The Gambling Habits of Online Poker Players
September 29, 2011 Ingo Fiedler*
[email protected]‐hamburg.de Abstract Online poker is a data goldmine. Recording actual gambling behavior gives rise to a host of research opportunities. Still, investigations using such data are rare with the excep‐ tion of nine pioneering studies by Harvard Medical School which are reviewed here. This paper fills part of the vacuum by analyzing the gambling habits of a sample of 2,127,887 poker playing identities at Pokerstars over a period of six months. A couple of playing variables are operationalized and were analyzed on their own as well as connected with each other in form of the playing volume ($ rake a player has paid in a time frame). The main findings confirm the results of the Harvard studies: most online poker players only play a few times and for very low stakes. The median player played 7 sessions and 4.87 hours over 6 months. Multitabling was observed only rarely (median 1.05) and most players pay very low fees per hour (median US$0.87 per hour per table). The play‐ ing volume is very low, too, with more than 50% of all players paying less than US$4.86 to the operators over 6 months. An analysis of the relationship between the playing ha‐ bits shows that they reinforce each other with the exception of the playing frequency which moderates gambling involvement. The average values of the playing habits are considerably higher due to a small group of intense players: the 99% percentile player has a playing volume that is 552 times higher than that of the median player (US$2,685), and 1% of the players account for 60% of playing volume (10% for even 91%). This group is analyzed more thoroughly, and a discussion shows that the first impulse to peg in‐ tense players as (probable) pathological gamblers is wrong. Rather, future research is needed to distinguish problem gamblers from professional players. Keywords: online, poker, gambling, habits, behavior. * Ingo Fiedler is a Research Associate at the Institute of Law and Economics at the University of Ham‐ burg, Max‐Brauer‐Allee 60, 22765 Hamburg, Germany. Tel: +49 (0)40 42838‐6454, fax: +49 (0)40 42838‐ 6443. 1
1. Introduction
Electronic gambling opens up a new era of research on gambling behavior. So far, analyses have been limited to too small samples or to gambling behavior in laboratories where a monitoring bias cannot be accounted for. Another research method was to interview people about their gambling behavior – a questionable approach since self‐reports of behavior are often inconsistent (Baumeister et al. 2007). People generally tend to underreport their gambling behavior and pathological gamblers lie about theirs.1 Now, electronic gambling and online gambling in particular automatically record actual gambling behavior. This allows reliable and objective analyses of huge and unbiased data sets. Such research how‐ ever, is in its infancy. Pioneering work in this field comes in the form of a series of nine papers from Har‐ vard Medical School (LaBrie et al. 2007, Broda et al. 2008, La Brie et al. 2008, LaPlante et al. 2008, Nelson et al. 2008, LaPlante et al. 2009, Xuan & Shaffer 2009, Braverman & Shaffer 2010, LaBrie & Shaffer 2011). Other research focusing on actual gambling behavior is still missing with the exception of Smith et al. (2009) who compare the gambling behavior of poker players before and after big wins and big losses. To expand the understanding of actual gambling behavior this study analyzes the gambling habits of a sam‐ ple of 2,127,887 poker playing identities at the largest online poker operator Pokerstars over a period of 6 months. This paper is structured as follows: the second section is a review of the paper series from Harvard Medi‐ cal School that focuses on the poker study by Nelson et al. (2009). The third section introduces the On‐ line Poker Database of the University of Hamburg (OPD‐UHH) and operationalizes the playing habits of poker players to make them measurable and comparable. The connections between the different playing habits are also illustrated and the key figure “playing volume” is defined. Section 4 presents the empirical results and analyzes a group of intense players in detail. The following section discusses the main finding
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Lying is a defining criterion of pathological gambling according to DSM‐IV
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that a small group of players account for the majority of the playing volume, by highlighting the necessity to distinguish between pathological and (semi‐)professional poker players.
2. Literature: The Paper Series from Harvard Medical School
All of the papers from Harvard Medical School on the actual behavior of online gamblers rely on a data set of approximately 47,000 betting accounts at the gambling operator bwin which were registered in February 2005.2 The studies can be divided into two separate groups. One group analyzes the gambling behavior of sport bettors, poker players and casino gamblers solely on a descriptive basis. The other group analyzes the gambling behavior of subsamples where problem gambling is indicated by account closing, self‐limitation or limitation by bwin. This allows the authors to investigate the differences be‐ tween recreational and probable pathological gamblers. The studies are unique in their approach be‐ cause they analyze actual gambling behavior. This kind of data set overcomes the typical limitations and biases of self‐reported data and allows an objective measurement of the gambling habits (see e.g. Xuan & Shaffer 2009). The advantages of a data set of actual gambling behavior are enormous, and the au‐ thors even see a paradigm shift in gambling research (Shaffer et al. 2010). The authors distinguish be‐ tween the heavily involved bettors (top 5% or top 1%) and the “majority” 95% (99%) of all participants. The main finding is that the group of the heavily involved bettors is significantly more active than the rest of the cohort. For example, the involvement of the intense poker players was roughly twice as long and they played 7 times as many sessions. They wagered 44 times and lost 6 times more money than the majority of the players. The analyses of the data set and the derived conclusions are manifold. Still, there are some limi‐ tations. The major limitation was addressed by the authors and is inherent to these kinds of data sets:
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Although the studies use the same data set, the number of accounts differs between 47.000 and 48.114.
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bwin is just one online gambling operator and players may have accounts at multiple sites. Multiple ac‐ counts seem especially likely for the most intense players. Hence, their playing behavior can only be ob‐ served partially and the results underestimate their true gambling involvement. This problem is aggra‐ vated in the study focusing on poker players by La Plante et al. (2009) because bwin is mainly a sports betting operator and it can be assumed that the sample mostly consists of people whose primary game is sports betting, meaning that the subsample of poker players consists primarily of players for which poker is their second or even third choice. Gamblers who mainly play poker games may instead sign up with other operators specializing in these games. But as these players are, by definition, more involved, the results of the bwin study underestimate the playing intensity of poker players.3 Although the authors admit this drawback as a bias, they do not see it as probably but rather as plausible. However, the choice of the operator is important for the players, especially in poker. The reason is that the larger the opera‐ tor and its network, the higher the liquidity of poker players there. This means players can choose be‐ tween more tables to find their preferred game structure and limit. Economists call this effect a (posi‐ tive) network externality (Katz & Shapiro, 1985). Compared to Pokerstars or Full Tilt Poker (at that time), bwin is a minor player in the poker market (Fiedler & Wilcke, 2011a) meaning that only few primary pok‐ er players will have signed up with bwin and if so, only as a second or third choice site to play at. Conse‐ quently, the results of poker players’ gambling habits are not representative but underestimated. Al‐ though the present study cannot overcome the inherent problem of people playing at multiple opera‐ tors, the data comes from the largest poker operators and, hence, the analyzed player pool is represent‐ ative for all online poker players. One issue particular to poker which was not addressed by Nelson et al. (2009) is the ambiguity of the term “money wagered”. “Money wagered” is a key variable for most gambling opportunities but not
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The same reasoning holds true for the casino study by La Brie et al. (2008).
