International Gambling Studies

ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/rigs20

Consumer preferences for network liquidity and
opponent quality in online poker
Bradley S. Wimmer & Kahlil S. Philander
To cite this article: Bradley S. Wimmer & Kahlil S. Philander (2023): Consumer preferences for
network liquidity and opponent quality in online poker, International Gambling Studies, DOI:
10.1080/14459795.2022.2160000
To link to this article: https://doi.org/10.1080/14459795.2022.2160000

Published online: 08 Jan 2023.

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https://doi.org/10.1080/14459795.2022.2160000

Consumer preferences for network liquidity and opponent
quality in online poker
Bradley S. Wimmer

a

and Kahlil S. Philander

b,c

a

Lee Business School, University of Nevada, Las Vegas, USA; bCarson College of Business, Washington State
University, Everett, USA; cSchool of Psychology, University of Sydney, Camperdown, Australia
ABSTRACT

ARTICLE HISTORY

Several online gambling platforms use marketplace business mod­
els where the operator facilitates wagers between players instead of
directly banking games. There is a large theoretical literature on
marketplace business models, but there is little empirical evidence
that suggests how it may apply to gambler preferences or behavior.
This study contributes to the understanding of consumers in gam­
bling markets by testing multi-sided market theory in online poker.
Using data collected from a diverse sample of online poker players
(n = 719), this study empirically demonstrates how players value
game availability and product quality. Our results show evidence
of diminishing marginal returns to scale and benefits from product
differentiation across a range of conditions found in the market.
Consumers prefer that operators grow their networks when size is
sufficiently small but would prefer more focus on the types of
players added to games as the network grows. From a policy
perspective, these findings provide support for using multi-sided
market theory as a framework for taxation and licensure in gam­
bling products.

Received 9 September 2022
Accepted 11 December 2022
KEYWORDS

Network effects; online
poker; externality; multisided markets; discrete
choice experiment

Introduction
Online poker sites, like many digital marketplace businesses, rely on network effects to
attract customers. These effects exist when the value that customers receive is a function
of the number of other users also on the platform (Evans & Schmalensee, 2016; Katz &
Shapiro, 1994; Rohlfs, 1974). Users typically create value for other consumers through
two mechanisms: counterparty quality and network liquidity (Cennamo, 2019; Rochet &
Tirole, 2006; Sriram et al., 2015). In online poker, quality tends to refer to the ability of a
user to find games or wagers that match their interests, such as action-oriented oppo­
nents with similar game preferences, while liquidity refers to the speed and volume by
which those matches can be filled. Larger networks can add value by providing players
with more options in terms of game stakes, variants (e.g. No Limit Texas Hold’em vs Pot
Limit Omaha), and opponent types (Fiedler & Wilcke, 2012).
Network effects can become externalities when users do not account for their effects
on other marketplace participants (Rochet & Tirole, 2006). For example, a professional
online poker player may add value to a poker site by being available for games with other
CONTACT Kahlil S. Philander

kahlil.philander@wsu.edu; 915 N Broadway, Everett, WA, USA, 98201.

© 2023 Informa UK Limited, trading as Taylor & Francis Group

B. S. WIMMER AND K. S. PHILANDER

players throughout the day but may reduce value by increasing the difficulty for recrea­
tional players to win. In both cases, professional players will generally not consider their
impacts on other players and the online poker operator may need to actively manage
these negative or positive externalities to maximize the site’s value. Effective intermedia­
tion of platform users has led online marketplace models to become some of the largest
businesses in the world (Coolican & Barros, 2021).
In this study, we focus on the identification and measurement of network size and
player quality value to better understand how these theoretical models may apply to
online poker markets. Despite the perceived importance of network effects to many
gambling products like daily fantasy sports, sports betting exchanges, pari-mutuel bet­
ting, and prediction markets, the application of network theory to policy decisions has
largely not been observed (van Damme, 2007, 2008). Our study contributes to the
literature as the first empirical study of multi-sided markets in any gambling industry
and one of the few empirical studies of multi-sided markets more generally.
The absence of prior empirical studies may be related to measurement challenges in
multi-sided markets. Estimating user trade-offs must overcome the econometric pro­
blems associated with simultaneously identifying the impact of participant characteristics
and network size on consumer utility. Since preferences are interdependent and usage
decisions are determined simultaneously, consistent estimation of liquidity effects
requires that researchers account for unobserved factors that affect an individual’s
demand for a product and its number of users (Manski, 1993; Rysman, 2019). We
overcome these econometric identification problems by using data from a discrete choice
experiment administered to online poker players. Discrete choice experiments circum­
vent identification and reflection problems because they rely on the randomization of
attribute characteristics to identify their effects on respondents’ utility and the prices
consumers are willing to pay for different product attributes (Hartmann et al., 2008).
Related literature
Multi-sided markets
An extensive theoretical literature examines multi-sided markets. This literature explores
the effects of cross and same-side externalities on profit-maximizing prices, the role of
competition and multi-homing on market outcomes and business strategies, as well as
the conditions under which network effects lead to winner-take-all outcomes
(Armstrong & Wright, 2007; Armstrong, 2006; Caillaud & Jullien, 2003; Parker & Van
Alstyne, 2005; Rochet & Tirole, 2003, 2006; Rysman, 2009; Weyl, 2010). The seminal
theoretical works by Rochet and Tirole (2003) focused on two-sided markets, and is selfdescribed as merging literature on multiproduct pricing (Baumol et al., 1982) with
literature on network effects (Katz & Shapiro, 1985; Rohlfs, 1974). Subsequent work
generalized these ideas to multi-sided markets (Evans & Schmalensee, 2016), such as a
three-sided social media platform with individual users, content producers, and adver­
tisers all using the same network.
In general, network effects exist when the number of participants using network goods
affects a user’s utility. Indirect network effects arise when the demand for a network good
depends on the availability of related goods. The effects are indirect because the demand
for related goods depends on participants’ usage of the network good. Network effects are

