Theoretical Loss and Gambling Intensity: a Simulation Study
Total Page：16
File Type：pdf, Size：1020Kb
GAMING LAW REVIEW AND ECONOMICS Volume 16, Number 5, 2012 Articles Ó Mary Ann Liebert, Inc. DOI: 10.1089/glre.2012.1655 Theoretical Loss and Gambling Intensity: A Simulation Study Michael Auer, Andreas Schneeberger, and Mark D. Griffiths any recent studies of Internet gam- long run, outcomes in games of chance are always M bling—particularly those that have analysed dependent on the house advantage: games with a behavioral tracking data—have used variables such big house advantage lead to higher losses for the ‘‘bet size’’ and ‘‘number of games played’’ as proxy gambler, while games with a lesser house advantage measures for ‘‘gambling intensity.’’1 However, nei- lead to lower losses. For instance, lottery games typ- ther bet size nor the number of games played ically have relatively high house advantages (e.g., takes into account the house advantage of a game. 50%), whereas casino games typically have rela- Players are risking less when they play games tively low house advantages: roulette games with with low house advantages. A low house advantage, a single ‘‘zero (0)’’ on their wheels, for example, therefore, corresponds to a high payout. Further- have a house advantage of 2.7%. more, data presented from these studies have typi- The ‘‘loss/win’’ variable—often referred to as the cally been presented by game type (e.g., data are gross gaming revenue (GGR)—is the difference be- only presented from online sports bettors or online tween ‘‘total bet’’ and ‘‘total win.’’ However, as a poker players). However, using a concise simulation measure of a player’s gambling intensity, it is not analysis of online gamblers playing a variety of suitable, as it is typically distorted by the occasional games, this short article argues that bet size cannot winning occurrences by gamblers, particularly in be reliably used across games and/or game types as the short-term. In the very long run, GGR is a a measure of gambling intensity. Griffiths and Auer2 outlined the many advan- tages and disadvantages of using behavioral track- ing data in the gambling studies field. The main 1A. Broda, D.A. LaPlante, S.E. Nelson, R.A. LaBrie, L.B. Bos- advantages of behavioral tracking data are that it worth, and H.J. Shaffer, Virtual harm reduction efforts for In- (a) provides a totally objective record of an indi- ternet gambling: effects of deposit limits on actual Internet sports gambling behaviour,5Harm Reduction Journal vidual’s gambling behavior on a particular online 27 (2008); R.A. LaBrie, S. Kaplan, D.A. LaPlante, S.E. Nelson, gambling Web site; (b) provides a record of events and H.J. Shaffer, Inside the virtual casino: A prospective longi- and can be revisited after the event itself has fin- tudinal study of Internet casino gambling, 18(4) Eur. J. Pub. Health 410–416 (2008); D.A. LaPlante, J.H. Kleschinsky, ished; and (c) usually comprises very large sample R.A. LaBrie, S.E. Nelson, and H.J. Shaffer, Sitting at the virtual sizes. These are the main reasons that such data poker table: A prospective epidemiological study of actual In- will be used here. ternet poker gambling behavior,25Computers in Human Behav. 711–717 (2009); D.A. LaPlante, A. Schumann, R.A. In this article, we describe what we believe is the LaBrie, and H.J. Shaffer, Population trends in Internet sports best and most stable measure for ‘‘gambling intensi- gambling,24Computers in Human Behav. 2399–2414 ty.’’ This measure is the ‘‘theoretical loss.’’ In the (2008); S.E. Nelson, D.A. LaPlante, A.J. Peller, A. Schumann, R.A. LaBrie, and H.J. Shaffer, Real limits in the virtual world: Self-limiting behavior of Internet gamblers,24J. Gambling Stud. 463–477 (2008); S. Dragicevic, G. Tsogas, and A. Kudic, Analysis of casino online gambling data in relation to Michael Auer is Business Unit Manager Predictive Analytics at behavioural risk markers for high-risk gambling and player a2mlab in London. Andreas Schneeberger is CEO of a2mlab. protection,11Int’l Gambling Stud. 377–391 (2011). Mark D. Griffiths is Professor of Gambling Studies in the 2M.D. Griffiths and M. Auer, Online versus offline gambling: International Gaming Research Unit, Psychology Division, at Methodological considerations in empirical gambling re- Nottingham Trent University in Nottingham. search, 7(3) Casino & Gaming Int’l 45–48 (2011). 