Author’s Note: This article continues our exploration of multi-theme games. Simply put, we were surprised by the clarity and strength of the visual results from our data. Furthermore, the analysis is a great example of an exploratory analytical process (see the Spielman diagram from “Gaming Floors of the Future, Part III” in the September issue of CEM) that we followed to come to our conclusion. We will hold off presenting more statistical analysis on this dataset to preserve its confidentiality. In future research, we plan to involve a wider set of properties and a larger dataset with more statistical analysis, and with this wider set of data we will be able to verify that these results are not specific to our sample properties.
Based on the framework we established in “Gaming Floors of the Future, Part III,” we have gathered some real data to begin to shed some light on the answers to some key questions that operators face as they deploy multi-theme games. The burning question is, with multi-games available, will players change their behavior to play longer on a single device instead of the very short time-between-devices pattern that they currently exhibit? Put simply, do players spend more time on multi-game machines?
According to Paco Underhill in Why We Buy: The Science of Shopping (2000), watching customers move around inside a retail space is one of the key ways that retailers developed their understanding of retail space shopping behavior. While following customers around with clipboards, as Underhill describes in Why We Buy, and recording their movements might give some further insight into gaming behavior, in gaming we have the beautiful gift of ever more detailed data that describes, in great detail, how patrons interact with our gaming devices. This article will show how to use this data to describe how customers respond to more choices on the gaming device. And this data shows that, no, players do not spend more time on multi-game machines.
In our sample dataset, multi-themed games do not drive players to play longer per session than single-themed games. In fact, we were quite surprised at both the answer to our question and the apparent clarity of the results. Quite simply, despite the best efforts of the manufacturers, session times remain very similar in duration between multi- and single-game devices.
As interesting as this remarkable conclusion is, the process by which we arrived at it was quite surprising and interesting in its own right.
First we extracted an anonymous sample of gaming data, covering eight months of play at six casinos. The dataset is from about 10,000 slot machines and the number of sessions per day is approximately 250,000, which over eight months adds up to about 60 million sessions. We then broke this dataset into two types: multi-themed and single-themed. We calculated the total time played on each device as well as the number of sessions. (We defined a session as started when a player sits down and starts gambling at a machine and ended when that player gets up and either leaves the casino or moves on to another game). Dividing the total time played by the total number of sessions gives us the average time-on-device for each machine.
Step 1: All of the Data
Totaling the results showed us that the time-on-device of multi-themed games was about 50 percent higher than for single-themed games. For the sake of later analysis, we put this result as a single dot on the scatter plot graph (see Figure 1).
The horizontal axis, or the x-axis, measures the average minutes played per session for the multi-themed games. The scale of the graph has been omitted to preserve the anonymity of the data. The vertical axis, or the y-axis, measures the average minutes played per session for the single-themed games. The diagonal line represents the “break-even line”—any dot on this line represents a data point where the average time on device for the multi-themed games is equal to the average time on device for the single-themed games. Anything below and to the right of this line represents multi-themed games playing longer, and anything above and to the left of this line represents single-themed games playing longer.
In this case, we have a graphical depiction of our result that overall, multi-themed games play longer than single-themed, since our lone dot is to the right of the break-even line.
Now, let’s dig a little deeper. There are three big factors when determining time-on-device:
1) Casino – A casino near a big population center could have more players that live nearby and come in for short sessions than a casino where most players have to drive a significant distance.
2) Denomination (or denom, for short) – For players who play across multiple denoms, their time on device for lower denom games may tend to be longer than for higher denom games, since higher denom games tend to be more expensive to play.
3) Game Type – Video poker games play very differently than video reel and stepper reel games, and thus could have different time-on-device results.
Step 2: Introduce Casino as a Dimension
Now let’s begin to introduce these factors into our analysis. As mentioned above, our data set comes from six different casinos. When we plot the average minutes played on multi-themed games versus single-themed games for all six casinos, we will find out if the different casinos have any difference in the time-on-device between single- and multi-themed games (see Figure 2).
We now begin to see that one casino has much higher time-on-devices for both single- and multi-themed games, but in all cases the multi-themed games have a longer time-on-device than the single-themed games, as all six dots are to the right of the break-even line.
Step 3: Introduce Denomination
What happens when we incorporate denomination into the analysis as well? In Figure 3, we see the results for all casinos and all denom groups. Here, the micro group denotes 1-cent, 2-cent and 3-cent games; the low group denotes 5-cent and 10-cent games; the mid group denotes 25-cent, 50-cent and $1 games; and the high group is $2 and above.
