on Problem
Gambling.

Five-year funding disclosures

Data availability

6.5. Conclusion and future directions
We found that big wins in online sports betting predict increased
engagement and losses, and risk in subsequent weeks, with diminishing
effects that ultimately dissipate after approximately four weeks. These
findings were true for two unique definitions of “big win”: Custer and
Prize Ratio. This work shows that the nuances of gambling are evident
through exhaustive examination of player records for research purposes.
The findings diverge from popular conceptions of big wins and their
influence on players. While fields of science might rely heavily on such
conventional wisdom in their infancy, doing so perpetually might
imperil the development of appropriate prevention and intervention
efforts. Yet, to fully understand the big win effect, it appears that mul­
tiple lines of evidence, from lived experience, tightly controlled scien­
tific experiments, and ecologically valid data sources are needed to come
together for comprehensive understanding of this phenomenon.
Author credit
Timothy C. Edson played a lead role in formal analysis (matched pair
and most exploratory and sensitivity analyses), supervision, writing,
conceptualization, methodology and project administration. Kahlil S.
Philander played a supporting role in formal analysis (fixed effects
sensitivity analysis), methodology, conceptualization, and writing.
Matthew A. Tom, Eric R. Louderback, Taylor G. Lee, John M. Slabc­
zynski, and Debi A. LaPlante played a supporting role in conceptuali­
zation, methodology, and writing.
Funding statement

The data that support the findings of this study are available from the

When this article was published, the Division on Addiction was

Computers in Human Behavior 142 (2023) 107657

corresponding author, upon reasonable request.

