When looking at the gaming floor of 10 years ago, the metrics were—and rightly so—focused on the “real estate” that we had deployed. The industry (and at least one of the authors) would routinely look at the numbers that a box was producing and use these numbers to optimize the gaming floor mix. There were key attributes of gaming machines, such as denomination and game type, that were very useful to shed light on the optimization strategies that we deployed. This article explores how most of these real estate metrics are now relics of the past and how optimization based on these metrics will, in many cases, result in a reduction in profit. We will consider two broad kinds of new metrics—cost-based metrics and revenue-based metrics—and how these metrics will change with the dynamic gaming floors of the future. When we look at the cost or price metrics, we dig into how the price of the gaming machine and the gaming experience needs to be considered from the analytical perspective. We then dig into revenue metrics and revenue models, showing how test and control can be used to determine the true revenue impacts of gaming optimizations.
Profit Optimization Models
Before we dig into the metrics, let’s look at some of the high-level objectives of the metrics. Simply put, we need metrics that provide a view of the business, or a model, that we can use to make good decisions about the effects of any change in the business.
In more formal terms, a model is a simplification of the real world that we can measure and use to make optimization changes to the gaming floor. The assumption is that the optimization of a model’s output is going to be similar to the real world; in other words, if our model shows an increase in revenue, then the real world should also show the same increase in revenue.
According to Wikipedia: “A mathematical model usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The values of the variables can be practically anything—real or integer numbers, boolean values or strings, for example. The variables represent some properties of the system, for example, measured system outputs often in the form of signals, timing data, counters and event occurrence (yes/no). The actual model is the set of functions that describe the relations between the different variables.”
To show how a model is made up, let’s consider an example of a model designed to optimize revenue on the gaming floor. For the purposes of this discussion, we will consider the model to have three parts: variables, equations and output. The variables are what we change, the equations are the relationships between the variables, and the output is the modeled value we calculate from the equations.
In the example shown in Figure 1, we are increasing the theoretical win of the gaming machine. In other words, if the revenue of a gaming machine increases, then the revenue of the property will increase. So, quite simply, according to this model any change that results in an increase in the revenue of the gaming machine will increase the overall revenue of the property.
Figure 1: A Theoretical Win Model
E1: DeltaTW = SUM_OF_ALL (DeltaTWPG)
Of course, this model is fundamentally flawed, as it does not account for cannibalization.1 A more accurate cannibalization adjusted model would look more like this:
E2: DeltaTW = SUM_OF_ALL (DeltaTWPG) – SUM_OF_ALL(Cannibalization Effect On Surrounding Games)
As you can see from this example, it is extremely important to consider all the factors in building a model. If you don’t, flaws in the basic assumptions about how much additional revenue the improvements could drive may result in incorrect business decisions.
Oversupply vs. Undersupply
When building models of the effects of changes to the gaming floor in the past, few would argue that the gaming market was oversupplied, at least in North America. This resulted in the proliferation of models that followed the design of the fundamentally flawed model described previously—essentially, models that did not take the effects of cannibalization into account. Today few would argue that the gaming world is not oversupplied. This fundamental change in the basic economics of gaming truly drive a need for a new kind of gaming metric.
This brings us to today, where the addition of a new gaming product onto the gaming floor in most markets will result in no measurable increase in revenue. The laws of supply and demand are at work, and these laws affect price equilibrium.
Figure 2: The Laws of Supply and Demand
Figure 2 illustrates that the price (P) of a product is determined by a balance between production at each price (supply S) and the desires of those with purchasing power at each price (demand D). The diagram shows a positive shift in demand from D1 to D2, resulting in an increase in price.
The four basic laws of supply and demand are: 2
1. If demand increases and supply remains unchanged, then it leads to a higher equilibrium price and quantity.
2. If demand decreases and supply remains unchanged, then it leads to a lower equilibrium price and quantity.
3. If supply increases and demand remains unchanged, then it leads to a lower equilibrium price and higher quantity.
4. If supply decreases and demand remains unchanged, then it leads to a higher price and lower quantity.
The key to understanding the supply and demand model is that there is an implicit relationship between price and demand, and in many gaming markets we are experiencing a decrease in demand and an increase in supply. According to the laws of supply and demand, this will lead to a lower equilibrium price and quantity.