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for poker. First of all, it is unclear what is “money wagered” in poker: the money a player puts on the table which is then at risk, or the sum which he actually puts in the pot during a hand, or each individual bet (meaning multiple bets per hand)? The following examples of different player bets point out why the variable “total wagered” should be considered carefully:
Player A sits down with US$100 at a No Limit Holdem US$0.50/US$1 table. He plays just one hand, folds his cards and leaves the table with US$99. Player B sits down with US$100 at a No Limit Holdem US$2/US$4 table. He plays just one hand, folds his cards and leaves the table with US$96. Player C sits down with US$100 at a No Limit Holdem US$0.50/US$1 table. He plays just one hand, bets all US$100 during the hand and leaves afterwards. Player D sits down with US$100 at a No Limit Holdem US$0.5/US$1 table. He plays 100 hands, folds 80 times without a betting, and during the other 20 hands his bets accumulate to a total of US$160. Player E sits down with 100% at a Limit Holdem US$0.50/US$1 table. He plays 1 hand, caps the betting on all streets to a total of $24 and leaves afterwards.
Interpreting each of those players to have wagered US$100 omits analyzing the level of risk in different games and the betting strategies players adopt. In addition, “money wagered” loses value with growing difference between the expected values of bets and between their riskiness (standard deviation of the outcomes). For example, “total money wagered” is perfect for interpreting money wagered on “red” in a roulette game. For money wagered on red and also numbers in roulette it loses some informative value as the riskiness of the bets differ. If now the expected value differs too, the variable “total money wa‐ gered” loses even more of its explanatory power. In poker the expected values and the riskiness of bets differ greatly and the differences are aggravated by the path dependency of decisions during a poker hand. This study avoids this problem by operationalizing and measuring a player’s playing intensity and playing volume, which not only depend on the game and betting structure but also on the number of opponents at a table.
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3. Data and Methods
3.1 The Online Poker Database of the University of Hamburg (OPDUHH)
Online poker is a data goldmine. All operators display a lot of information in their lobbies about the people playing at their tables. It is easy to determine the origin of a player (city and/or country), the game type, betting structure, the limit of the table they are playing at, and of course the time and the date. Financed by the city of Hamburg, the Institute of Law & Economics at the University of Hamburg collected this data in the OPD‐UHH in collaboration with independent market spectator PokerScout. Software electronically gathered player data for the following poker networks: Pokerstars, Full Tilt Poker, Everest Poker, IPN (Boss Media) and Cake Poker. This software scanned each cash game table4 of the aforementioned poker sites and copied the displayed information into a SQL database.5 Data collection was conducted for each poker site over a period of six months, enabling data for 2,127,887 poker identities, including their country of origin and their playing habits, to be obtained. It took about ten minutes to scan all the operator’s tables and collect information about players seated at the tables. This translates to about 6 data points per hour or 25,920 over the course of six months and allows not only to determine the playing time per session of the players, but also to analyze differences in time. The period of the data collection ran from September 10, 2009 to March 11, 2010.6
3.2 Operationalization of Playing Habits
Before measuring the playing habits of online poker players it is essential to operationalize the different observed variables and their interactions, otherwise misunderstandings and confusion about their mean‐ ing might occur. While total playing time, for example, is easy to understand, the playing volume of a
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Play money tables were not observed. For a more detailed description regarding the technical approach of the data collection see Sakai & Haruyoshi 2005. 6 Note that the period of data collection had to be extended due to technical problems such as downs of the server, software updates and disconnections.
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player is not clear. What’s more, operationalization helps to overcome the typical question concerning “total money wagered” which is a key variable for most gambling opportunities but not for poker. The information in the OPD‐UHH can be broken down into seven different variables to analyze the playing habits of an online poker player (they can also be connected with the origin of the player to allow country or region specific analyses). These variables are: 1) number of sessions, 2) playing time per session, 3) number of tables played simultaneously in a session (multitabling), 4) game structure (for example Texas Holdem or Omaha), 5) betting structure (for example No Limit or Fixed Limit), 6) number of players/seats at the table, 7) the size of the big blind7. Note: a session begins when a player who has not been active in the last 20 minutes sits down at any table. This is different from the study of Nelson et al. (2009) which defines a session (although not explicitly) as a player seated at a table and buying chips – regardless of whether he has played immediately beforehand at a different table. In addition, the present study’s definition of a session allows to observe if a player is seated at multiple tables at the same time, a specific feature of online poker. While analyzing each variable individually is interesting, they can also be combined with the in‐
formation of the playing duration (the time between the first and last observation of a player). The most meaningful interpretations, however, are possible when the variables are connected with each other. Variables 1), 2), 3), and 7) are quantitative and can therefore be related to each other. For example, mul‐ tiplying the number of sessions with the playing time per session yields the total playing time over six months. However, variables 4), 5), and 6) are qualitative. Analyzing them separately is not meaningful. But excluding them distorts the picture of the playing habits. For example, playing an hour of Fixed Limit
In the game of poker the players have to post a small and a big blind. Regularly, the small blind is half the big blind. Both blinds are the minimum bet the players have to make before they get their cards. Only one player has to post the big blind and one the small blind (in exceptional cases there is only one big blind or two small blinds and one big blind) while the rest of the players at a table do not have to post any blind. The players posting the blinds are determined by the so called button which moves clock‐ wise around the table from player to player after every hand to ensure that every player has to post the blinds equally over time.