direct when users are directly affected by others’ use of a product. Communication
services, such as telecom networks, e-mail, and social networks, exhibit direct network
effects because more subscribers increase the number of potential network interactions
(Katz & Shapiro, 1985, 1994; Rohlfs, 1974; Schmalensee, 2011).
Schmalensee (2011) observes that many of today’s internet-based services and appli­
cations do not require long-term customer commitments and have low switching costs.
Consumers may also multi-home, consuming several differentiated but related services
on different platforms. Others propose that differences in the abilities of users, their roles
and interactions, and perceived trust also affect the value of networks (Afuah, 2013; Lee et
al., 2006). While many internet-based services like social networks benefit from direct
network effects, network effects are not the only factor important to platforms competing
in markets with differentiated products (Cennamo, 2019; Schmalensee, 2011; Sriram et
al., 2015).
Despite the importance of marketplace businesses, the growing theoretical literature is
largely untested due to econometric difficulties associated with estimating direct network
effects (Rysman, 2019). Some studies have found evidence of direct network effects in
specific settings. Tucker (2008) and Ryan and Tucker (2012) provide evidence of direct
network effects using data on employee adoption of video-messaging machines. This
work shows that the magnitude of estimated direct network effects differs by employee
type. Other studies examined the mobile phone market. Sobolewski and Czajkowski
(2012) demonstrate the impact of direct network effects on market outcomes in the
Polish wireless telephone market using data from a discrete-choice experiment. Kim and
Kwon (2003) argue that increases in market share provide information about a network’s
quality. Björkegren (2019) demonstrates the importance of network effects on inframar­
ginal users, presenting evidence that most of the benefits from universal-service require­
ments accrue to users not directly affected by the government programs that expand
Rwanda’s mobile phone network.
Other literature estimates the impact of indirect network effects in two-sided markets.
For example, Rysman (2004) shows that internalizing network effects in the market for
Yellow Pages increases surplus and that competition significantly improves market
performance. Kaiser and Wright (2006) and Song (2021) find significant relationships
between the demand for advertising and readership in the market for magazines;
Cennamo and Santalo (2013) demonstrate the importance of product differentiation in
the market for video games and Chu and Manchanda (2016) show that both product
variety and the quality of users significantly affect the number of buyers and sellers on
Alibaba Group’s Taobao.com platform.
While these studies provide some insight into indirect network effects in the presence of
Manski’s reflection problem, the marketplaces considered are not generally peer-to-peer
platforms like poker, but instead have buyer-seller relationships. The nearest comparisons
for online poker may be in the sharing economy (Knote & Blohm, 2016) and financial
markets (Cantillon & Yin, 2011), where platform users will often be buyers and sellers on
different occasions but there may also be a ‘professionalization’ with one group of users,
similar to professional online poker players. Cullen and Farronato (2021) examine the
TaskRabbit small job marketplace and find that network effects are constrained by geo­
graphic proximity requirements. They note that winner-take-all equilibriums may not
emerge as marketplaces must compete on quality characteristics. Fradkin (2017) examines

B. S. WIMMER AND K. S. PHILANDER

Airbnb users and finds substantial value is created by the platform by more effectively
facilitating matches between renters and hosts. In US equity markets, O’Hara and Ye (2011)
find that fragmentation reduces asset spreads and improves speed of execution, particularly
for small and illiquid securities.
Online poker
Online poker is a player-versus-player game that requires the simultaneous participation
of multiple players. Players in online games compete against opponents seated at virtual
tables that include as few as two and as many as ten participants. Games can consist of
hundreds of virtual tables and thousands of players. Poker sites generate revenue by
charging players a fee known as the ‘rake.’ The rake can be a time-based fee or a
percentage surcharge on the total wagered, up to a maximum amount per hand. Player
utility is increasing in the money won at the tables and the enjoyment received from
playing the game.
Users’ expected profit from playing poker depends on their ability, skill, and style
relative to their opponents. Successful poker strategies require information on opponent
characteristics and styles of play. The rate at which players ‘Voluntarily Put Money in the
Pot’ (VPIP) is a characteristic used to define player types. VPIP reflects the percentage of
hands where a player places a bet when not required to do so. It equals the percentage of
hands where a player places a bet before the dealer reveals the hand’s first three
community cards but does not count forced bets known as blinds. The big blind equals
the game’s minimum unforced bet. The small blind typically equals one-half of the big
blind (for more game rules, see pokernewsdotcom (Director), 2013).
Players who tend to remain in hands when the probability of winning a showdown (i.
e., a comparison of final hands) is relatively low are considered Loose players. By contrast,
those who generally play only premium hands are considered Tight players. Loose play
increases a game’s action by increasing pot sizes and the likelihood that showdowns
decide hands. Studies on the profitability of poker strategies find that Loose play generally
correlates with losing play, especially in low-stake games (Johansson & Sönströd, 2009;
Siler, 2010). VPIP therefore provides a useful proxy of product differentiation through
user composition, as high VPIP sites will generally be seen as more favorable, both in
terms of providing more entertainment to recreational players and more profitable
situations for professional players.

H1: The quality of users on the platform significantly affects the demand for online poker.
Since opponent characteristics impact a player’s expected profit and enjoyment, it is
not uncommon for players to search for favorable opponents. Players search by playing
multiple hands of poker simultaneously at different virtual tables – a practice known as
multi-tabling. Multi-tabling enables players to gather information about more oppo­
nents, allowing them to identify and compete against participants with favorable char­
acteristics. To the extent that more popular sites improve a game’s liquidity and attract a
wider variety of participant types, increases in site size facilitate players’ search efforts.
Many players engage in ‘table selection,’ where they search for tables that include players
with attractive characteristics. We assume that players know the distribution of

