Richard Bellman1 coined the term “Curse of Dimensionality” to describe how adding extra dimensions to a mathematical space exponentially increases the volume. As an example, a customer inside a casino trying to decide on which slot game to play and which restaurant to eat at will have 100 possible choices, assuming that the player is interested in only 10 of the slot games on the casino floor and eating at one of the 10 different restaurants inside the casino. If the dimensionality of the problem is increased to five by adding table games, movies playing in the casino theater and sports books, then assuming 10 choices for each of the three additional products, the total number of choices from which the player must choose goes up to 100,000.
The Curse of Dimensionality affects data analysis and data visualization as well. We briefly discuss how to deal with high dimensional data from a casino floor in performing market basket analysis.
The 20 Dimensional Rubik’s Cube
Understanding a gaming floor is like trying to solve a 20 dimensional Rubik’s Cube. No matter how you twist the cube, there are always hidden dimensions that are the hidden drivers in analyzing the data.
The trick now lies in deciphering the behavioral market basket analysis into a form that is understandable and actionable. One of the best ways of doing this is to visualize the market baskets on the gaming floor. These high-density gaming floor images enable operators—armed with the knowledge of when and where events are likely to take place—to apply their visual processing capability to critical thinking required to take strategic and tactical actions.
Behavioral Market Basket Analysis and Your Gaming Genome
Behavioral market basket analysis, including the mathematics behind it, has been covered in previous articles. The important thing to remember is that market basket analysis “simply” clusters the purchasing behaviors into similar groups building up the gaming genome.
To quote “The Numerati” by Stephen Baker: “These bits of our behavior set in thousand of buckets, all of them created automatically by machines. Most of them—like my green-pepper bucket—are never used. If you strung all of your buckets one after the next, you’d see your own special combination, your unique shopping genome.”
Interaction Analysis
This 20 dimensional Rubik’s Cube can be further extended with interaction analysis. In playing, the analysis takes into account not only the mixture of product, but also the mixture of interaction and product. It has often been said that some kinds of customers do not mix with others, even if they both desire to play in the same area, or similarly that there are players who are attracted to play near other players. The old gaming adage of “players like to play together alone” is now taken to the next step.
In an earlier article2, it was estimated that the volume of data stored in the gaming industry would increase to 35PB by 2016. This huge growth in the volume of data swamps the Rubik’s Cube with data. Fortunately there are now new extensions to the humble relational database that enable us to exploit the highly scalable query engines to crunch down the results to a useful level. The Open Geospatial Consortium3 is providing the common framework for much of this important work. The following illustrative examples show how the spatial queries can be applied to both filter down the results as well as the outputs that can then be further processed to produce understandable results.
Types of Analytical Requirements
As we approach the problem of analytics in this world of massive data, we can divide the analytical space into four parts.
1. When one has “Known Relationships” and “Known Data,” traditional reporting and analysis techniques are appropriate.
2. When one has “Known Relationships” and “Unknown Data,” predictive technology is applied to build models of what is happening in the data.
3. When one has “Unknown Relationships” and “Known Data,” the challenge is to discover the relationships in the data—in other words, to discover the right questions to ask.
4. Finally when we have “Unknown Relationships” and “Unknown Data,” then we are researching and possibly building scenarios.
The following examples show how we can bring together the results of complex clustering and spatially extended queries then present these results in a visual form. This visual form enables a much wider audience to enjoy the understanding and insight that comes from these data sources.
Where Bruce Meets Beverly
Bruce and Beverly are names given to behavioral clusters of customers. The business question is, how do we see where these types of customers have plays near each other? This kind of interaction can be used to design the correct mix of the gaming floor. These kinds of interaction analysis may have applicability in the future where downloadable games can be used to control the nature of the gaming floor in real-time.
Temporal-spatial queries can be used to identify if similar customers may have had a gaming experience at a similar location. The following pseudo-SQL (meaning the syntax has been simplified) generates a circle at all locations where a customer belonging to a customer cluster has interacted with a gaming device within 10 feet of another customer at 10 p.m.
SELECT
c1.cust_id
c1.geom.TRANSFORM(c1.X, c1.Y).BUFFER(10)
FROM
customer_interactions c1
customer_interactions c2
WHERE
c1.geom.DISTANCE (C2.geom) <= 10
and c1.Cluster = “Beverly”
and c2.Cluster = “Bruce”
and c1.hour = c2.hour
and c1.hour = 10 p.m.
In words, build a 10 buffer zone around all locations where customers of type-Bruce played within 10 feet of customers of type-Beverly at 10 p.m.
The following illustrative example shows the results of this query where the four regions of interaction are indicated spatially. The heat map shown around the gaming machines represents the total revenue for the casino, ranging from purple and red on the upper end to blues at the lower end of the scale. The slot machines are colored by denomination.
Figure 1 illustrates how, despite the fact that there are massive numbers of possible interaction questions, we can see that groups Bruce and Beverly interacted near each other at locations 1, 2, 3 and 4 on the casino floor.
These visual diagrams are understandable by nontechnical people and can be used to enable more accurate time- and space-based operational decisions, such as where and when to run specific promotions or when a downloadable game should be changed.
Interaction Heatmapping
The illustrative example in Figure 1 shows how different segments of customers can be selected with spatially extended SQL and then displayed to show areas of interaction. The next step is to consider broader analysis where we open the restrictions in the query to allow a much larger result set.