Ledgerwood, D. M., Dyshniku, F., McCarthy, J. E., Ostojic-Aitkens, D., Forfitt, J., &
Rumble, S. C. (2020). Gambling-related cognitive distortions in residential treatment
for gambling disorder. Journal of Gambling Studies, 36(2), 669–683.
Legal Sports Report. (2020). Legislative tracker: Sports betting. https://www.legalsportsre
port.com/sportsbetting-bill-tracker/.
Leino, T., Torsheim, T., Pallesen, S., Blaszczynski, A., Sagoe, D., & Molde, H. (2016). An
empirical real-world study of losses disguised as wins in electronic gaming machines.
International Gambling Studies, 16(3), 470–480.
Leonard, C. A., & Williams, R. J. (2016). The relationship between gambling fallacies and
problem gambling. Psychology of Addictive Behaviors, 30(6), 694.
Madden, G. J., Petry, N. M., & Johnson, P. S. (2009). Pathological gamblers discount
probabilistic rewards less steeply than matched controls. Experimental and Clinical
Psychopharmacology, 17(5), 283–290.
McAuliffe, W. H., Louderback, E. R., Edson, T. C., LaPlante, D. A., & Nelson, S. E. (2022).
Using “markers of harm” to track risky gambling in two cohorts of online sports
bettors. Journal of Gambling Studies, 1–33. https://doi.org/10.1007/s10899-02110097-0
Mehra, Y. P. (2001). The wealth effect in empirical life-cycle aggregate consumption
equations. FRB Richmond Economic Quarterly, 87(2), 45–68.
Merrett, F. (2006). Reflections on the Hawthorne effect. Educational Psychology, 26(1),
143–146.
Moore, D. S., McCabe, G. P., & Craig, B. A. (2009). Introduction to the practice of statistics
(6th ed.). New York: W.H. Freeman and Company.
Myrseth, H., Brunborg, G. S., & Eidem, M. (2010). Differences in cognitive distortions
between pathological and non-pathological gamblers with preferences for chance or
skill games. Journal of Gambling Studies, 26(4), 561–569.
National Gambling Treatment Service. (2021). Annual statistics from the national gambling
treatment service. November 30. 1st April 2020 to 31st March 2021 https://www.bega
mbleaware.org/sites/default/files/2021-11/FINAL_GA_Annual%20stats_report_
2020-21_English.pdf.
Nelson, S. E., Edson, T. C., Louderback, E. R., Tom, M. A., Grossman, A., & LaPlante, D. A.
(2021). Changes to the playing field: A contemporary study of actual European
online sports betting. Journal of Behavioral Addictions, 10(3), 396–411.
Parke, A., & Parke, J. (2019). Transformation of sports betting into a rapid and
continuous gambling activity: A grounded theoretical investigation of problem
sports betting in online settings. International Journal of Mental Health and Addiction,
17(6), 1340–1359.
Pickering, D., & Blaszczynski, A. (2021). Paid online convenience samples in gambling
studies: Questionable data quality. International Gambling Studies, 21(3), 516–536.
R Core Team. (2022). R: A language and environment for statistical computing. Vienna,
Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Redish, D., Jensen, S., Johnson, A., & Kurth-Nelson, Z. (2007). Reconciling reinforcement
learning models with behavioral extinction and renewal: Implications for addiction,
relapse, and problem gambling. Psychological Review, 114(3), 784–805.
Rockloff, M. J., & Hing, N. (2013). The impact of jackpots on EGM gambling behavior: A
review. Journal of Gambling Studies, 29(4), 775–790.
Roethlisberger, F. J., & Dickson, W. J. (1939). Management and the worker. Harvard Univ.
Press.
Saxton, J., Rodda, S. N., Booth, N., Merkouris, S. S., & Dowling, N. A. (2021). The
efficacy of personalized normative feedback interventions across addictions: A
systematic review and meta-analysis. PLoS One, 16(4), Article e0248262.
Shah, B. R., Laupacis, A., Hux, J. E., & Austin, P. C. (2005). Propensity score methods
gave similar results to traditional regression modeling in observational studies: A
systematic review. Journal of Clinical Epidemiology, 58(6), 550–559.
Skinner, B. F. (1963). Operant behavior. American Psychologist, 18(8), 503–515. https://
doi.org/10.1037/h0045185
Smith, G., Levere, M., & Kurtzman, R. (2009). Poker player behavior after big wins and
big losses. Management Science, 55(9), 1547–1555. https://doi.org/10.1287/
mnsc.1090.1044
Stefan, S., & David, D. (2013). Recent developments in the experimental investigation of
the illusion of control. A meta-analytic review. Journal of Applied Social Psychology,
43, 377–386, 10.1111/j.1559- 1816.2013.01007.x.
Stuart, E. A., King, G., Imai, K., & Ho, D. (2011). MatchIt: Nonparametric preprocessing
for parametric causal inference. Journal of Statistical Software, 42(8). https://doi.org/
10.18637/jss.v042.i08. Advance online publication.
Thaler, R. H., & Johnson, E. J. (1990). Gambling with the house money and trying to
break even: The effects of prior outcomes on risky choice. Management Science, 36(6),
643–660.
Trippiedi, M. (2014). Daily fantasy sports leagues: Do you have the skill to win at these
games of chance? UNLV Gaming Law Journal, 5, 201.
Turner, N. E., Jain, U., Spence, W., & Zangeneh, M. (2008). Pathway to pathological
gambling: Component analysis of variables related to pathological gambling.
International Journal of Gambling Studies, 8(3), 281–298. https://doi.org/10.1080/
14459790802405905
Turner, N. E., Zangeneh, M., & Littman-Sharp, N. (2006). The experience of gambling
and its role in problem gambling. International Gambling Studies, 6(2), 237–266.
Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological
Bulletin, 76(2), 105–110. https://doi.org/10.1037/h0031322
Tversky, A., & Kahneman, D. (1973). Availability: A heuristic for judging frequency and
probability. Cognitive Psychology, 5(2), 207–232. https://doi.org/10.1016/00100285(73)90033-9
Weatherly, J. N., & Phelps, B. J. (2006). The pitfalls of studying gambling behavior in a
laboratory situation. In P. Ghezzi, C. A. Lyons, M. R. Dixon, & G. R. Wilson (Eds.),
Gambling: Behavior theory, research, and application (pp. 105–125). Context Press.

Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.chb.2023.107657.
References
Auer, M., Hopfgartner, N., & Griffiths, M. D. (2018). The effect of loss-limit reminders on
gambling behavior: A real-world study of Norwegian gamblers. Journal of Behavioral
Addictions, 7(4), 1056–1067.
Barton, K. R., Yazdani, Y., Ayer, N., Kalvapalle, S., Brown, S., Stapleton, J., …
Harrigan, K. A. (2017). The effect of losses disguised as wins and near misses in
electronic gaming machines: A systematic review. Journal of Gambling Studies, 33(4),
1241–1260.
Basham, C. A., & Karim, M. E. (2022). An E-value analysis of potential unmeasured or
residual confounding in systematic reviews of post-tuberculosis mortality,
respiratory disease, and cardiovascular disease. Annals of Epidemiology, 68, 24–31.
Braverman, J., LaPlante, D. A., Nelson, S. E., & Shaffer, H. J. (2013). Using cross-game
behavioral markers for early identification of high-risk internet gamblers. Psychology
of Addictive Behaviors, 27(3), 868.
Braverman, J., Tom, M. A., & Shaffer, H. J. (2014). Accuracy of self-reported versus
actual online gambling wins and losses. Psychological Assessment, 26(3), 865–877.
https://doi.org/10.1037/a0036428
Celio, M. A., & Lisman, S. A. (2014). Examining the efficacy of a personalized normative
feedback intervention to reduce college student gambling. Journal of American
College Health, 62(3), 154–164.
Chan, G. C., Lim, C., Sun, T., Stjepanovic, D., Connor, J., Hall, W., et al. (2022). Causal
inference with observational data in addiction research. Addiction, 117(10),
2736–2744.
Cohen, J. E. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ:
Lawrence Erlbaum Associates, Inc.
Custer, R. L. (1984). Profile of the pathological gambler. Journal of Clinical Psychiatry, 45
(12), 35–38.
Custer, R., & Milt, H. (1985). When luck runs out. New York: Facts on File.
Davies, C., & Producer & Director). (2022). Gambling: A game of life and death [Video
file]. Retrieved from https://www.youtube.com/watch?v=0effz_xDBlw.
Donaldson, P., Langham, E., Rockloff, M. J., & Browne, M. (2016). Veiled EGM jackpots:
The effects of hidden and mystery jackpots on gambling intensity. Journal of
Gambling Studies, 32(2), 487–498.
Edgerton, J. D., Melnyk, T. S., & Roberts, L. W. (2015). Problem gambling and the youthto-adulthood transition: Assessing problem gambling severity trajectories in a
sample of young adults. Journal of Gambling Studies, 31(4), 1463–1485.
Edson, T. C., Tom, M. A., Philander, K. S., Louderback, E. R., & LaPlante, D. A. (2021).
A large-scale prospective study of big wins and their relationship with future
financial and time involvement in actual daily fantasy sports contests. Mar 18
Psychology of Addictive Behaviors. https://doi.org/10.1037/adb0000715. Epub ahead
of print. PMID: 33734785.
Efron, B. (1988). Logistic regression, survival analysis, and the Kaplan-Meier curve.
Journal of the American Statistical Association, 83(402), 414–425.
Fortune, E. E., & Goodie, A. S. (2012). Cognitive distortions as a component and
treatment focus of pathological gambling: A review. Psychology of Addictive
Behaviors, 26(2), 298–310.
European Gaming and Betting Association. (2019). European online gambling key
figures 2018. https://www.egba.eu/uploads/2019/12/European-OnlineGambling-Key-Figures-2018.pdf.
Gainsbury, S. M., Abarbanel, B. L., Philander, K. S., & Butler, J. V. (2018). Strategies to
customize responsible gambling messages: A review and focus group study. BMC
Public Health, 18(1), 1–11.
Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the
misperception of random sequences. Cognitive psychology, 17(3), 295–314.
Granero, R., Fernandez-Aranda, F., Valero-Solís, S., Pino-Gutiérrez, A. D., MestreBach, G., Baenas, I., … Jiménez-Murcia, S. (2020). The influence of chronological
age on cognitive biases and impulsivity levels in male patients with gambling
disorder. Journal of Behavioral Addictions, 9(2), 383–400.
Gray, H. M., LaPlante, D. A., & Shaffer, H. J. (2012). Behavioral characteristics of
Internet gamblers who trigger corporate responsible gambling interventions.
Psychology of Addictive Behaviors, 26(3), 527–535.
Haneuse, S., VanderWeele, T. J., & Arterburn, D. (2019). Using the E-value to assess the
potential effect of unmeasured confounding in observational studies. JAMA, 321(6),
602–603. https://doi.org/10.1001/jama.2018.21554
Heirene, R. M., Wang, A., & Gainsbury, S. M. (2021). Accuracy of self-reported gambling
frequency and outcomes: Comparisons with account data. Psychology of Addictive
Behaviors. Advance online publication. https://doi.org/10.1037/adb0000792
Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2011). MatchIt: Nonparametric
preprocessing for parametric causal inference. Journal of Statistical Software, 42(8),
1–28.
Kassinove, J. I., & Schare, M. L. (2001). Effects of the“ near miss” and the“ big win” on
persistence at slot machine gambling. Psychology of Addictive Behaviors, 15(2), 155.
King, G., & Nielsen, R. (2019). Why propensity scores should not be used for matching.
Political Analysis, 27(4), 435–454. https://doi.org/10.1017/pan.2019.11
Landsberger, H. A. (1958). Hawthorne revisited (Ithaca).

Computers in Human Behavior 142 (2023) 107657

Weatherly, J. N., Sauter, J. M., & King, B. M. (2004). The “big win” and resistance to
extinction when gambling. The Journal of Psychology: Interdisciplinary and Applied.
https://doi.org/10.3200/JRLP.138.6.495-504
Weston, M. A. (2021). Daily fantasy sports and the law in the USA. The International
Sports Law Journal, 21, 121–139. https://doi.org/10.1007/s40318-021-00192-0

Zhou, K., Tang, H., Sun, Y., Huang, G. H., Rao, L. L., Liang, Z. Y., et al. (2012). Belief in
luck or in skill: Which locks people into gambling? Journal of Gambling Studies, 28(3),
379–391.