participant characteristics but cannot observe an opponent’s type without competing
against them.
Players search by simultaneously playing multiple hands of poker at different virtual
tables. Multi-tabling enables players to gather information about the strategies, charac­
teristics, and skill sets of more opponents. Increased play also evens the effects of luck and
statistical noise on player returns and reduces the variance of player earnings. Increases
in site size create direct network effects by improving a game’s liquidity, expanding player
choice sets, and facilitating users’ search for favorable opponents. While an increase in
site size generates various benefits, it is unclear the extent to which more games affect a
player’s utility. Limitations on users’ ability to play multiple poker hands simultaneously
constrain the returns players receive from search and multi-tabling. Since multi-tabling
allows players to search for favorable opponents, we expect that players who Multi-Table
are willing to pay a premium for increases in network size and increases in a game’s share
of Loose players.
The benefits associated with increases in site size and improved liquidity depend
partly on the extent to which search affects a player’s expected returns. There is no
return from search when players’ opponents are identical. Search returns increase in the
dispersion of participant characteristics and the size and number of bets (Stigler, 1961). A
player’s search intensity and the number of hands played simultaneously depend on a
player’s ability and the expected returns from search. Increased dispersion in player
characteristics increases the expected returns from search because increased uncertainty
increases the option value of search. Search models predict that this option value is higher
for Inexperienced players because Inexperienced players are more uncertain about the
quality of opponents than Experienced players (Kim et al., 2010; Weitzman, 1979).

H2: Users that search the platform for better matches have a higher willingness to pay for
network size and quality of users.

Methods
Empirical framework
Player utility is increasing in the earnings and the enjoyment they receive from playing
poker. The empirical analysis uses McFadden’s (1974) random utility model to estimate
the effects of game characteristics on the players’ utility for online poker games. The
analysis assumes that poker player i = 1, 2, . . . , I obtains utility from poker game j = 1, 2,
. . . , J. Consumer i’s actual utility, U�ij , equals the sum of mean utility, Vj , and an
unobservable additive error term, εij . The analysis assumes that mean utility varies over
game and site characteristics. An individual consumer’s deviation from this mean utility
equals εij .
Assume that players are either Loose or Tight players, where the number of Loose
players in game j equals Lj and the number of Tight players equals Tj . The total number of
players equals Nj ; where Nj ¼ Lj þ Tj . We assume that players observe the total number
of players participating in a game and know the distribution of player types. The effect of

B. S. WIMMER AND K. S. PHILANDER

an increase in the number of participants on a player’s utility depends in part on
participant characteristics. An increase in the number of Loose participants creates
value because it creates more action and increases a player’s expected profit. The increase
in site size improves a game’s liquidity and the returns from search. Identifying the effects
of an increase in site size on mean utility requires that the empirical analysis controls for
the composition of participant characteristics. Consumer i’s expected utility from pokergame alternative j equals:
Vij Nj ; Lj ; Tj ; Ii ; Pj ; Xj ; Fj

�

�
� �
þ εij ¼ λ Ii
Pj � þ Xj β þ h aj Lj ; Tj ; δ
Fij þ εij ;
þ v Nj ; γ

(1)

where Ii equals player i’s income, Pj equals the price of game j, and λ equals the marginal
utility of income. The vector Xj contains other game characteristics, and β contains the
� �
associated vector of coefficients. The function h aj Lj ; Tj ; δ captures the composi­
tional effects of a game’s participants’ characteristics on mean utility. The function
�
aj Lj ; Tj measures the composition of a game’s player characteristics and δ equals the
�
vector of coefficients to be estimated. The function v Nj ; γ measures the effects of
network size on mean utility; γ is the vector of the function’s coefficients. Player i’s
entry cost for game j equals Fij : Because our discrete choice experiment does not ask
respondents to distinguish between the effects of game characteristics on their expected
earnings and enjoyment from playing the game we assume that the terms Xj β,
� �
�
h aj Lj ; Tj ; δ , and v Nj ; γ capture both the pecuniary and non-pecuniary effects of
game characteristics on a player’s utility.
Given the mean utilities described by Equation (1), the probability that consumer i
chooses alternative j equals:
�
�
Prij ¼ U�ij > U�ik ; " k�j

�
¼ Vj þ εij > Vk þ εik ; " k�j
�
¼ εik εij < Vj Vk ; " k�j

(2)

The analysis assumes that the random error term is distributed iid Type I extreme
value and estimates mean utility using the logit probability formula (McFadden, 1974).
The probability that a representative consumer selects alternative j equals:
�
exp Vij ð Nj ; Lj ; Tj ; Ii ; Pj ; Xj ; Fij Þ
�
Prob ðy ¼ 1Þ ¼ P
exp Vik ð Nk ; Lj ; Tj ; Ii ; Pk ; Xk ; Fik Þ

(3)

k

Any factor that increases the utility player i receives from game j increases the
probability that consumer i selects game j. Maximizing the log-likelihood function
derived from Equation (3) estimates the mean indirect utility function.
This study’s hypotheses test propositions about the price players are willing to pay for
changes to site size and other factors. Estimates of the representative user’s compensating
variation for the characteristics of a poker game’s attributes are used to test these
hypotheses. The compensating variation equals:

CV ¼

1� 1
V
λ

�
Vo ;

(4)

Where V o is the indirect utility function from Equation (1), evaluated at base-level
attributes, and V 1 equals indirect utility with altered attributes (Holmes & Boyle, 2003).
The compensating variation produces a willingness-to-pay estimate that equals the
change in income required to hold a consumer’s utility constant when a product’s
characteristics change. The representative user’s marginal utility of income equalsλ. In
our setting, a player’s compensating differential is increasing in the player’s expected
earnings and recreational value.