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Holdem with 9 other players cannot be compared with playing an hour of Pot Limit Omaha with 6 play‐ ers. Someone sitting down with US$100 in the Fixed Limit game is considerably less exposed to risk than someone in the Pot Limit Omaha game. Hence, the qualitative variables have to be operationalized and quantified. The one thing they have in common is that they all relate to the rake (the fee paid to the operator). Ceteris paribus: the more players at a table, the less rake is paid per player to the operator. In Omaha more rake is paid than in Holdem, in No Limit games the rake is higher than in Fixed Limit games. However, the magnitude of these effects is not static and also depends on the size of the big blind. Hence, it is necessary to combine these three variables with the size of the big blind. This yields the average rake paid by a player per 100 hands – a quantitative variable which can be related to the other variables of the playing habits. These values are important for the players as they determine – together with bonuses and rebates – the price they are charged for playing poker. Thus, they also differ from operator to operator. No Limit Texas Holdem is by far the most popular poker variant: 58.73% play this variant (see Appendix A). Figure 1 shows the average absolute and relative rake charged by the operators (industry average) for No Limit Holdem games with 6 and 10 players in relation to the size of the big blind. While the absolute amount of rake paid per 100 hands on a limit increases in the size of the big blind (the mon‐ ey at stake) it is evident that it decreases relatively to the size of the big blind. While a player at US$0.01/US$0.02 pays US$0.25 or 12.5 big blinds on average per 100 played hands to the operator at a table with 6 seats, he pays US$15.49 or 2.58 big blinds per 100 hands on a US$3/US$6 table. While the absolute amount increases sharply, the relative price in relation to the stakes (the big blind) is only 1/5. The reason for this lies in the rules for collecting the rake. Two are important here: 1) if the players do not see a flop, the operator does not take any rake and 2) the maximum rake paid is capped at a given amount (usually US$5). Both rules work in favor of the high stakes players: the pots grow larger but the
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rake is capped and the higher the limits, the tighter the players (meaning they play fewer starting hands) so they see fewer flops, which means they pay less rake.
Figure 1: Rake paid to the operators per 100 hands in No Limit Texas Holdem (industry average) 40 20 35 30 US$/100h 25 20 15 10 5 0 18 16 14 12 BB/100h 10 8 6 4 2 0 US$/100h 10max BB/100h 10max
Poker is a zero sum game between the players so the average rake paid to the operator equals the play‐ ing costs for the average player. While it is common for poker players to use rake paid per 100 hands to compare how much they have to pay, it is much more feasible for research questions to standardize the variable in time units.8 This allows a joint analysis with the playing time of a player and a comparison with the expenses for other games like slot machines. The average rake paid per hour by a player is an important variable and shall be denoted with the term playing intensity. The higher the stakes, the more hands per hour played, the less opponents faced, the riskier the betting structure and the poker variant, the higher the playing intensity in form of the average rake paid per hour to the operator.
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The number of hands per hour differs in relation to the players at a table, the betting structure, the poker variant, and some‐ what in relation to the size of the big blind. This means that the conversion of already large variety of values for the average rake paid per 100 hands for the different poker games yields about 2,400 values for the rake per hour in the end. The values can be found in the appendix of Fiedler & Wilcke, 2011.
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Figure 2 shows the relationship between the different variables of the playing habits (number of sessions, average playing time per session, average number of tables played simultaneously and playing intensity). They can be aggregated to the top figure playing volume. This is defined as the product of the playing time over a 6 month period times the number of average tables played simultaneously times the average $ rake paid to the operator. The playing volume of a player states how much money a player has paid to the operator in the 6 months of the observation period.
Figure 2: The different variables of the playing habits and their relationship
Playing volume Number of sessions Ø Playing time per session Game structure Betting structure Table size (seats) Big blind Playing time over 6 months Ø Number of tables played simultaneously Playing intensity = $ rake per hour
4. Empirical Results
4.1 Number of Sessions
The total number of sessions observed over the 6 months period is 51,141,167. At 2,127,887 playing identities9 the average number of sessions played is 24.03. As the nicknames of the player identities were recorded, the number of sessions each player played was also determined. The median player only played 7 sessions over 6 months. Presumably, there are lots of players who only played a few times,
It is not for all playing identities that data were recorded. The reason is that at the beginning and at the end of the observation periods for each operator the session length could not be determined and, therefore, not be accounted for. For players who were only observed at these points, there exists no data on their number of sessions or playing time resulting in a small differ‐ ence between the total number of observed players and the number of players with data on their number of sessions.
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while a small number of intense players played frequently and created the large gap between the mean and median number of sessions played. This hypothesis is strengthened by the standard deviation of 49.3 sessions – 7 times as high as the median. The gap between the mean and the median values can be found in every variable of the playing habits and is investigated more deeply in each case. It leads to two conclusions: (1) a small group of heavily involved poker players is responsible for the majority of the playing volume, and (2) the median values describe the gambling behavior of the typical online poker player more accurately than the mean values. The number of sessions played shows that a relatively large proportion of the players did not
play very often over the course of 6 months: 403,592, equivalent to more than 18% of all player identi‐ ties, only played once. Nearly half a million identities were observed between two and four times and 18.2% between five and ten times. Another 17.2% played between 11 and 25 times while 10.3% of the sample was observed between 26‐50 times. 7.1% played between 50 and 100 sessions and 3.5% be‐ tween 100 and 180 sessions. A group of 2.1% of the sample was seen more often than 180 times at the tables – they played more than one session per day.
4. 2 Playing time per session
The average poker player stayed at the table for 50.27 minutes per session. At 42 minutes, the median player had an average session length of only slightly less. In comparison to the number of sessions the gap is relatively small and the average is not affected by a few extremely long sessions. The standard deviation of 37.76 minutes (0.9 times the median) supports this finding. Still, there is a gap between a majority playing short sessions (25% of the players played less than 25.5 minutes and 70% played less than an hour per session on average) and some people playing long sessions regularly (10% play 94.8 minutes or more per session and nearly 5% two hours or more). Analyzing the session length not by player but by sessions shows that nearly one third (32.4%) of all sessions ended in less than 30 minutes. 38.2% lasted between 31 and 60 minutes, 17.8% 61 to 90 minutes, and 6.8% 91 to 120 minutes. For 11
another 3.7% of the sessions a length of two to three hours was recorded and 1.1% of the sessions lasted more than 3 hours without a break.
