Authors’ Note: When looking at gaming floors of the future from an analytical perspective, in many ways the final goal is to optimize the revenue of that floor. In this article we will discuss single-variable approaches to doing this, as well as some common and costly traps to avoid. In later articles, we will dig deeper into multi-variable analysis and show how these more advanced models can provide even more precise floor optimization.
In the August 2010 issue of CEM, we discussed the danger of averaging the performance of the gaming floor and showed an example how of averaging the performance of different types of games can lead to incorrect conclusions. Fortunately, gaming machines are heavily classified by type, and the type of game provides a very useful analytical grouping mechanism. In this article, we will assume that our slot floor consists of games that can easily be classified into groups via the game configuration. (In future articles we will explore whether we can apply multi-variant methods to classify multi-games devices.)
Game configuration usually consists of game type, game theme and denomination, although other factors can be brought into play if necessary, such as max bet and number of reels. For this article, the assumption is that the multi-themed products are similar enough to be clustered into game configuration groups; for example, it is reasonable to group all video poker products by denomination, even though it is known that the pay tables may have subtle differences across a single denom.
Traditional Win Per Unit Per Day
Traditionally, slot operators have made decisions on which games to get more of and which games to remove based largely on a single factor: win per unit per day (WPU for short). If we have three units of a given configuration and over a 90-day period these units give us $27,000 in win, or WPU is $27,000 / (3*90) = $100. Using a WPU analysis of game performance can be a quite straightforward approach. Consider this example: If there was one game configuration (the main factors of a game configuration are the game type, the game theme and the denomination) that averaged $200 WPU, and another that averaged $100 WPU, the temptation would be to acquire more of the $200 WPU games and less of the $100 WPU games.
But digging deeper into our example, let’s look at how focusing on this single metric can decrease the revenue on the gaming floor. Let’s compare four $5 denom Wheel of Fortune games that generate $400 WPU, and four 1-cent denom Wizard of Oz games that generate $300 WPU. In this example, looking at WPU alone might make an operator think that they could make more money by removing one Wizard of Oz game and adding one Wheel of Fortune game. The challenge is that the yield of the game is also important.
Adding a second variable—utilization—changes the picture completely. For example, Wizard of Oz games are extremely popular (high utilization), whereas the Wheel of Fortune games have significantly less play (less utilization), albeit at a much higher average bet. To illustrate the effect of utilization, let’s compare two replacement scenarios.
For this example, the current state of our casino is four Wheel of Fortune games and four Wizard of Oz games, which generate the following WPU:
4 Wheel of Fortune Games @ $400 WPU = $1,600 Per Day
4 Wizard of Oz Games @ $300 WPU = $1,200 Per Day
Let’s say we replace one Wizard of Oz game with one Wheel of Fortune game. In this scenario, most of the play from the current Wheel of Fortune games spreads out to the new Wheel of Fortune game. In addition, the Wizard of Oz games have such high utilization (they are more popular in this example), that they have little room to handle the increased demand per machine created by removing one game. Our potential outcome for Scenario A is:
5 Wheel of Fortune Games @ $330 Per Day = $1,650 Per Day
3 Wizard of Oz Games @ $320 Per Day = $960 Per Day
This is actually a decrease from the control scenario. In other words, adding the higher revenue game decreased our revenue and made our floor less optimal.
Let’s say we replace one Wheel of Fortune game with one Wizard of Oz game. In this scenario the current play on the for Wheel of Fortune games simply consolidates to the three remaining Wheel of Fortune games. The additional Wizard of Oz game finds incremental revenues, with little dilution of play from the previous four games. Our potential outcome for Scenario B is:
3 Wheel of Fortune Games @ $500 WPU = $1,500 Per Day
5 Wizard of Oz Games @ $290 WPU = $1,450 Per Day
This is an increase from the control scenario. In other words, adding a lower revenue game actually increased our revenue.
But slot operators clearly already know this, as the high-limit slot areas often have the best performing games in terms of WPU and as you don’t see the number of high-limit games increasing in quantity on the main floor—most customers simply cannot afford to play them.
The key to insight provided by these two scenarios is the additional metric, utilization. Utilization is defined as “the percent of time throughout the day that the game is actively being played by a customer.”
Utilization is difficult to measure precisely as, in the end, it depends on a judgment call regarding a player’s behavior and the definition of what it means to be actively playing a game.