Now the question is, in the context of the gaming world, what is price? This is a difficult question because the gaming experience is one where the end customers determine the final cost. They can, for example, decide to spend less each trip or decide to bet a lower amount. This customer-driven price decision in many ways isolates the economics of the game from the operator. (In a previous CEM article on the effects of hold, we described how the hold percentage is simply not a measure of the price of the gaming experience.)3
Let’s consider some new gaming metrics that are candidates for being considered “price” in an economic sense. (See Figure 3.)
Figure 3: Candidates to be Considered “Price”
Both of the metrics in Figure 3 seem like reasonable candidates for economic price, and with the massive reductions in debt load that gaming companies have undertaken in recent years, it certainly seems that there has been a massive lowering of the equilibrium price of the gaming experience.
Following the laws of economics, it seems likely that we are about to see a lower equilibrium price for the price of games as well. This lowering of pricing equilibrium may well come about through unforeseen effects of new technology; for example, downloadable games have the potential to lower pricing equilibrium by structurally changing the pricing model. These changing price metrics can lead us to another set of metrics that show the return capital investment. However, before we build a return-on-investment model, we must consider revenue.
Multi-Game Revenue Metrics
So let’s look at the current world through this lens. Even though we have fixed game themes, we still have configuration options to choose from when we place a game on the floor:
1. Minimum bet. This is often driven by denomination.
2. Maximum bet.
3. Minimum bet to achieve maximum benefit. (For example, a game may have a maximum bet of $5 and a minimum bet of 1 cent, but a player may have to bet $1 to be eligible for the bonus rounds.)
4. Number of lines. This can impact the above options.
5. Probability and payout for each possible outcome. This is reflected in the hold percentage, but games can have the same hold percentage while having different probabilities and payouts for each outcome. Fortunately for us, once we’ve selected a game to put on our floor, the hold percentage is typically the single number that drives all of these outcomes.
6. Presence or lack of a progressive jackpot.
7. Denomination. While not as important to the game mechanics as some of the other configuration options listed here, it is still very important to the customer. Many customers love penny games, even though their max bet may in some cases be higher than $1 games!
8. Presence or lack of a multi-denom option.
9. On multi-game cabinets, which exist even in a non-server based world, the choice of games and denoms to make available is a configuration option operators must select when placing the game.
Then we need to understand how best to optimize the configuration of each cabinet, which leads us to our next important concept when building multi-game metrics: test and control. Test and control provides a way of cutting through all the variability in the gaming floor and truly measuring the effects of change.
Test and Control
Let’s say that we have two configurations, A and B, available to us for a particular game. If the game is new and we have more than one location for this new game, testing configuration A against configuration B is simple: Put both configurations on the floor and see which one does better.
But what if our two locations aren’t equal? Maybe one is on the end and another is in the middle of a bank. The other issue is that we rarely have to choose between two configurations—we have to choose between many more than that. In the case of multi-game cabinets, there could be hundreds or thousands of possible combinations. To make matters even more complicated, many of our existing games have different configurations available, and we want to see if we can optimize those configurations.
Enter the control group. The purpose of a control group is to help us forecast how a game would perform if we hadn’t made any changes to it. Suppose we have a game called Big Sevens, and we want to optimize its configuration. For the sake of simplicity, let’s pretend that, instead of the game having all the configuration options we discussed in the previous section, it only has one configuration option, denomination. Currently, Big Sevens is a 1-cent game, and we want to see if it will perform better as a 2-cent game.
As a 1-cent game, over the past three months, Big Sevens has done $100 WPU. We make the change to a 2-cent game and find that it does $150 WPU over the next three months. So we made $50 more per day right? Wrong! It turns out that we were coming into season when we made the change, so we expected the game to perform better than $100 per day anyway.
