Where’s the Money? Part 5: Gaming Density and Yielding the Floor

Historically, casinos have held to the theory that more is more. That is, the more games you can place on the floor, the more money you can make as a casino operator. In capacity-constrained environments, this is largely true, since the significant demand by a large number of customers justifies the additional gaming devices, even if the added devices cause the customers to have a lesser experience. The math on this is simple. Suppose we have 1,000 units and 10,000 customers spending $50 per day. Our win per unit is $500, and our total win per day is $500,000. Now let’s say we add 200 units and, in doing so, are able to add 2,000 more customers. However, some of the customers reduce their play by virtue of feeling “cramped,” in turn reducing our customer spend per day to $45. Now we have 1,200 units and 12,000 customers spending $45 per day. In this case, our win per unit declines to $450, but we don’t care because our win per day has increased 20 percent to $540,000.

Many casinos, however, have realized that this model breaks down as competition increases and demand for their particular casino declines. We want to explore the best use of gaming space in this reduced-demand environment, specifically focusing on the customer. Quite simply, competition is driving down margins, and you don’t have to look further than the aggressive marketing programs of late to understand that margins are being pressed. These margins are leading us to look at a number of critical ways to improve profit, including yield management, the correction of theoretical win allocation and its effect on bonus (free play) offerings.

Corrected Theoretical Hold
The theoretical hold percentage has always been a marginal calculation when looking at the player experience. As we’ve said before, “players’ behavior results in quite different play effects during the game, while maintaining the same EV.”1

When we add the impacts of different pay tables on the game machine—especially, but not limited to, multi-game machines—it is a mathematical truth that the theoretical win calculation for both the players and the machine are systematically inaccurate. This inaccuracy leads to the controversial argument that the free play allocation made by many operators is systematically incorrect. (In future articles, we will show how the corrected theoretical win can dramatically change the perception of some of some games and/or customers.)

Now, before we examine a real-world example from Silverton Casino, where a reduction in density was part of a strategy to increase the yield on the gaming floor, let’s explore some of the theoretical basis behind yield management.

The Infinite Gaming Floor
First, let’s suppose that we have as much gaming space as we need—essentially, an infinitely large gaming floor—and we want to know how much space to place between our games. For simplicity, we will assume that we are dealing only with slot machines. In this hypothetical example, we do not have to worry about supply (we’re assuming we have as much as we want/need) or demand (since demand is relative to supply and we can always adjust the supply per our liberal hypothesis). Our goal is to isolate how space between games influences customer spend, from the customer perspective.

At one extreme, we space the games so far apart that we effectively provide one game for each customer. In this extreme example, from the customer perspective, once they make their way to a game, the next game is so far away it cannot be reached in a reasonable amount of time. Imagine now that you are the customer, and all you are provided is a single slot machine! It is highly likely that you will not play all of your gaming wallet (if any at all) on that machine, and that you are not going to return to this fantastical casino any time soon.

At the other extreme, we place the games on every available square foot of space. There are no aisles, as games are placed in long rows with chairs touching each other, and the customer doesn’t have enough room to move between games. As with our first extreme example, as a customer you are likely to be very unhappy with your experience and unlikely to return.

So, what is the optimal spacing from the customer perspective? That is, what density of the gaming floor will cause the customer to have the best experience and maximize the likelihood that the customer will play all of their gaming wallet at that casino? Considering our two extreme examples, and recognizing that the answer lies somewhere in between, we end up with a sort of “Laffer Curve” for gaming density (see Figure 1).

Figure 1: Laffer Curve for Gaming DensityWhile Arthur Laffer argued that the optimal taxation rate lied somewhere between 0 percent and 100 percent2, we argue that the optimal gaming density for a customer lies somewhere between zero (where the games are stacked as closely together as possible) and infinity (where the games are so far apart as to be unreachable by the customer). Our goal is to find the top of the curve.

Now, in practice, our hypothetical example is impossible to replicate. However, heavily competitive environments act as a proxy for this example, since demand at a given casino is reduced by the presence of immense competition.