Discrete choice experiment
A discrete choice experiment manipulates product characteristics and prices, creating
series of hypothetical choices that obtain the optimal variation in the data needed to
estimate the value of product characteristics (Allenby et al., 2014; Hensher et al., 2005).
This study’s experiment presents respondents with pairs of hypothetical internet poker
games of No-Limit Texas Hold ’em that differ in attribute characteristics. The experi­
mental design randomizes attribute characteristics, including the number and types of
players participating in online poker games. The study’s respondents face a forced-choice
design where they are required to choose one of the two hypothetical poker games
presented in each choice experiment. Allenby et al. (2014) suggest that forced-choice
designs may elicit more information about product attributes than studies that include
outside options.
The primary limitation of a discrete choice experiment is the requirement that
responses to hypothetical scenarios reflect observed behavior. In general, data based on
stated choices bias results when choice sets do not fully reflect reality, respondents have
incomplete preferences, or respondents have a vested interest in the study’s results
(Quaife et al., 2018). We consulted active poker players with extensive online poker
experience, individuals from the industry, and conducted two focus groups with online
poker players to ensure the study’s realism and the reasonableness of the experiment’s
attributes. The experts we consulted reviewed several versions of the survey and provided
comments that we used to select the game attributes included in the discrete choice
experiment and the variables used to measure these attributes.
All focus group members were at least 21 years of age and had experience playing online
poker for money. Focus group members were selected from a pool of candidates who
responded to flyers posted on the University of Nevada-Las Vegas (UNLV) campus.
Selection was based on a first-come, first-served basis for the candidates who had active
online-poker accounts. Each participant was awarded a $50 cash stipend. Two focus groups
were held on the UNLV campus before the survey was administered. The first focus group
included six respondents. Respondents completed a hard copy of the survey and discussed
various aspects of its design. The main objectives of the first focus group were to determine
whether the survey included the correct characteristics, the attribute levels were realistic,
and if respondents would make trade-offs when choosing between poker-site options. The
focus group also explored whether respondents were able to hold all factors not included in
the discrete choice experiment constant when taking the experiment.

B. S. WIMMER AND K. S. PHILANDER

The second focus group included three individuals from UNLV with experience in
playing online poker. These respondents completed an online survey using Qualtrics.
The second focus group assessed the look and feel of the survey and participants
discussed survey design and whether they could make the required trade-offs between
poker-game attributes and their characteristics. Poker experts consulted on this project
noted that online poker players regularly make financial decisions based on hypothesized
probabilistic trade-offs, suggesting that respondents have the background to understand
and assess the trade-offs presented in the experiment. The UNLV Institutional Review
Board approved the focus groups and the study.
Respondents accessed the survey online via Qualtrics. Survey respondents completed
eight discrete choice experiments, where the characteristics of the attributes included
differed depending on the respondent’s preferred stake. Survey respondents indicate
whether they preferred Micro, Small, or High stakes, where the game’s minimum bet
defines its stake. The minimum bet ranges from $0.02 to $0.50 for Micro-Stake players
and ranges from $0.50 to $2.00 for Small-Stake players. The top minimum bet equals $10
for games classified as High-Stake poker. The hypothetical poker games presented to
respondents hold the minimum bet constant at the cutoff to define a player’s preferred
stake. Specifically, Micro-Stake respondents choose between hypothetical games with
different levels of attribute characteristics, holding the minimum bet constant at $0.50.
The experiment’s minimum bets, respectively, equal $2 and $10 for Small-Stake and
High-Stake respondents.
The survey includes nine blocks of discrete choice experiments, each with eight
different choice sets for each stake level. Qualtrics randomly assigns respondents to
blocks of discrete choice experiments based on their preferred stake. Respondents
received the following instructions: “(w)hile this is a hypothetical choice and not a real
one, we ask you to consider your preferences and make choices just as if you were
choosing a website to play No-Limit Texas Hold ’em,” before taking the experiment. The
survey asks respondents to hold all other game characteristics constant while making
their choices and provides respondents with links to definitions of the attributes and
characteristics included in the study.
The final choice set includes five different poker-site attributes. A fractional design
ensures that the experiment questions are balanced and orthogonal (Aizaki, 2012). The
number of levels included for each attribute ranges from two to six, creating 288 different
combinations. The fractional design includes seventy-two of these combinations.
Orthogonality precludes variables that equal the interaction of attributes included in
the experiment in the empirical models estimated.
The experimental design includes six different levels for the network-size attribute.
We used the industry monitor PokerScout.com to determine the number of players
included in the network-size attribute. Specifically, we monitored games offered by stateregulated poker sites in Nevada in the year following the launch of the first stateregulated sites in the U.S. and games conducted on PokerStars, the world’s largest online
poker site. These data show that the Nevada-based site failed to create a single game at
times, while the largest poker site had 10,077 active cash-game players competing across
multiple game variants and stakes at the time of the observation. Fiedler’s (2011) data on
market shares imply that the largest pool of compatible users (Micro-Stake, No-Limit
Texas Hold ’em players) on the global platform included 2,866 players (28.4% of total).

To capture the full range of site sizes available to players on different sites and in various
jurisdictions, the range of size varies from 50 to 4,000 Players for respondents who prefer
Micro and Small-Stake games. This range equals 25 to 2,000 Players for High-Stake
respondents. The lower range for High-Stake respondents reflects the market conditions
experienced by High-Stake players.
The empirical analysis uses vectors of categorical variables to estimate the effects of
size on utility. The variable Nn is a categorical variable that equals
� one
P when size equals n
and zero otherwise. For Micro and Small-Stake games:v Nj ; γ = γtn Nn , n = {50, 150,
n
500, 1,250, 2,000, and 4,000} and t = {m, s}. The term γtn equals the
vector of related
coefficients. The study uses 50 Players ðN50 Þ as the excluded category in the Micro and
Small-stake regressions. Using categorical variables to measure the effects of size on
utility imposes no restrictions on the functional form of the estimated effect of size on
mean utility and estimated compensating variations. The High-Stakes regressions include
� P
the following set of categorical variables: v Nj ; γ = γhn Nn , n = {25, 75, 225, 500, 1,000,
n