4.3 Total playing time over 6 months
As discussed before, the combination of the number of sessions and their lengths yields the total playing time of a player over the observation period of 6 months. This is possible because each nickname is unique on each poker platform and the players can be recognized and tracked. It is noticeable that the average playing time over 6 months was 25.28 hours for the average player while the median player only played 4.88 hours over the course of 6 months. Hence, the average value is again impacted by a small group of intense players, a hypothesis supported by the huge standard deviation of 65.21 hours (13.36 times the median value). It means that the gap between the average and the median values of the num‐ ber of sessions and the playing time per session is amplified by combining them to the total playing time. Analyzing the relative frequency of the classified total playing time shows that a large proportion of the players play poker rarely: 22.9% of all players did not play for more than an hour, 27.6% of the observed player identities played between 1 and 5 hours poker for real money over the course of 6 months, and 20% have a total playing time between 5 and 15 hours. 12.8% of the players were observed for 15 to 35 hours and 10.6% of the sample for 35 to 100 hours (which still is not to be categorized as excessive if poker is a hobby for them). The proportion of players who spent more than 100 hours at the virtual poker tables however, is not to be disregarded. 6.1% of all players have played more than 33 mi‐ nutes each day on average.
4.4 Multitabling
Online poker offers the possibility to play at more than one table at the same time. This is called multi‐ tabling and only possible because the players do not have to sit physically at the poker table but in front of a computer screen where they can arrange multiple tables next to each other. In contrast to the anec‐ 12
dotal evidence, online poker players do not tend to multitable frequently. In the average session the player played at 1.31 tables simultaneously and in the median session at 1.05 tables. The gap is not very large and the standard deviation of 1.04 tables also suggests that the mean value is only marginally af‐ fected by a small group playing many tables. Still, there is a gap between a majority playing just on one or partially at a second table and some people playing on more tables regularly: 10% of the players play at 1.65, 5% on 2.36, and 1% at 6.03 tables on average. Analyzing multitabling not by player but by session shows that multitabling is most often not practiced on a regular basis (which yields a high average over all sessions of a player) but instead some‐ times tried out by a lot of players (yielding only slightly increased averages per sessions for many play‐ ers). Still, in 60.3% of all sessions the player was singletabling. In 15.8% of all sessions two tables were played simultaneously. In another 5.8% three tables were played at the same time and 5.1% of all ses‐ sions were played at four tables simultaneously. Five or six tables were observed in 4.4%, seven or eight tables in 2.2%, and nine to 12 tables in 3.1% of all sessions. In 3.2% of the sessions the player played at 12 or more tables at the same time. Hence, massive multitabling is not exercised regularly by many play‐ ers but only sometimes by several players. Given that on average about 70 hands are played per table per hour, a player playing at 12 tables simultaneously completes 840 hands per hour – or 14 per minute. While most combinations of cards are folded directly and on “autopilot” by the practiced player, it takes a lot of effort to analyze the informa‐ tion in hands where he sees a flop. The player does not only have to evaluate the strength of his own hand but also has to consider a lot of other factors including the possible hands his opponent may hold in this particular situation as well as the perceived range of hands his opponent gives him. As the hand plays out, the information to be processed and evaluated by a player can get quite complicated and training videos for poker players and hand analysis in poker forums like 2+2 show that it is easily possible 13
to think about a single poker hand for a couple of hours. Hence, playing 14 hands per minute requires a very high amount of concentration and focus or – on the other hand – suggests recklessness.
4.5 Playing intensity
The playing intensity is defined as the average rake paid by a player per hour to the operator. It depends on the game structure (for example Holdem or Omaha), the betting structure (for example No Limit or Fixed Limit), the number of players seated at the table, and the size of the big blind corresponding to the money at stake. The playing intensity is the cash flow from the players to the operator and equals the average loss per hour of an average skilled player. The average playing intensity was US$2.40 per hour per table. The median player paid considerably less rake: US$0.87 per hour per table. Paired with the relatively large standard deviation of US$4.46 (5.06 times the median amount) this leads to the conclu‐ sion that there is a small group of players with a high playing intensity who drive the mean value. Com‐ pared with the cost of other gambling opportunities like slot machines, online poker is quite inexpensive (for most players). Key reasons for cheap offers are operators situated in small countries (“tax oases”) who pay low taxes and a very small fee or nothing at all for their license. But the main reason is probably that the marginal costs of the operator are (nearly) zero because they do not have to pay dealers or cov‐ er rent costs. Instead they use scalable software which costs the same, regardless of how many tables are offered. Nearly every fifth online poker player (19.9%) pays US$0.20 or less per hour per table to the op‐
erator and 18.1% have a playing intensity between US$0.20 and US$0.50. Another 15.1% of the observed playing identities played with an intensity of US$0.50 to US$1 per hour per table. Hence, 53.1% of all players pay less than US$1 rake per hour or, the other way round, the operators earn less than US$1 per hour with more than half of their customers. The group of players paying US$1‐2 per hour accounts for 15.7% of the sample and the players with an intensity between US$2 and US$5 account for 17.7% of the
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sample. Another 11.3% pay between US$5‐15 and only 2.0% of all player identities were observed to pay more than US$15 per hour per table.
4.6 Top figure: Playing volume over 6 months
The multiplication of the total playing time, multitabling and playing intensity yields the playing volume. It is the top figure regarding playing habits and states how much money a player has paid to the operator over the observation period of 6 months. The aggregated playing volume of all players equals the opera‐ tors’ revenues and the players’ losses. While the analysis of the individual variables of the playing habits was already greatly influenced
by a small group of heavily involved poker players, this finding becomes even more evident through an analysis of playing volume. The total observed playing volume over 6 months for all players was US$378 million.10 This leads to an average player loss of US$177.51. The emphasis, however, is the huge gap be‐ tween the mean and the median playing volume: 50% of the sample paid only US$4.86 over 6 months to the operators. The standard deviation of US$1,935 is 398 times the median amount and amplifies this difference. It can only be explained by a small group of players who have a huge playing volume and strongly impact the average value. These figures suggest that there is a small group of excessive poker players. This hypothesis is supported by further evidence in this subsection before the group of heavily involved players will be analyzed separately in the following section. 29.8% of all player identities paid less than US$1 rake over 6 months. Their playing volume is negligible. Presumably, they deposited a small amount, lost it in a few hands to their opponents, and never logged in again. Nearly one million player identities or 20.6% of the sample have a playing volume of US$1‐5 which can be regarded as marginal. Also the playing volume of the 15.0% of the players who
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The total playing volume can be extrapolated to the total market for a whole year to state the market size and also be broken down by operators to state their revenues market shares. This was done in Fiedler & Wilcke, 2011a.