We see more variety in the data, but the results are still clear: multi-themed games play longer than single-themed games. What is interesting, though, is that low denom games tend to strongly favor multi-themed games, whereas micro denom games cluster near to the break-even line. In fact, at one casino, we see that in the micro denom, the single-themed games play slightly longer than the multi-themed ones.
Step 4: Now Introduce Game Type
Having looked at this three different ways and seeing the same results, we should be confident in the conclusion that multi-themed games play longer. However, we have neglected the differences between game types, as noted above. Let’s bring that into the picture and see what happens in Figure 4.
Here each dot represents a casino/denom group/game type pairing where both multi- and single-themed games are available, and we have a reasonable sample of data (at least 100 sessions); this implies that each dot is computed from a large number of data points. As you can see, our early conclusion falls flat on its face! No longer are the dots grouped to the right of the break-even line. Instead, the results are completely scattered. Figure 5 summarizes the graph, showing the number of times a casino denomination game type dot has more time per session. For example, with high denomination there is only one result, and it shows higher time for the single-theme session.
Overall, single-themed games play longer than multi-themed games 14 times, multi-themes play longer 13 times, and the games are played for roughly the same duration seven times.
The Danger of Averaging
But how can multi-themed games possibly dominate in the aggregate, even when we break the results down by casino, or even casino and denom, but not dominate when we incorporate game types? The reason is found in the difference between straight averages and weighted averages.
Averages are one of the fundamental tools used in analysis, and yet even this basic analytical method contains at least two fundamental issues. The first issue with averages is that outliers in the data—which, by the way, are common in gaming—can skew the results significantly. For example, the fortunes of one high roller in Las Vegas can skew the numbers for the entire Strip. The second issue is that we must always consider the difference between a straight average and a weighted average.
To explain further, consider Mr. Big and Mr. Small. Both sell apples and oranges, and we want to know who has the better fruit, using the average size of the fruit as the measure. Now, in this particular state, oranges flourish, but apples are more difficult to grow, resulting in oranges that, on average, are three times as large as apples.
So, we measure the average size of the fruit and find that Mr. Big’s fruit weighs 5.6 ounces on average and Mr. Small’s fruit weighs 8 ounces on average. Mr. Small is better, right? Wrong! Consider the data in Figure 6.
As you can see, Mr. Big has better apples on average, and Mr. Big has better oranges on average. The only reason Mr. Small has the highest overall average is because he has a much higher mix of oranges vs. apples. This is why it is important to understand when to use weighted averages and when to use straight averages.
Where would you go if you wanted better fruit? Does the fact that Mr. Small has a larger inventory of oranges matter to you more than the quality of the oranges? It should not.
Going back to our slot machines, the reason multi-themed games dominate single-themed games is due to the high presence of video poker machines. Much like our Mr. Small, a significant share of multi-themed games are video poker, so even though multi-themed video poker games don’t have longer time-on-device than single-themed video poker games, their heavier presence causes the multi-themed weighted averages to be much higher when game type is removed from the analysis.
The Age of Analytics
Giving players more choice is a powerful change to how they interact with gaming devices, and in the end, we have little doubt that this control will change player behavior. The question is how the behavior will change, as based on our six sample properties, we used we found no real change in the session time between single- and multi-themed games. Following this and some qualitative views of the data, we are drawn to look more closely at the effect of multi-games. Questions still remain, such as does one game dominate all play on a multi-game device, and is the game advertised on the top-box heavily favored by players?
As we continue our exploration of analytics for gaming devices of the future, we will tackle some of these questions.
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[at]yahoo.com.
Dr. A. K. Singh is a professor at UNLV. He has taught statistics, mathematics and operations research courses at New Mexico Tech and advanced statistics classes including Time Series Forecasting and Data Mining at Harrah Hotel College at UNLV. He has more than 80 publications in theoretical and applied statistics and can be reached at aksingh[at]unlv.nevada.edu.
Dr. Ralph Thomas is Vice President of Database Marketing for Seminole Hard Rock Gaming. During his years in the casino industry, Thomas has focused on maximizing profitability by applying statistical analysis to the company database. Previously, Thomas spent 15 years in academia, as both a student and a lecturer of mathematics. He can be reached at ralph.thomas[at]stofgaming.com.