and 2000}. The analysis uses 25 players ðN25 Þ as the excluded category in the High-Stake
model.
The discrete choice experiment includes a set of categorical variables that measure a
game’s Average VPIP. The discrete choice experiment includes hypothetical poker games
where the Average VPIP equals 37%, 28%, or 19% (Walker, 2014). The analysis labels
these different Average VPIPs as Loose, Neutral, and Tight and creates corresponding
categorical variables. The variable Loose VPIP equals one when a game’s Average VPIP
equals 37%, and zero otherwise. Tight VPIP equals one when a game’s Average VPIP
equals 19%, and zero otherwise. The analysis uses Neutral VPIP (28%) as its excluded
category. The survey informs respondents that a game’s Average VPIP applies to tables
that include six players.
The experiment includes the variable Cost, where Cost equals the time-based rake per
hour of play at a table. The study bases its Cost levels on data collected at rakeatpoker.
com. The Cost levels used differ according to the respondent’s preferred stake. The
variable cost does not include any loyalty or reward bonuses. Since bonuses typically
equal a share of a player’s rake payments, bonus payments do not affect relative prices.
The survey also includes Regulation and site Security characteristics. These variables
address the importance of dependability and trust in the market for online poker. In the
discrete choice experiment, a site is defined as Regulated when licensed by its State
Gaming Commission, while an unregulated site does not have this approval.
A site has Average Security when it regularly passes security audits administered by
private firms and adopts policies that guarantee that it does not use player balances for
operational expenses. Sites have Above-Average Security when they have Average Security
and use secure private third-party options for deposits and withdrawals. Sites with
Above-Average Security also use additional security measures such as security keys. The
analysis added the Security variables due to comments made by members of the first
focus group, who noted that an increase in the number of a game’s players signals a more
secure environment. This comment led to the inclusion of explicit controls for game
security. Table 1 provides definitions of the variables included in the discrete choice
experiment.

B. S. WIMMER AND K. S. PHILANDER

Table 1. Discrete Choice Experiment Attributes and their Levels.
Attribute
Stakes

Regulation
Security
Cost

Players

Average
VPIP

Levels

Explanation
Size of the Big Blind at a short-handed
table with six players playing No-Limit
Texas Hold’em, the most popular
variant of online poker (Fiedler, 2011).
The poker website is regulated by the
government entity in the state where
the respondent lives.
The quality of the website’s security
features compared to the overall
industry standard.
Per-Hour Rake for a short-handed table
with 6 players playing No-Limit Texas
Hold’em
Number of players on a site playing NoLimit Texas Hold’em at Specified Stakes.

Micro
< $0.50

Small
$0.51–$2.00

Middle
$2.01–$10.00

High
Above $10

Yes/No

Yes/No

Yes/No

Yes/No

Average/
Above
Average
$1.50, $2.50,
$3.50 or
$4.50.

Average/
Above
Average
$5.00, $8.25,
$11.50 or
$14.75.

Average/
Above
Average
$9.00,
$15.00,
$21.00 or
$27.00.
25, 75, 225,
500, 1,000 or
2,000 Players.

Average/
Above
Average
$10.00,
$17.00,
$23.00 or
$30.00.
5, 25, 60,
150,
300 or 500
Players.
19%, 28%
and 37%

50, 150, 500, 50, 150, 500,
1,250, 2,500, 1,250, 2,500,
or 4,000
or 4,000
Players.
Players.
Voluntarily Put Money in the Pot equals the 19%, 28% and 19%, 28% and
percentages of hands that a player calls
37%
37%
or raises before the first three
community cards (flop) are dealt. Bets
in the big and small Blinds are not
included in the calculation of VPIP.

19%, 28%
and 37%

Respondents are asked to identify their preferred stake level. The levels of attributes for several characteristics in the
experiment are based on a respondent’s preferred stake level. The levels for Players are based on data on the peak number
of players on regulated sites in the United States, as well as data on the number of players on unregulated international
sites. These data were obtained from PokerScout.com, which is a website that tracks and reports data on the number of
poker players on different sites. According to PokerBank.com, a player with a VPIP below 24% is considered a tight player,
while players with VPIP above 32% are considered loose, which was validated in the focus groups.

The analysis uses the median experience category to define Experienced players in the
empirical models. The variable Experienced equals one, and zero otherwise, for respon­
dents with ten or more years of experience playing poker for money at any venue.
We posted links to the survey on several different poker-related forums. Members of
the online poker community posted links to the survey on their social media accounts.
Respondents must have played poker online for real money and be at least 21 years old to
be eligible for the survey. Participation was voluntary, anonymous, and uncompensated.
Of the 1,481 people that started the survey, 937 started the discrete choice experiment,
and 884 answered all experiment questions. The study includes only respondents from
the United States who prefer Micro, Small, and High-Stake games. Respondents whose
choices in the experiment did not provide any variation in the options selected were
removed from the data because they do not provide information about the trade-offs
players make when choosing sites. The final data set includes 5,033 decisions from 719
respondents. In addition to the discrete-choice experiment, the survey elicited informa­
tion about respondent playing habits, experience playing poker, education, income, and
other demographic information. Table 2 summarizes these data for the 719 players
included in the study.

Table 2. Summary Statistics (Standard deviation in brackets).
Variable
Age Mean (Years)
Income Mean (000s)
Male (Proportion)
High School or Less
(Proportion)
College or More
(Proportion)
Pro Poker Player
(Proportion)
Weekly Mean Hours
Playing Poker
Money Motivation
(Proportion)
Experience (Share of Sample)
Less than One Year
Fewer than Five Years
Five or More Years
Ten or More Years
Multi-Table Frequency (Proportion)
Always
Often
Sometimes
Observations

All
38.54
(12.18)
61.83
(33.89)
0.87
(0.34)
0.11
(0.31)
0.54
(0.50)
0.10
(0.30)
17.51
(25.91)
0.74
(0.44)

Micro
39.63
(13.18)
55.71
(35.67)
0.86
(0.35)
0.13
(0.34)
0.55
(0.50)
0.03
(0.17)
13.17
(18.24)
0.61
(0.49)

Small
38.77
(11.60)
61.02
(31.87)
0.86
(0.35)
0.12
(0.33)
0.53
(0.50)
0.09
(0.28)
17.22
(24.97)
0.76
(0.43)

High
36.77
(11.66)
71.31
(32.94)
0.90
(0.31)
0.04
(0.20)
0.54
(0.50)
0.22
(0.41)
23.51
(33.61)
0.88
(0.33)

0.03
(0.17)
0.20
(0.40)
0.80
(0.40)
0.41
(0.49)

0.06
(0.24)
0.30
(0.46)
0.70
(0.46)
0.34
(0.47)