To quantify this, we use a 1-cent game called Big Eights as our control group. Big Eights, as it turns out, did $90 WPU out of season and $135 WPU in season. If we do the math, we can see that the variance is actually the same (50 percent) for our changed game and our control game. So our change to Big Sevens had zero impact on the game’s performance! This, however, assumes that Big Eights was a good control group ... which leads us to our next section.
What is a Good Control Group?
The purpose of a control group is to help us predict what a particular game would do if we left it alone, which allows us to compare how it actually did when we made a change. In our Big Sevens example, based on the performance of Big Eights, we can predict that Big Sevens will do 50 percent better in season (go from $100 to $150 per day) if we leave it as a 1-cent game. Since it did exactly $150 when we changed it to a 2-cent game, we can conclude that the game plays equally well at 1 cent as it does at 2 cents. There are, however, many pitfalls to selecting control groups.
Pitfall #1: Seasonality
The control group must have the same seasonality pattern as the test group. Some games have different seasonality patterns than others. This can be due to different purchasing habits of in-season tourists, or sometimes it’s simply due games being at capacity year-round. (In future articles, we will show how to analyze the effects of seasonality.)
In our example above, we hope that since Big Eights is a 1-cent game, it has similar seasonality patterns as the 1-cent Big Sevens.
Pitfall #2: Cannibalization
The control group cannot be impacted by the change made to the test group. When we make a change to our test group, it may impact other games that are either nearby or that have similar play behaviors. (This idea of cannibalization is discussed in detail in the November 2010 issue of CEM.) If the control group is impacted by any change we make to the test group, then it should not be considered to be a good control group! In our example above, what if by removing the 1-cent version of Big Sevens, we actually migrated play from Big Sevens to Big Eights? In that case, we have overstated the seasonality represented by the 50 percent increase in Big Eights. Perhaps seasonality was only causing a 40 percent change, and our change to Big Sevens caused the other 10 percent. Thus, by having an incorrect control group, we reported a change as being neutral, when in reality it caused a 10 percent lift. (The 50 percent variance minus the 40 percent due to seasonality.)
Pitfall #1 and Pitfall #2 can also easily combine to make an even more dangerous situation for our analysis. In looking for games that have similar seasonality, we become more at risk of finding control group games that are impacted by the change to the test group.
Pitfall #3: Play Trends
The control group also needs to have similar play trends as the test group. Over time, the popularity of a game changes. Some games get more popular as customer word-of-mouth spreads, whereas other games have worn out their welcome and are declining in popularity. If we were to use a game that was increasing popularity as a control group for a game that had decreasing popularity, we would not achieve accurate results.
Just as Pitfalls #1 and #2 are a dangerous combination, Pitfall #3 is a similarly dangerous in combination with Pitfall #2.
Once we are able to define accurate control groups, we can rapidly test different configurations for our games. It is our experience that 30 days is more than enough data to determine if a new configuration is better than an old configuration. As operators, we should constantly be testing new ideas with our existing products. Even better is if we come up with theories about why a particular change worked or didn’t work. (Asking the customer is a great idea here!) These theories will lead us more quickly to the best possible configurations for our games—and remember, there are hundreds and sometimes thousands of possible configurations for our games.
New Metrics in the Server-Based World
Now flash-forward 10 years to a fully functional downloadable games environment. We, as operators, have the ability to give our customers any combination of game themes and configurations at a single location. The number of combinations went from hundreds or thousands to millions, billions and beyond, and the laws of supply and demand have fundamentally altered the pricing equilibrium of these products. Fortunately, we can learn the new metrics models and operational techniques to manage this future right now, with the use of the multi-game product—but only if we take the time to look at the numbers.
Footnotes
1 CEM, November 2010, “An Analyst’s Guide to Slot Floor Optimization.” Cardno, Singh and Thomas.
2 http://en.wikipedia.org/wiki/Supply_and_demand#cite_note-0: Taken from Besanko & Braeutigam (2005) p.33.
3 CEM, July 2010, “Gaming Floors of the Future, Part 1: Downloadable Games.” Cardno, Singh and Thomas.
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. 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.
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