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paid between US$5 and US$15 is very small. Relative to the observation period of 6 months even ex‐ penses of US$15‐50 by approximately 200,000 players (14.2%) is not much. Nearly every tenth person (9.4%) has a playing volume of US$50‐150 over 6 months which cannot be disregarded but is not exces‐ sive either and is still below the average value. 6.3% of the players paid between US$150 and US$500 rake to the operators and they are potentially at risk. 4.7% of the sample paid more than $500. Given the small fees in online poker, their playing volume can be called excessive. Before analyzing the group of the intense players in more detail in the next section, it is to be highlighted that the playing volume of a player equals the payment to the operator but does not equal the players’ losses. Players can also lose money to their opponents (or win from them). Presumably, un‐ trained players who play poker infrequently lose money on average to their opponents while the trained players usually win (for empirical evidence, see Fiedler & Rock 2009). Hence, players with a low playing volume tend to have higher losses than the rake paid to the operators, while players with a high playing volume have less expenses or even winnings. For this reason, an interpretation of an individual’s playing volume as his total losses is not meaningful. The playing volume can only be interpreted as players’ losses when aggregated. Still, the use of playing volume to determine the involvement of an individual player is reasonable. It allows the conclusion that most players have a small playing volume and are not at risk to develop an addiction, while a small group has an excessive playing volume and may be patho‐ logical and/or professional gamblers.
4.7 Playing habits combined with playing duration
Some of the variables of the playing habits like the number of sessions are necessarily affected by the playing duration which is the time between the first and last observation of a player. On average the players were observed 55.32 days and the median player 27 days. The standard deviation of 60.83 days is more than twice as large as the median value and points out that the distribution is affected by some players who were observed over the whole data collection period. Combining playing duration with the 16
number of sessions yields an average of .74 and a median of .60 sessions per day. This suggests – sup‐ ported by the relatively low standard deviation of .66 sessions/day – that even the most intense players do not play much more often per day than recreational players. On the other hand this value might be biased by the group of players who were only observed on one day and stopped playing thereafter. They have a sessions/day ratio of at least one and account for more than 20% of the sample. This is a draw‐ back not inherent to the ratio playing time/playing duration. On average the sample played 38.70 mi‐ nutes per day. The median value is 20 minutes per day and the standard deviation 53.62 minutes/day. Here we find again that the average is strongly affected by a small group of players with a high exposure. The most interesting combination is playing volume per playing duration. The average rake/day is US$2.48 and more than 9 times larger than the median value of US$.27/day. This suggests, again, that a small group of players account for most of the playing volume. However, although the standard devia‐ tion of 14.44US$/day is relatively huge, it is not as large compared to the median value as in the analysis of playing volume without consideration of the playing duration (53.5x to 398x). This leads to the conclu‐ sion that the small group of the most involved poker players dominate in every variable of the playing habits.
4.8 Relations between the different variables of the gambling habits
The above results suggest that the variables of the playing habits reinforce each other. This hypothesis can be tested by analyzing the relationship between them which allows conclusions about whether they reinforce each other or there is a moderating variable to be drawn. In fact, it is obvious that total playing time has to be positively related to the number of sessions as it is defined as the product of number of sessions and average session length. However, the relationship is not necessarily positive between all variables. For example, there might be a negative relationship between playing intensity and number of tables: The higher playing intensity, the more money is at stake, hence people may decide to play at fewer tables. A Kolmogorov‐Smirnov‐Lillefors test for normality of a random 1% sample shows that all 17
variables are not normally distributed (all significant at p<0.001).11 Therefore, the relationships are calcu‐ lated as non‐parametric rank‐order correlations according to Spearman (ρ). Table 1 presents the results. As is to be expected by its definitions, the relationships between total playing time and number of ses‐ sions and session length is exceptionally positive as well as the correlation of playing volume to all other variables of the playing habits. This is also true for the correlations between playing duration to number of sessions, playing time, and playing volume.
Table 1: Nonparametric Spearman correlations among the variables of the gambling habits (n= 2,127,887).
Session Total Sessions Length Playing Time Sessions ‐ .360** .939** Session Length ‐ .644** Playing Time ‐ Tables Playing Intensity Playing Volume Playing duration Sessions/day Time/day Rake/day ** Correlation significant at p<.01. Tables Playing Playing Playing Sessions/ Time/ Rake/ Intensity Volume Duration Day Day Day .534** .160** .793** .831** ‐.171** .139** .264** .428** .031** .527** .235** .049** .612** .483** .587** .141** .836** .749** ‐.100** .345** .399** ‐ .113** .564** .416** ‐.037** .246** .357** ‐ .633** .187** ‐.106** ‐.078** .674** ‐ .667** ‐.130** .243** .689** ‐ ‐.607** ‐.290** ‐.029** ‐ .771** .448** ‐ .642** ‐
More meaningful are the correlations between number of tables played which is strong positive
to number of sessions and session length (and hence to total playing time) and playing duration. This means that people who play longer and more often also tend to play at more tables (and vice versa). Another interesting finding comes from the correlations of playing intensity. Although playing intensity is positively related to all other variables of the playing habits, the correlation is relatively weak (especially to the session length) compared to the other relationships between the variables. This suggests that when people play more often, for a longer time, and at more tables they only slightly increase their stakes.
11
Sessions: K‐S=.322, session length: K‐S=.117; total playing time: K‐S=.350; number of tables: K‐S=.382; playing intensity: K‐ S=.296; playing volume: K‐S=467; betting days: K‐S=.186; sessions/day: K‐S=.177; playing time/day: K‐S=.236; rake/day: K‐ S=.432.
18
Analyzing the relationship between the combination of playing habits with playing duration yields important results. The correlation between sessions/day and playing duration is strongly negative. This means that the higher playing frequency of a player the more likely he is to stop gambling. With the exception of the correlation to session lengths, sessions/day shows a weak negative correlation to all other playing habits. This means that playing very often in a short period of time reduces overall gam‐ bling involvement. This finding might be counterintuitive when it comes to pathological gambling. But it is reasonable for recreational players who have a given limit for their expenses and stop when it is reached (they reach it faster when they play more frequently). However, playing frequently does not mean playing long sessions. And the correlations of the time spent playing poker per day are different from those of sessions/day. While time/day is negatively correlated to playing intensity and playing dura‐ tion it is positively related to the other playing variables. Rake/day is also positively related to all va‐ riables of the playing habits with the exception of playing duration. Overall, it can be concluded that the only moderator for gambling involvement is playing frequency while all other playing habits reinforce each other.