0.02
(0.13)
0.17
(0.37)
0.83
(0.37)
0.42
(0.49)

0.02
(0.13)
0.11
(0.32)
0.89
(0.32)
0.49
(0.50)

0.35
(0.48)
0.24
(0.43)
0.24
(0.43)
100%

0.26
(0.44)
0.27
(0.45)
0.26
(0.44)
31.85%

0.35
(0.48)
0.25
(0.43)
0.23
(0.42)
42.98%

0.46
(0.50)
0.19
(0.40)
0.24
(0.43)
25.17%

Results
Table 3 contains the conditional logit model results and their associated compensating
variations, or WTP estimates. It also includes incremental estimates for the effects of size
on the estimated compensating variation. Estimates are grouped by stake, beginning with
estimates for Micro-Stake games. Overall, the data fit the models well. McFadden’s R2
ranges from 0.274 in the Micro-Stake regression to 0.316 in the High-stake model.
The estimated coefficients on Loose and Tight VPIP receive their expected signs and
are highly significant in all the specifications reported. These findings support the notion
that users view Loose and Tight players as distinct user types. The coefficients on the
categorical game-size variables are positive, significant, and increase in the number of a
game’s Players at a decreasing rate. The variable Cost receives a negative coefficient that is
significant in the three models presented. The coefficients on the remaining variables
receive their expected signs and are highly significant. Overall, these results support the
notion that participant characteristics and size significantly impact a poker player’s
utility.
Compensating-variation calculations use the estimated Cost coefficients to measure a
respondent’s marginal utility of income. The results for Loose VPIP and Tight VPIP are

Logit
0.56***
(0.08)
0.53***
(0.08)
−0.63***
(0.05)
−0.43***
(0.10)
0.34***
(0.10)
0.69***
(0.15)
1.04***
(0.19)
1.54***
(0.21)
1.73***
(0.19)
1.91***
(0.17)
−806.96
0.274
3,206

−0.68***
(0.15)
0.54***
(0.16)
1.09***
(0.25)
1.65***
(0.31)
2.44***
(0.35)
2.75***
(0.33)
3.03***
(0.32)

WTP
0.89***
(0.12)
0.84***
(0.13)

1.09***
(0.25)
0.56**
(0.25)
0.79***
(0.20)
0.31*
(0.18)
0.28
(0.22)

Incremental WTP

Logit
0.39***
(0.07)
0.57***
(0.07)
−0.196***
(0.01)
−0.63***
(0.08)
0.21***
(0.08)
0.70***
(0.12)
1.13***
(0.16)
1.59***
(0.19)
1.61***
(0.17)
1.83***
(0.15)
−1,098.8
0.267
4,326
−3.24***
(0.43)
1.08***
(0.40)
3.58***
(0.63)
5.76***
(0.84)
8.13***
(0.96)
8.20***
(0.89)
9.37***
(0.81)

WTP
2.01**
(0.34)
2.93**
(0.37)

Small Stake

3.58***
(0.63)
2.18***
(0.64)
2.37***
(0.59)
0.08
(0.59)
1.17
(0.60)

IncrementalWTP

2,000 Players

1,000 Players

500 Players

225 Players

75 Players

Loose

Tight

Cost

Security

Regulation

Logit
0.60***
(0.09)
0.57***
(0.09)
−0.112***
(0.01)
−0.68***
(0.12)
0.34***
(0.10)
0.76***
(0.18)
1.52***
(0.22)
1.70***
(0.23)
2.14***
(0.24)
2.32***
(0.25)
−600.65
0.316
2,534

−6.09***
(0.97)
3.01***
(0.91)
6.81***
(1.65)
13.58***
(2.28)
15.18***
(2.37)
19.06***
(2.38)
20.69***
(2.29)

WTP
5.35***
(0.74)
5.05***
(0.77)

High Stake

6.81***
(1.65)
6.77***
(1.58)
1.59
(1.30)
3.88***
(1.28)
1.63
(1.59)

IncrementalWTP

+Robust standard errors, clustered by respondent, in parentheses. Standard errors in WTP estimates were calculated using Delta method. ***p <0.01, **p <0.05, *p <0.1. Estimated Network
Effects based on comparison to 50-player networks.

Log PseudoLikelihood
McFadden’s R2
Observations
Respondents

4,000 Players

2,500 Players

1,250 Players

500 Players

150 Players

Loose

Tight

Cost

Security

Regulation

Micro Stake

Table 3. Conditional Logit and WTP Estimates – by Stake+.