To illustrate how much judgment is involved in measurements of utilization, Table 1 shows a list of player activities and their suggested effect on utilization.
Table 1: Comparing Utilization to Handle Pulls
Our slots system provides a measure of games played (or handle pulls), and this measure can be used as a proxy for utilization. Looking at Table 1, the difference between the two measures is very apparent. For example, players with a lower rate of play skew the numbers to make it look like the machines have low occupancy. The utilization can be calculated by combining the games played with the expected, often maximum rate of play of each game.
In our example above, bringing precise utilization into the equation may help operators make optimal decisions. In our example, the four Wheel of Fortune games may have $400 WPU, but they only have 2 percent utilization, whereas the four Wizard of Oz games may only have $300 WPU but 40 percent utilization. In this example, the slot operator would be better off choosing to execute Scenario B, replacing one Wheel of Fortune game with one Wizard of Oz game.
Now enter the impact of machine location, which we have discussed in a previous issue of CEM (see Cardno and Singh’s “Fuzzy Spatial Association and Gravity Modeling,” December 2009). Often lost in slot floor optimization is the impact of location on performance. This is likely due to the difficulty in measuring the impact of location. Sure, one can easily identify parts of a slot floor that are very low or very high traffic locations—non-smoking rooms come to mind for casinos that allow smoking on the main floor, as these tend to be low performing areas overall. However, what about the more subtle differences between a bank of machines that is near a restroom vs. a bank of machines that is surrounded by other banks of machines? What about games at the end of a row vs. games in the middle?
In order to properly optimize a slot floor, one must first remove the “location bias” from the performance metrics of each game theme. The challenge with location is that it is, by its nature, two dimensional and its effects can be subtle. The best measure of the effect of location is to compare the performance of a gaming device to the performance of adjacent games. This leads to questions like, “What is the best location for this game?” or observations like “This game performs better than its neighbors in this area.” One powerful method of calculating the value of a location is to combine the effect of gravity modeling and spatial association rules, which was discussed in depth in the previous article on the subject. This combination provides us with a relative measure of the effectiveness of the game in the area and its relative effect on other games.
The four categories of gaming device that result from gravity modeling and spatial association rules are as follows:
The optimization question is now: What game configuration can I add to this floor to maximize incremental revenues, and what game can I replace to minimize loss of revenues?
These more sophisticated breakdowns of the gaming floor show that WPU alone is probably going to lead to sub-optimal gaming floor decisions. WPU gaming floor decisions quite simply ignore the effect that one game has on another. Consider, for example, the effect of “cannibalization.”
Cannibalization of Game Performance
Imagine that we have a game configuration—let’s call it Wild 7s—that we know has a $200 WPU (from here on out, we will assume that adjustment for location has been done for all the data). If we get another Wild 7s machine, we may find that this additional unit also has a WPU of $200. But suppose I told you that next to the Wild 7s game was a bank of 10 games called Wild 8s, which also had a WPU of $200 … and that after the additional Wild 7s game was added to the floor, the WPU of the Wild 8s was only $195. By introducing this extra Wild 7s game at $200 WPU, we lost $50 (10 x $5) per day from our Wild 8s bank, and the incremental value of the Wild 7s game, therefore, was actually $150 per day, not $200. This $50 was cannibalized from the Wild 8s.
Of course, it’s possible that the extra Wild 7s game could also simply cannibalize from the existing Wild 7s, which would happen if utilization on Wild 7s was low before the new game was introduced. Either way, measuring cannibalization is a key component to the optimization question.
For most slot floors, the amount of cannibalization for a new machine is likely related to the utilization of that game theme and the relationship it has with its surrounding games. For example, a “loner” has little impact on the surroundings games and outperforms its neighbors. By measuring the impact that each slot machine change has made in the past, a slot operator can quantify this correlation and determine how cannibalization is a function of utilization for that particular casino.
Being able to accurately model cannibalization is a key step to optimizing a slot floor. Extremely accurate cannibalization models lead to very highly optimized gaming floors where changes to the gaming floor are always considered in terms of their overall effect on the bottom line revenue.