4.8 The group of intense players
The playing habits of intense players differ from those of casual players. Table 2 presents a summary of the results for the different variables of playing habits and compares the mean and median with those in the top 10%, top 5% and top 1% players.
Table 2: Summary of the playing habits (n=2,127,887). Ø Median Number of sessions 24.03 7 Session length in min. 50.27 42.0 Total playing time in h 25.28 4.88 Number of tables 1.31 1.05 Playing intensity ($ rake/h) 2.40 .87 Playing volume in $ 177.5 4.86 Playing duration 55.32 27 Sessions/day .74 .60 Playing time/day 38.70 20.00 2.48 .27 Playing volume in $/day
σ 49.30 37.76 65.21 1.04 4.46 1,935 60.83 .66 53.62 14.45
Top 10% 63 94.78 62.78 1.65 6.12 173.9 160 1.50 98.34 4.42
Top 5% 108 118.6 117.6 2.36 9.90 460.1 175 2 142.03 9.15
Top 1% 247 182.3 318.0 6.03 19.75 2,685 182 3 259.00 35.42
Total 51,141,167 ‐ 53,785,011 ‐ ‐ 377,714,269 ‐ ‐ ‐ ‐
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The increase in the session length from the median player (42 minutes) to the intense players is moderate. The top 10% player played 94.8 minutes on average per session, the top 5% player 119 mi‐ nutes and the top 1% player 182 minutes. The increase is considerably higher with the number of ses‐ sions. While the median player only played 7 sessions over the course of 6 months, the top 10% player played 63, the top 5% player 108, and the top 1% player 247 sessions. Hence, it can be deduced that the huge difference between the total playing time of the median player (4.88 hours) and intense players (63, 118 and 318 hours) is due to the number of sessions and only slightly affected by the playing length per session. Multitabling is uncommon among recreational players and median players only play 1.05 tables at the same time, but it is common among intense players: the top 10% player played 1.65, the top 5% player 2.36 and the top 10% player 6.03 tables simultaneously. The ratio intense player to me‐ dian player is also notable when it comes to playing intensity. While the median player pays US$0.87 rake per hour to the operator, the top 10% player pays US$6.12, the top 5% player US$9.90, and the top 1% player even US$19.75 or nearly 21 times the median amount. Combining playing habits with playing volume widens the gap between median and intense players greatly. The median player paid US$4.86 rake to the operators over 6 months and the top 10% player already 36 times as much (US$174) which equals the average of US$178. The average is mainly driven by the most intense players. The top 5% player was observed to have paid US$460 and the top 1% player even US$2,685 – 552 times the median amount. The analysis by percentiles supports the evidence that most online poker players only have a very low playing volume and a small group plays intensely (see figure 9). The playing volume increases exponentially with rising percentile. The 90% percentile player nearly pays nearly twice as much as the 85% player, the increase to the 95% percentile is 164% and to the 99% percentile even 483%.
Figure 3: Playing volume in $ rake paid over 6 months by percentiles ((n=2,127,887).
20
3000 2500 $ rake 2000 1500 1000 500 0
460 294 362 174 204 243 89 65 0.1 0.2 0.4 0.7 1.1 1.6 2.4 3.4 4.8 6.7 9.4 13 19 27 41 852 608
2685
1334
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 91 92 93 94 95 96 97 98 99 Percentile
Hence, the operator needs more than 500 recreational poker players to get as much revenue as he gets from one very intense player and it can be concluded that the operators generate most of their revenue from the intense players. This finding is validated by the comparison of the aggregated playing volume of the intense players to the whole sample (see table 3). 10% of the players account for 91.06% of all rake paid, 5% for 83.1% and still more than half of each dollar (59.59%) is generated by just 1% of the players. Their share of the total expenses is more than the 80/20 Pareto principle, which states that for most consumer goods about 80% of the revenues come from 20% of the customers. Viewing such numbers in the context of gambling, the first idea that comes to mind is that the intense players are ei‐ ther pathological gamblers or at risk of becoming pathological. But this conclusion may be premature in the light of the skill element in poker and the professional players.
Table 3: Aggregated playing volume of the intense players and their share of the total playing volume Player group Playing volume in $ rake paid Share of total playing volume 225,086,489 Top 1% 59.59% Top 5% 313,888,432 83.10% Top 10% 343,956,948 91.06% All 377,714,269 100%
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5. Discussion and Perspectives
5.1 Intense poker players – are they pathological gamblers?
One major challenge arises when analyzing games with skill elements. In poker – and to a somewhat lesser extent in sports betting – the influence of skill is large enough that professionals can play with a positive expected value and win in the long run (see pokertableratings.com and sharkscope.com for the results of professional poker players). Skill matters a great deal in the game of poker (Cabot & Hannum, 2005). Players have several possibilities to influence the outcome of the game. These are: folding, calling, betting, raising, and re‐raising before the flop, on the flop, on the turn, and on the river. If the game is played as No Limit, the player can also decide how much to bet, raise, or re‐raise. These decisions de‐ pend on many influential factors, such as the position at the table, the size of the pot (pot odds), the range of the possible hands of the opponent(s) and, of course, on the cards of the player and the com‐ munity cards. The skill in poker is to interpret and weigh up these factors accordingly and then make the best decisions (Fiedler & Rock 2009). In poker, relative skill matters (Dreef et al. 2003). There are relatively skilled players who consis‐ tently win money from their opponents and relatively unskilled players who lose this money (although this group may be skilled in relation to other players). Due to the fees in form of rake the players have to pay to the operator, most players lose overall, including those who are better than their opponents. Still, there are players who are so skilled that they overcompensate this disadvantage and win money in the long run.12 The group of the winning players can be broken down into three subgroups: 1) the successful recreational players, 2) the semi‐professional players, and 3) the professional players. The successful recreational players are the largest of these groups. They may be long‐term winners but their skill is only sufficient to beat the lowest limits. That means they either win just small amounts of money and poker is
12
See for example websites which keep track of the results of poker players like pokertableratings.com.