269 270 AUER ET AL. more reliable indicator of gambling intensity, as The house advantage is a key structural factor that (statistically) it corresponds to the theoretical loss. influences game attractiveness to players and This means that theoretical loss is the most reliable helps determine the casino’s revenue stream. High and robust indicator of gambling intensity. The the- house advantages tend to be less attractive to the oretical loss of any given game is represented by the gambler but yield high profits. Based on our experi- product of the bet size and the house advantage. ence in the field of gambling, as well as our knowl- Over very long periods of time, the theoretical edge of the different gaming platforms, we chose 13 loss corresponds to the GGR with increasing accu- games to be part in the simulation study. Table 1 dis- racy. The following formula shows the calculation plays these 13 games and their house advantages. of the theoretical loss for a bet on a single game These house advantages are mean average values, (g). The house advantage depends on the specific because different operators sometimes modify game in question. games slightly. For example, slot machines and video poker, in particular, can vary greatly across Theoretical Lossg ¼ Total Betg  House Advantageg operators. Therefore, we provided two house advan- The more diverse the gambling behavior, the more tages each for slot machines and video poker. the bet size will typically deviate from the theoreti- Viewing the different house advantages also re- cal loss. For players playing only one game, a high flects the problem of using bet size or number of bet size will always be accompanied by a high the- games as a measure of gambling intensity. Betting oretical loss. However, if the gambling behavior is 10 euros on keno actually corresponds to betting more diverse, players with high bet sizes will not almost 100 euros on roulette with a single zero. necessarily have a high theoretical loss. Given the However, to date, all published studies using be- reliance on variables such as bet size and/or number havioral tracking data have only used bet size as of games played as proxy measures for gambling in- the measure of gambling intensity. Using the num- tensity, this article examines the properties of theo- ber of games as a measure of gaming intensity retical loss using a mathematical simulation study would be an even-worse measure, as it also ne- of up to 300,000 gamblers, playing as many as 13 glects the amount bet. different games. The hypothesis was that the robust- ness of bet size and number of games played as Simulation parameters measures of gambling intensity would decline as As mentioned above, the first advantage of a sim- gaming becomes more hybrid. ulation study is that gamblers could play up to 13 different games with varying house advantages. A second advantage is that the simulation can be con- METHOD ducted with different numbers of players. We simu- lated up to 300,000 players, playing the 13 games. The authors programmed a procedure in the sta- For each of the players, the simulation calculates a tistical package R that simulates different numbers of players, playing as many as 13 different forms Table 1. Game Type and House Advantage of gambling games with varying house advantages. Used in the Simulation Study A simulation study is most appropriate to show that Game Type House Advantage the bet size and the number of games does not com- pletely explain the theoretical loss, since an empir- Keno 25.0% Big 6 Wheel 10.0% ical study with a sample of gamblers always carries Roulette (double zero) 5.6% the problem of validity. For this reason, the mathe- Video poker (high house advantage) 4.8% matical approach of a simulation study was chosen. Sports betting 4.5% (However, the authors also plan to publish a similar Slots (high house advantage) 3.3% Roulette (single zero) 2.7% study with real-world online behavioral data.) Slots (low house advantage) 1.8% Baccarat (banker) 1.7% Game types Baccarat (player) 1.6% Blackjack 0.8% As argued above, casino operators offer a wide Craps (double odds) 0.6% Video poker (low house advantage) 0.5% variety of games with different house advantages. THEORETICAL LOSS AND GAMBLING INTENSITY 271 specific game-preference pattern. On real world Table 3. Explained Proportion of Theoretical Loss by Bet Size and Number of Games Played platforms, it is known that gamblers also play a va- for Different Numbers of Games Played riety of different games.3 Once the game prefer- ences had been determined, up to 5,000 games per R2 player were simulated. Each simulated player had Number of an individual number of games simulated. The # Games Bet Size Games Played ‘‘drawing’’ of games happens according to the [1:50] 52% 29% game preference pattern. Finally, the bet size per [1:100] 55% 31% game being played has to be determined. Each play- [1:1,000] 56% 32% er’s range of bet size lies in an individual interval. [1:2,500] 56% 32% [1:5,000] 56% 32% The minimum bet size for each player is a natural number drawn from the interval (1:100). To com- pute the maximum bet size, a natural number be- from 1 to 200 monetary units.