Pearson’s Correlation
Pearson’s Correlation measures the strength of dependence between two variables. The table in Figure 2 is a series of (x,y) scatter plots and the associated Pearson’s Correlation coefficient of x and y for each set. Note that the correlations illustrated reflect the non-linearity and direction of a linear relationship (as in the top row), but not the slope of that relationship (middle row), nor many aspects of non-linear relationships (bottom row). Also note that the figure in the center has a slope of zero, but in that case the correlation coefficient is undefined because the variance of y is zero.3

The graph in Figure 1 illustrates a correlation of 0.66, which may look something like a merge of the second and third images in Figure 2. We can also see that a 0.8 correlation can, to a human, look like a clear dependence between two variables.

Figure 2: Correlation Examples

Yield Case Study
Silverton Casino was the basis of a previous series of CEM articles that focused on the casino’s Penny Alley area. Penny Alley area was a low-capital initiative that resulted in a 19 percent increase in theoretical win per device.4 Our example here is based on the Seasons Buffet and its aptly named mini casino, Seasons.

Originally, the Seasons mini casino was the second largest mini casino in the Silverton in terms of machine count. Seasons is adjacent to the buffet and has a high correlation (0.66) between buffet counts and player counts in area. Before yield management alterations were made, 80 percent of the games underperformed, and although the area had high observed foot traffic, it had low retention, signaling that players did not find the area attractive. In Figure 3, the heat map diagram of the revenue of each slot machine shows that while there are some concentrated areas of revenue, the gaming floor before the changes was clearly a low-utilization area.

 Figure 3: Seasons Mini Casino Before Change
Before making changes to Seasons, Silverton investigated if the lack of attractiveness of the area was related to the product or to the layout, or both. Season’s mini casino contained a high number of unpopular, lower-denomination video poker machines and several banks of uprights laid out vertically through the center of the area, creating a visual wall. This led to the initiative to enhance the area by both correction of the product and improvement in the layout.

The slots improvement initiative, lead by Salinda Conklin, VP of slots for Silverton Casino, had three main components:

1) Removing the visual barrier that split the section. This created a clear path to another gaming area and a restaurant that was previously hidden behind the barrier.
2) Cleaning up the game mix based on the product demand in the Seasons mini casino.
3) Adding more visually appealing slot configs (several rounds, shorter banks).

Overall, the unit count was decreased by 27 percent. The remaining mix was tweaked to include more of the games that players preferred in the area and also games that players in that area tended to play elsewhere on the floor.

These changes to the Seasons resulted in an increase in total revenue with fewer games, and therefore a dramatic increase in the yield. Total revenue for the area increased by 2 percent despite removing over a quarter of the games. Yield (in this case measured patrons relative to machine count for the area compared to floor) increased 25 percent. (See Figure 4.)

Figure 4: Change ResultsNow when looking at the post-change heat map of the gaming floor of Seasons (see Figure 5), it becomes immediately apparent that players are spreading their play across the gaming floor. While there is still opportunity for improvement, for example, banks 05-037 and 05-022, this improvement can be executed in the context of a much more effective overall layout and product mix.

Finding the Money
So, in our Seasons example, we discovered a lower bound on the optimal spacing between games. Whatever the density was a year ago (call it t_0), we found that the optimal spacing t* between games satisfies t*>t_0.

This is an important realization for casinos in highly competitive environments. This model can also be applied to any environment, albeit with very different results. In both a high-demand and a low-demand environment, the Laffer Curve of gaming density versus customer revenues will apply; however, the graph will look much different for high-demand versus low-demand environments. In particular, the optimal spacing t* will be much lower (i.e., will provide for less space and more games) the higher the gaming demand.

These results show how the yield management of gaming machines can be a profitable exercise. Furthermore, they indicate that careful analysis of the density of gaming machines and the layout on the floor may result in profit improvement with less capital deployed.

Figure 5: Seasons Mini Casino After ChangeFrom here, the key issues that we will explore in further articles are how to apply customer data to dig deeper, how cannibalization could affect our results, and how new metrics such corrected theoretical win can be applied to gain actionable insight across the whole property. What is truly exciting about these actions is that they often involve minimal capital, and yet, as we have shown once again, they can drive incremental revenue.


1 CEM, April 2010 “The Long and Short of It: Slot Games from a Player’s Perspective,” Singh, Cardno, Gewali.
2 http://en.wikipedia.org/wiki/Arthur_Laffer, extracted September 2011.
3 http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient, extracted September 2011.
4 CEM, December2010-March 2011, “Mini Casinos Meet Mini Games at Penny Alley: A Case Study of Silverton Casino,” Cardno, Singh, Thomas, Evans.

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