22
not attractive for purely financial reasons or they fulfill the peter‐principle and are “water boys” who climb to limits where more money is at stake but where they are not good enough any longer to win. Still, they probably play more than the average recreational player. The group of the semi‐professional players consists of individuals whose skill is sufficient to have success in a financially meaningful context. However, the people in this group have a full‐time occupation. Hence, they only play in their free time but on higher limits than the successful recreational players and they see poker as a lucrative possibility for an additional source of income. The group of the professional players is very small. It consists of play‐ ers who are sufficiently skilled to consistently win money by playing poker to an extent that they do not need another job. They are not necessarily more skillful than the players in the semi‐professional group but they spend considerably more time playing poker and regard it as their job. All of these players have an incentive to play often and (and for larger amounts) and a higher than average playing volume. This may be reached by playing high limits, playing many tables, many or long sessions or a combination of these. All semi‐professionals and professionals and a large number of the successful recreational players have a high “involvement” and can be found in the group of intense players. Hence, they affect the dis‐ tributions of the playing variables. This is a huge problem when trying to identify excessive or even pa‐ thological poker players (and sports bettors) by their playing volume. On the other hand, not all intense players are winning players which indicates that also patholog‐
ical players are in the group of intense players. Thus, the question is how many players of the intense players are pathological and how many are professionals, and also whether these players are only good at poker and play due to the financial incentive, or whether they are (also) addicted to poker. According to Weinstock & Petry (2009) pathological and professional gamblers differ only in the degree of their impulsivity. However, this data set does not cover the betting patterns of the players which may give insights to the degree of impulsivity. As Smith et al. (2009) analyze betting patterns of poker players but not in direct connection to impulsivity, the question has to be addressed by future research which ana‐ 23
lyzes actual playing behavior in more detail. Until such research is available, it can only be suspected that the group of the intense players mostly consists of (semi‐)professional players, pathological players and (semi‐)professional players who are addicted to poker but have not suffered any negative financial con‐ sequences (yet).
5.2 Limitations
Although the study yields many findings there are some limitations. Poker players can easily play on mul‐ tiple sites and, somewhat less likely, on the same site with multiple user names. This data set cannot take this fact into consideration and as a consequence every observed nickname at each site is inter‐ preted separately. Thus, players with multiple accounts are interpreted as multiple players. This is a problem inherent to all analyses of actual playing behavior: they are always partial analyses as gambling behavior at different locations or games is not recorded. Underestimation is the result. For this study, it mainly affects the playing behavior of intense players as they are most likely to play at multiple sites. On the other hand, it may also be possible that more than one person uses the same player identity (ac‐ count sharing), for example friends or family members. A more important limitation is that cash flows between the players were not observed. Thus, it
cannot be determined whether a player is winning or losing. However, this is important information which would help to give a clearer insight into high volume play. It was shown for example, that players who play more often lose less (Nelson et al., 2009) and even win (Fiedler & Rock, 2009). Thus, it can be suspected, that the group of the intense players in this sample is losing less than the rest of the sample. However, this hypothesis could not be investigated.
5.3 Conclusions and Perspective
Electronic gambling and online gambling in particular offer the possibility of analyzing large unbiased data sets of actual playing behavior and invite new promising research. Harvard Medical School was the 24
first to do this in a series of nine papers. One group of papers described gambling behavior and the main conclusion was that most players do not play very often, while a small group plays intensely. However, the conclusions for the poker players by Nelson et al. (2009) have to be considered carefully because these data sets are not representative as bwin is mainly a sports betting operator and only offers poker on the side. Furthermore, the authors did not address the role of skill in poker which can lead to profes‐ sional gamblers influencing the variables of gambling behavior. This paper advances research in this field forward by analyzing actual gambling habits of online poker players by means of a large and unbiased sample of 2,127,887 player identities from the Online Poker Data base of the University of Hamburg (OPD‐UHH) who were tracked over 6 months at five dif‐ ferent poker operators. In addition to a player’s city or country of residence, software recorded who sits at how many and what kind of tables every ten minutes. This data was operationalized into the following variables: number of sessions, time spent per session, total playing time and the playing intensity in form of $ rake paid per hour and table to the operator. This way of operationalizing the variables of playing habits makes sense, not only against the background that poker is a game between players and not against the house, but also because the variables of the playing habits can be analyzed in isolation as well as in combination with each other. This allows the key figure “total playing volume” to be defined, indicating how much rake a player has paid to the operator over a given time frame (here 6 months). The main finding confirms the results of the Harvard studies: most online poker players only play
rarely and for low stakes. The median number of sessions is 7 and the median playing time over 6 months is 4.88 hours. Regarding the playing intensity, it is notable that most players pay very low fees per hour (median is US$0.87 per hour per table). Also, a different definition of the term “session” al‐ lowed to analyze multitabling, a specific feature of online poker made possible due to the virtual nature of game play. It was found that most players do not make use of the unique opportunity of online poker to play at multiple tables at the same time. The median player was observed at 1.05 tables simultaneous‐ 25
ly. Hence, the total playing volume of the median player is also very low: more than 50% of all players paid less than US$4.86 in rake to the operators over 6 months. However, the average values of the play‐ ing habits are considerably higher than the median values and they are highly affected by a small group of intense players. For example, the 99% percentile player has a 552 times higher playing volume than the median player (US$2,685). This is a value much higher than that found by Nelson et al. (2009). This small group of players accounts for most of the playing volume: operators earn 59.6% of their revenues from only 1% of the sample. 5% of the players account for 83.6% and 10% for 91.1% of playing volume. The group of high volume players is not only interesting for the industry because of the revenue
they generate but also for research on gambling addiction. However, it is wrong to label every one of them as a (probable) pathological gambler, because in the long run skill plays a key role for the outcome in poker. Sophisticated players are able to play with a positive expected value. Thus, in contrast to typical gambling where no skill is involved, the group of intense players in poker consists of pathological gam‐ blers as well as (semi‐)professional players earning a living by playing poker. When analyzing poker it is important to keep this in mind. Consequently, it is important that future research addresses the issue of a reliable distinction between professional and pathological poker players. There are two different alter‐ natives to accomplish this goal. One approach is to dig deeper into the actual betting decisions of poker players (or other gamblers) to find tendencies of chasing, reinforcement or irrationality. The other ap‐ proach is to combine data on playing habits with interview data. Both ideas seem promising and capable of pushing the boundaries of current research forward.