B. S. WIMMER AND K. S. PHILANDER

consistent with the proposition that players are willing to pay a premium for games with
relatively Loose players. For instance, Micro-Stake players are willing to pay $0.54 for an
increase in Average VPIP from Neutral to Loose. The results are consistent with the
proposition that participant characteristics significantly affect a game’s value and support
the notion that Loose and Tight players are distinct player types whose participation
decisions differentially impact the amount players are WTP to play online poker.
The results suggest that the size of the network matters. For instance, the average
Micro-Stake player is willing to pay $1.09 per hour to increase the size from 50 to 150
Players, holding other factors constant. The effect of size on WTP estimates increase at a
decreasing rate for Micro-Stake respondents, with incremental effects suggesting that
network effects are exhausted at 2,500 Players.
Estimated incremental game-size effects for High-Stake respondents are less clear. The
data do not reject the null hypothesis that the estimated compensating variation for a
change in size from 225 to 500 Players equals zero. By contrast, the results indicate that
increasing size from 500 to 1,000 Players significantly increases a High-Stake respon­
dent’s WTP estimate. The average High-Stake respondent is willing to pay $3.88 to grow
size from 500 to 1,000 Players. Overall, the data provide evidence that size matters and
that the effects of size on WTP estimates increase at decreasing rates. The analysis also
shows that the effects of size on player utility become less important in higher stake
games. The finding that direct network effects become less extensive in higher-stake
games is consistent with the proposition that search returns are lower in relatively highstake games where the dispersion of participant characteristics is more compressed
(Johansson & Sönströd, 2009; Siler, 2010). While the estimated effects of size on WTP
estimates increase in stake, this is not the case when we normalize estimates by a game’s
minimum bet. The estimated effect of increasing size from 50 to 500 players equals 3.3
bets in Micro-Stake games and 2.88 bets in Small-Stake games. High-Stake players are
willing to pay only 1.518 bets to increase size from 25 to 500 players.
The results presented in Table 4 compare the WTP estimates of Single and Multi-Table
players. Since Multi-Tabling increases the likelihood that players compete against oppo­
nents with favorable characteristics, players who Multi-Table should be willing to pay a
premium for relatively Loose games and games with more network players. Multi-Table
players are willing to pay more than twice as much as Single-Table players for an increase
in Average VPIP from Tight to Neutral in both Micro-Stake ($0.97 versus $0.34) and
Small-Stake games ($4.06 versus $1.62). They are also willing to pay significantly more
than Single-Table players ($1.57 versus $0.50) to increase the size of a Micro-Stake game
from 50 to 150 Players.
The last six columns in Table 4 present results that compare estimated WTP estimates
for Inexperienced and Experienced respondents. Inexperienced respondents competing in
Micro-Stake games are willing to pay significant premiums for bigger games and games
with Loose Average VPIP. They are willing to pay over four times more than Experienced
respondents ($0.91 versus $0.21) for an increase in Average VPIP from Tight to Neutral.
They are also willing to pay $1.41 more than Experienced respondents ($1.53 versus
$0.13) to increase size from 50 to 150 players. The estimated difference in WTP across
player types persists for games with 500, 1,250, and 2,500 Players, although the estimated
gap narrows slightly. The estimated differences in WTP estimates between the
Inexperienced and Experienced players narrow considerably and are not statistically

Single
0.80***
(0.17)
0.93***
(0.18)
−0.34
(0.21)
0.55**
(0.24)
0.50
(0.34)
1.11***
(0.42)
1.96***
(0.49)
2.73***
(0.47)
3.01***
(0.45)
−361.27

1,484

Multi
0.95***
(0.17)
0.76***
(0.19)
−0.97***
(0.20)
0.51***
(0.21)
1.57***
(0.33)
2.06***
(0.43)
2.81***
(0.50)
2.70***
(0.45)
2.91***
(0.45)
−431.40

1,708

Dif
0.15
(0.24)
−0.17
(0.26)
−0.63**
(0.29)
−0.04
(0.32)
1.07***
(0.47)
0.95
(0.60)
0.86
(0.70)
−0.03
(0.65)
−0.11
(0.64)
2,604

Multi
1.95***
(0.38)
2.00***
(0.40)
−4.06***
(0.55)
1.29***
(0.47)
3.59***
(0.72)
5.65***
(0.99)
8.17***
(1.19)
7.91***
(1.09)
9.24***
(0.98)
−643.57
1,694

Single
2.15***
(0.65)
4.73***
(0.73)
−1.62***
(0.68)
0.39
(0.70)
2.84**
(1.14)
5.47***
(1.42)
7.51***
(1.52)
8.16***
(1.48)
9.22***
(1.37)
−423.29

Small Stake
Diff
−0.19
(0.75)
−2.74***
(0.83)
−2.44**
(0.88)
0.90
(0.84)
0.75
(1.35)
0.18
(1.73)
0.66
(1.93)
−0.24
(1.84)
0.01
(1.68)
2,100

Inexp
0.83***
(0.15)
0.88***
(0.16)
−0.91***
(0.19)
0.55***
(0.19)
1.53***
(0.31)
2.01***
(0.38)
2.80***
(0.44)
3.10***
(0.41)
3.21***
(0.41)
−511.74
1,078

Exp
0.96***
(0.21)
0.77***
(0.21)
−0.21
(0.22)
0.46*
(0.27)
0.13
(0.35)
0.81
(0.49)
1.54***
(0.54)
2.00***
(0.48)
2.64***
(0.48)
−277.28

Micro Stake
Dif
−0.13
(0.26)
0.11
(0.26)
−0.70**
(0.30)
0.09
(0.33)
1.41***
(0.47)
1.20*
(0.62)
1.26*
(0.69)
1.11*
(0.63)
0.57
(0.63)

2,492

Inexp
1.52***
(0.48)
2.71***
(0.49)
−3.61***
(0.62)
1.11*
(0.57)
3.43***
(0.86)
6.77***
(1.19)
8.64***
(1.39)
9.19***
(1.36)
10.00***
(1.22)
−656.98

1,792

Exp
2.57***
(0.46)
3.03***
(0.54)
−3.02***
(0.61)
1.10**
(0.54)
3.80***
(0.95)
4.47***
(1.18)
7.87***
(1.34)
7.28***
(1.12)
8.97***
(1.06)
−421.68

Small Stake

Inexperienced and Experienced Respondents

Dif
−1.05
(0.66)
−0.32
(0.73)
0.59
(0.87)
0.02
(0.79)
−0.37
(1.28)
2.30
(1.68)
0.77
(1.93)
1.91
(1.76)
1.03
(1.62)

+Robust standard errors, clustered by respondent, in parentheses calculated using Delta method. ***p < 0.01, **p < 0.05, *p < 0.1. Estimated Network Effects based on comparison to 50-player
networks. ++The total number of respondents is lower in these regressions because of missing data on players’ Experience and Multi-Tabling behavior.

Log
Pseudolikelihood
Observations++
Respondents++

4,000 Players

2,500 Players

1,250 Players

500 Players

150 Players

Loose

Tight

Security

Variables
Regulation

Micro Stake

Multi-Table and Single-Table Respondents

Table 4. WTP Estimates by Self-Reported Player Characteristics+.

B. S. WIMMER AND K. S. PHILANDER

significant in Small-Stake games. Results from Micro-Stake games provide the most
support for the proposition that search amplifies the effects of size and participant
characteristics on WTP estimates.