SELECT
c1.cust_id
count (Interactions)
FROM
customer_interactions c1
customer_interactions c2
WHERE
c1.geom.DISTANCE( C2.geom) <= 10
and c1.Cluster = “Beverly”
and c2.Cluster = “Bruce”
and c1.hour = c2.hour
Group By Location
In words, build a 10 buffer zone around all locations where customers of type-Bruce played within 10 feet of customers of type-Beverly at any time of the day or night.
The underlying complexity of Figure 2 and the reduction to a simple picture is a remarkable use of computing power. Consider what is happening for each rated customer interaction (lowest level stored in the database in which we have calculated the total number of interactions between any two players of type Bruce and Beverly). This vast calculation is then rendered back into a simple and understandable heat map visualization. Simply put, where it is hot, Bruce interacts near Beverly.
Digging Deeper with Demographics
One of the best studies on the behavior of gamblers in the United States is Harrah’s Entertainment’s Profile of the American Casino Gambler (2002 – 2006).4 Many other industries utilize data on customer preferences (i.e., recency, frequency, product category, amount spent and demographic data—age, education, income, gender, ethnicity) and spatial (geographic) information in their market basket analysis to increase their share of the market.5
As an example, IHOP, the popular restaurant chain, makes detailed studies of the demographics and other characteristics of an area in order to decide where to place a new outlet.6 Lewin, Singh, and Cardno7 discuss how you can incorporate customer demographics information in performing market basket analysis of casino floor data.
The next illustrative example shows customers from a particular demographic segment can be selected with SQL and then relevant information displayed on a casino floor map shows areas of interaction. A pseudo-query to obtain a list of customers who have children and their interactions data is shown below.
SELECT
Sum (Revenue), Location
FROM
customer_interactions
WHERE
Presence of Children = TRUE
Group By Location
The data obtained from this query can be used to create a heat map of the casino floor displaying results of market basket analysis on gaming and demographic data. The heat map of Figure 3 shows the revenue generated by customers who have children. The floor manager can easily determine from Figure 3 the type of slot games players with kids prefer.
Taking Action
In the market basket analysis article8, we characterized casinos as small cities offering hundreds of products and services to their customers. Market basket analysis, combined with information visualization tools, provides means to sift through large customer transaction data collected from loyal customers and find actionable information that can be used to optimize casino operations.
Moreover, once the casinos replace the freestanding slots games of today with the downloadable games that are being installed in the new CityCenter project of MGM MIRAGE and Dubai World9, the customer transactions data will also have other additional information, such as the kinds of shows customers are watching and the kinds of drinks customers are ordering. This additional information, combined with customer demographics data, will take the market basket analysis of casino customer data to a new level. For example, with this type of information, casinos that cater to locals can add personal touches and provide its customers the same experience that a small corner tavern provides.
Measuring the Results
The information deciphered from market basket analysis can be used to optimize casino marketing. Casinos typically spend substantial amounts of money on promotions to increase their slot volume. Lucas and Bowen10 used multiple linear regression (MLR) on data collected from a medium-sized Las Vegas casino catering to locals and attracting guests from the feeder markets of Southern California and Phoenix. There were three promotions used by this casino, each based on the idea of customers qualifying for cash drawings by winning top awards on their slot games. Each customer winning a qualifying jackpot was given a drawing ticket, with no limit placed on the number of tickets one customer could get. Lucas and Bowen showed, among other things, that the promotions did not significantly impact the slot volumes. We recommend that the MLR approach be used on other marketing efforts to measure the marketing results.
1 www.groups.dcs.st-and.ac.uk/~history/Printonly/Bellman.html.
2 Singh and Cardno, “The Petabyte Era of Gaming Data.” Casino Enterprise Management, September 2008, pp. 20-22.
3 www.opengeospatial.org/standards.
4 http://findarticles.com/p/articles/mi_m0EIN/is_/ai_89209832; www.americangaming.org/industry/faq_detail.cfv?id=60 www.hotel-online.com/News/PR2004_4thOct04_HarrahsSurvey.html; www.harrahs.com/harrahs-corporate/about-us.html).
5 Gordon, Larry (2008). “Leading Practices in Marker Basket Analysis – How Top Retailers Are Using Market Basket Analysis to Win Margin and Market Share.” (www.irgintl.com/pdf2/1.pdf).
6 “The New Science of Siting Stores.” Business Week, July 6, 2005, www.businessweek.com/technology/content/jul2005/tc2005076_7033.htm.
7 Lewin, Singh and Cardno, “Market Basket Analysis Part III: Using Demographics and Spatial Information.” Casino Enterprise Management, February 2009, pp. 10-15.
8 Singh and Cardno, “Let’s Talk Turkey: Applying Retail Market Basket Analysis to Gaming.” Casino Enterprise Management, December 2008, pp. 10-14.
9 Singh and Cardno, “Gaming 2018: Searching For a Simpler World.” Casino Enterprise Management, October 2008, pp. 14-18.
10 “Measuring the Effectiveness of Casino Promotions.” Hospitality Management 21 (2002) 189–202.
Dr. A. K. Singh has taught statistics, mathematics and operations research courses at New Mexico Tech, Socorro, N.M., and statistics and mathematics courses at University of Nevada, Las Vegas. He has more than 75 publications in theoretical and applied statistics.
Andrew Cardno has more than 16 years of experience in business analytics, ranging from modeling health care drive times to casino gaming floor analytics. He often presents on the future of analytics across the world and has spent the last seven years living in the United States and working with corporations around the world. He can be reached at andrewcardno@yahoo.com.
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