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Appendix: Poker players per variant and limit
Microstakes Lowstakes Midstakes Highstakes Total Absolute % Var % Tot Absolute % Var % Tot Absolute % Var % Tot Absolute % Var % Tot Absolute % Tot Texas Holdem NL 3,015,319 48.43% 28.44% 2,567,389 41.24% 24.22% 621,010 9.97% 5.86% 22,404 0.36% 0.21% 6,226,122 58.73% Texas Holdem FL 936,269 52.55% 8.83% 674,773 37.87% 6.37% 158,451 8.89% 1.49% 12,334 0.69% 0.12% 1,781,827 16.81% Texas Holdem PL 178,560 33.15% 1.68% 335,521 62.30% 3.17% 24,329 4.52% 0.23% 170 0.03% 0.00% 538,580 5.08% Texas Holdem ML 8,943 68.81% 0.08% 3,913 30.11% 0.04% 93 0.72% 0.00% 47 0.36% 0.00% 12,996 0.12% Omaha NL 652 56.99% 0.01% 313 27.36% 0.00% 155 13.55% 0.00% 24 2.10% 0.00% 1,144 0.01% Omaha FL 15,657 54.97% 0.15% 7,730 27.14% 0.07% 5,073 17.81% 0.05% 21 0.07% 0.00% 28,481 0.27% Omaha PL 404,516 41.06% 3.82% 404,347 41.04% 3.81% 162,187 16.46% 1.53% 14,203 1.44% 0.13% 985,253 9.29% Omaha Hi/Lo NL 31,771 24.61% 0.30% 74,929 58.04% 0.71% 22,190 17.19% 0.21% 200 0.15% 0.00% 129,090 1.22% Omaha Hi/Lo FL 50,068 33.54% 0.47% 67,797 45.41% 0.64% 28,307 18.96% 0.27% 3,120 2.09% 0.03% 149,292 1.41% Omaha Hi/Lo PL 79,438 48.29% 0.75% 69,120 42.02% 0.65% 15,736 9.57% 0.15% 209 0.13% 0.00% 164,503 1.55% Omaha Hi/Lo ML 16 44.44% 0.00% 20 55.56% 0.00% 0 0.00% 0.00% 0 0.00% 0.00% 36 0.00% 7 Card Stud NL 9 52.94% 0.00% 3 17.65% 0.00% 5 29.41% 0.00% 0 0.00% 0.00% 17 0.00% 7 Card Stud FL 70,155 44.41% 0.66% 72,992 46.21% 0.69% 13,889 8.79% 0.13% 929 0.59% 0.01% 157,965 1.49% 7 Card Stud PL 37 48.05% 0.00% 38 49.35% 0.00% 2 2.60% 0.00% 0 0.00% 0.00% 77 0.00% 7Card Stud Hi/Lo FL 29,303 39.07% 0.28% 35,860 47.82% 0.34% 8,930 11.91% 0.08% 903 1.20% 0.01% 74,996 0.71% 5 Card Stud FL 0 0.00% 0.00% 251 100.00% 0.00% 0 0.00% 0.00% 0 0.00% 0.00% 251 0.00% 5 Card Draw NL 0 100.00% 0.15% 15,382 100.00% 0.15% 0 0.00% 0.00% 0 0.00% 0.00% 15,382 0.15% 5 Card Draw FL 43,448 50.27% 0.41% 38,356 44.38% 0.36% 4,569 5.29% 0.04% 49 0.06% 0.00% 86,422 0.82% 5 Card Draw PL 4,513 14.76% 0.04% 17,279 56.52% 0.16% 8,727 28.55% 0.08% 52 0.17% 0.00% 30,571 0.29% 5 Card 7‐A Draw FL 5,512 26.98% 0.05% 13,085 64.05% 0.12% 1,831 8.96% 0.02% 0 0.00% 0.00% 20,428 0.19% 5 Card 7‐A Draw PL 12,348 45.89% 0.12% 14,561 54.11% 0.14% 0 0.00% 0.00% 0 0.00% 0.00% 26,909 0.25% Triple Draw Lowball 2‐7 NL 0 0.00% 0.00% 2,102 100.00% 0.02% 0 0.00% 0.00% 0 0.00% 0.00% 2,102 0.02% Triple Draw Lowball 2‐7 FL 8,738 39.34% 0.08% 9,613 43.28% 0.09% 3,059 13.77% 0.03% 799 3.60% 0.01% 22,209 0.21% Triple Draw Lowball 2‐7 PL 0 0.00% 0.00% 791 100.00% 0.01% 0 0.00% 0.00% 0 0.00% 0.00% 791 0.01% Single Lowball 2‐7 NL 0 0.00% 0.00% 4,242 88.30% 0.04% 552 11.49% 0.01% 10 0.21% 0.00% 4,804 0.05% Razz FL 29,375 41.13% 0.28% 32,027 44.85% 0.30% 9,372 13.12% 0.09% 643 0.90% 0.01% 71,417 0.67% Soko FL 0 0.00% 0.00% 1,865 100.00% 0.02% 0 0.00% 0.00% 0 0.00% 0.00% 1,865 0.02% Badugi FL 0 0.00% 0.00% 18,395 87.19% 0.17% 2,339 11.09% 0.02% 363 1.72% 0.00% 21,097 0.20% HORSE/HEROS FL 8,589 42.04% 0.08% 10,676 52.25% 0.10% 1,127 5.52% 0.01% 40 0.20% 0.00% 20,432 0.19% HOSE FL 360 72.43% 0.00% 111 22.33% 0.00% 24 4.83% 0.00% 2 0.40% 0.00% 497 0.00% 8‐Game FL 0 0.00% 0.00% 19,189 82.39% 0.18% 2,881 12.37% 0.03% 1,221 5.24% 0.01% 23,291 0.22% Other Mixed Games FL 1,480 71.64% 0.01% 574 27.78% 0.01% 10 0.48% 0.00% 2 0.10% 0.00% 2,066 0.02% SUMME 4,935,076 46.55% 4,513,244 42.57% 1,094,848 10.33% 57,745 0.54% 10,600,913 100.00% *NL = No Limit, FL = Fixed Limit, PL = Pot Limit, ML = Mixed Limit. Note that this table refers to the total sample of players in the OPD‐UHH. Poker variant*
30