Discussion
Overall, the empirical analysis produces three main results. First, game participants view
Loose and Tight players as distinctly different user types and are willing to pay a premium
for product differentiation through user composition. Second, the results show that an
increase in size increases users’ utility at a decreasing rate. While bigger networks confer
benefits on game participants, the total impact of additional players on others’ utility
depends on the types of players added to the network. Finally, the data support the
proposition that some increases in players’ search returns and intensity amplify the
effects of size and Average VPIP on respondents’ WTP estimates.
The findings provide several takeaways. The first order effects are that poker players
value both game availability and product quality. Prior gambling studies have shown that
product availability impacts demand (Abbott, 2020; Philander et al., 2022), but this
appears to be the first study to empirically demonstrate that product quality also impacts
consumer demand. The diminishing marginal returns to scale and the product differ­
entiation results suggest that consumers would prefer that operators grow their networks
when size is sufficiently small but account for the types of players added to games as the
network grows. Poker players appear to prefer sites with game availability but once the
network reaches an adequate size, participants will prefer a site with more actionoriented players. These findings are consistent with rewards program used by market
leader PokerStars, which rebates net losers more than net winners (MacAdam, n.d.).
The results provide insight into other marketplace-based business where users value highquality matches and may explain why some markets with network effects can fragment into
niche strategies rather than accrue to a single winner. It also explains other peer-to-peer
markets where marketing platforms that appeal to niche groups of users have become a
popular competitive strategy (Blackwell, 2016). The returns to better user composition and
lower search costs may offset losses from a smaller pool of eligible matches.
From a regulatory and policy perspective, these findings provide support for using multisided market theory as a framework for taxation and licensure in several gambling products.
In marketplace businesses like online poker, betting exchanges, and prediction markets,
policymakers that wish to maximize public welfare should consider how licensing models
will allow operators to reach requisite scale for liquidity effects but also encourage competi­
tion on product quality. A monopoly provider may produce a large network but the marginal
value of those effects may be less than if there were multiple operators that needed to compete
on quality. However, a more open licensing framework may excessively fragment liquidity in
the short-run if the total addressable market is too small. Our online poker findings suggest
that growth in network size is accretive until active Micro-Stake user counts reach 2,500
players, Small-Stake user counts reach 1,250 players, and High-Stake user counts reach 225
players. If markets appear well below these levels, policymakers should be more proactive in
pursuing strategies that will grow network size, such as interjurisdictional player pooling
compacts or smaller license quotas.

B. S. WIMMER AND K. S. PHILANDER

It remains an open question whether Loose sites are desirable because players prefer more
volatility, higher expected returns, or both outcomes that result from high VPIP play. Future
studies should consider using a structural approach that allows researchers to analyze the
effects of pricing and exclusionary strategies on user behavior and equilibrium outcomes.
Validation of these findings with other gambling products would provide an additional layer
of insight into gambler preferences. Although we made significant efforts to reduce potential
sources of bias, we were limited by interpretation of self-reported data based on hypothetical
choices. Future studies could also consider validating our results through modeling player
choice decisions using site and account data.

Conclusion
This paper applies insights from the literature on multi-sided markets to a peer-to-peer
network with heterogeneous users. By estimating the effects of participant characteristics and
network size on the utility of online poker players, we find evidence of direct network effects
but also determine that the type of players added to games matters. The standard network
effects theory suggests that regulators should not allow competition because network effects
lead to natural monopolies. Our results show that this is not the case and that the composition
of user types is just as important as total number of users. Poker players value the network
liquidity that comes from larger sites but also value the quality of their opponents. We find
that the value for these characteristics generally increases with stake size, but not when we
normalize estimates by a game’s minimum bet. Micro-Stake players are willing to pay $0.56
per hour to increase network size from 150 to 500 players and $0.54 per hour for Loose games.
Small-Stake players are willing to pay $2.18 per hour to increase size from 150 to 500 players
and $1.08 per hour for Loose games. High-Stake players are willing to pay $6.77 per hour to
increase size from 75 to 225 players and $3.01 per hour for Loose games.

Acknowledgements
The authors thank Scott Savage for his comments, Melissa Redona for help with data collection, A.
K. Singh for help with survey design, and Peter Counts, Darren Heyman, Brent Todd, and Dan
Stewart for their input on the survey. The authors also thank volunteer participants in the focusgroup and survey.

Disclosure statement
Since 2016, KP has received research funds from the Washington State Gaming Commission,
Manitoba Gambling Research Program, UNLV International Centre for Gaming Regulation, U.S.Japan Business Council, Board of Regents of the Nevada System of Higher Education. He has received
consulting payments from British Columbia Lottery Corporation, Responsible Gambling Council of
Canada, Intralot, the Commonwealth of The Bahamas, West Virginia Lottery, Indiana Gaming
Commission, and iDevelopment and Economic Association. He has received reimbursement for travel
from the National Conference of State Legislators, National Council for Problem Gambling,
International Association of Gaming Advisors, National Centre for Responsible Gambling,
Responsible Gambling Council of Canada, North American State and Provincial Lottery Association,
Evergreen Council on Problem Gambling, Global Gaming Expo Asia, and Alberta Gambling Research
Institute. He is a member of the National Council for Problem Gambling, and formerly was the
Director of Social Responsibility at the British Columbia Lottery Corporation.

Funding
No funding was received for this study.

Notes on contributors
Bradley S. Wimmer is Professor of Economics at the University of Nevada, Las Vegas (UNLV). His
research issues include the associated effects regulation and deregulation have on the market for
telecommunications. Wimmer also researches the effects of asymmetric information, certification
worker incentives, franchising and the minimum wage.
Kahlil Philander is an Assistant Professor in the School of Hospitality Business Management. He
also holds an appointment as an Honorary Lecturer in the School of Psychology at the University
of Sydney. His research interests are in gambling economics.

ORCID
Bradley S. Wimmer
Kahlil S. Philander

http://orcid.org/0000-0002-9047-5258
http://orcid.org/0000-0002-0747-0772

Data availability statement
Due to the nature of this research, participants of this study did not agree for their data to be
shared publicly, so supporting data is not available. The authors will collaborate with external
researchers to replicate the findings.

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