Introduce the Customer
When modeling slot machines, there is one more key ingredient: the customer! Consider two games that have the same WPU and utilization metrics—again, let’s refer to them as Wild 7s and Wild 8s. The customers who play Wild 7s play only this game, and they rarely choose other games on the floor. Meanwhile, the customers who play Wild 8s tend to split their time between Wild 8s and Wild 9s. Armed with this knowledge about customers, what changes should be made in terms of which game to get more of? What about in terms of which game to remove? If Wild 7s and Wild 8s are both performing well, it may not matter too much which one we select. However, if they are not performing well, a choice is required. In this case, removing the Wild 8s is likely to be optimal, since those customers would hopefully just shift their play to Wild 9s. Removing the Wild 7s is again likely to be sub optimal, since we would risk losing all play from those customers.
Loyalty and Devotion
With this in mind, let’s add one more metric to the mix: devotion, or game loyalty. For each game configuration, quantify the amount of loyalty that customers have for that game—do they play other games or not? With this information, we can now leverage game loyalty and utilization to better measure cannibalization. Just as games with higher utilization will have a lower cannibalization score than games with lower utilization, games with higher devotion will lower a cannibalization score as well.
Combining all of this results in an information arsenal for each game. We know its WPU, and we’ve adjusted for locational effects on this metric. In addition, using the games’ utilization and loyalty scores, we can estimate how much play will be cannibalized from the rest of the floor if additional gaming units are added. The data might look something like this:
110% location score
40% Utilization - Adjusted for location
The product loyalty or devotion scores a 75 percent devotion score.
60 percent cannibalization score (which includes the devotion score in its derivation).
[Note: This is not a simple formula. It is a complex calculation that will require some regression analysis or an advanced statistical method called Generalized Linear Models to be applied on the slot floor.]
Each new unit will produce:
$200 total WPU
- $120 cannibalized from rest of floor
$80 incremental WPU
Applying this measure to all machines on the floor, and optimization might appear easy. Remove games with a low incremental WPU and add games with a high incremental WPU. But how do we know when the gaming floor truly is optimized and we can go play golf? Well, when the incremental WPU for each machine is the same!
But in the real world, the optimization can always be improved, since the data changes over time and since we need to take into account the new products that are constantly being churned out by the slot manufacturers. And, in the end, there are inaccuracies in our models that require qualitative analysis and further experimentation.
New Technology and Downloadable Games
These analysis assumptions so far have not been made on a server-based floor, so now let’s dig into how to analyze downloadable games, with their seemingly endless configuration options.
As we discussed in the July 2010 issue of CEM, the number of game configurations available for a single machine is extremely large; this huge number of combinations removes the ability to place games into groups of similarly configured game types, and this grouping was key to our above analysis.
If switching to a server-based floor causes us to be unable to analyze the floor, what is the motivation behind the switch? The answer lies in how the server-based floor is setup. This series of articles is devoted to understanding what the server-based world is going to be like. It’s quite possible that it comes down to the following questions:
1. Does the presence of multiple themes instead of a single theme cause the customer to either spend more or to visit more often? In October’s article, we showed that multi-themed games do not have a longer time-on-device than single-themed games, at least for the sample of data we reviewed. Downloadable games may cause players to spend more or to visit more often, these questions will be covered in future articles in this series.
2. If the answer to Question 1 above is yes, does this incremental play offset the loss of a robust set of analysis for single-themed games?
3. Is there a possible optimal floor whereby a slot floor consists of a combination of single-themed downloadable games that are optimized as described in this article and multi-themed downloadable games with massive libraries of games available for the customer to choose? In the case of the single-themed games, the presence of a server-based environment allows this level of optimization to occur during any time period we choose, since we can change game themes on the fly. So instead of optimizing the floor once then going golfing for a month before returning to optimize again, we are instead monitoring our slot floor hour-by-hour (or possibly even more frequently) and optimizing our slot floor for every possible time of day and day of week, dynamically. (It is the authors’ view that this dynamic gaming floor may hold the keys to the true value in downloadable games.) In the case of the multi-games, these would be placed into much broader categories of games than single themed games, but in doing so we are still able to optimize the floor around customers who prefer this level of complexity and flexibility.
The Analytical Framework
The optimization of a gaming floor is, of course, possible, and by digging past the single-metric approach we have described a method that provides more analytical depth. Armed with this knowledge, the gaming floor turns from a sea of color to a sea of numbers—and, done well, a lot more green. The gaming floor of the future is so dynamic, we are going to need much more sophisticated methods, but for the analytically driven the results are likely to be there.
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.