Authors’ Note: Hold percentage has long been used as the metric that determines the cost of play. Doing so is dangerously misleading for many reasons, including the variability of the rate of play of customers, and that the rate of play is determined by a combination of the player, the bonus rounds and the game. As the player is involved in the rate of play, it is absurd to consider any cost-of-play calculations that do not look at actual player behavior. In this article, we collaborate with Robbie Sawyer, vice president of slots at Grand Casino Mille Lacs, to examine a more meaningful and mathematically accurate measure of the cost of play. We thank Sawyer for his participation in writing this article. Grand Casino Mille Lacs has a variety of the newest, most exciting casino slot machines around, including multi-line/multi-coin, traditional three-reel and poker. The gaming floor has more than 1,900 video slots, keno and poker machines to choose from. The gaming floor is also home to more than 266 nickel machines and games in 1¢, 2¢, 10¢, 25¢, 50¢, $1, $5, $10, $25, single and multi-denominations.
“If we could raise our hold by one tenth of 1 percent, we would make an extra million dollars!”
Anyone who has worked in slot operations has heard this statement from the chief financial officer—and often from the chief executive officer, general manager, vice president of marketing, director of food and beverage, hotel front desk clerk, housekeeping and pretty much everyone else working for the casino. The problem with this statement is it is both oh-so-alluring and so completely, utterly wrong.
Let’s begin with the allure, which is more money, of course. If we just raise the “price” a teeny, tiny fraction, we will make more money at no risk or cost. It’s so easy! Or at least it would be if the vice president of slots had a little dial back in his or her office that could instantly change the hold percentage of the entire casino floor. And if by making that change to the entire casino floor, every other factor (particularly coin-in) would hold constant.
Later we will examine this concept of volume-price a little deeper, but first let’s take an in-depth look at why this statement is so wrong.
How Does Actual Hold Percent Change?
When looking at actual hold percentages, it is important to understand what can cause this number to fluctuate over time and to reconcile the reason behind these fluctuations.
Let’s suppose that a casino changes the games on its floor. Before anyone gambles on this new floor, the hold has already changed, because the games have changed. But what type of hold are we referring to? In this case, it’s the arithmetic hold. Arithmetic hold is defined as the average hold of each machine on the gaming floor without any regard to the volume of play. One can think of arithmetic hold as the hold percentage lever for the casino operator. If an operator is instructed by the CFO to raise the hold percentage of the casino floor, the attempt to do so likely will involve raising the arithmetic hold.
But, of course, this does not always work. That is because there are two other considerations when looking at hold percentages: customer choice and Lady Luck.
If arithmetic hold is the lever of the casino operator, theoretical hold (or theo) is the measurement of customer choice applied to the arithmetic hold. Defined as theoretical win divided by coin-in (which is equivalent to a weighted average of coin-in by theo hold over all the machines being measured), the theo hold of a casino floor is heavily dictated by customer choice.
As a simple example, suppose that our casino operator has two machines, one set at 1 percent hold and the other set at 9 percent hold. The arithmetic hold of this casino floor is then 5 percent. However, if the customers put all of their money into the 1 percent hold game, then the theo hold is only 1 percent—and any effort by the operator to raise the hold percentage by adjusting the 9 percent game will be completely futile. Put simply, if customers prefer lower hold games, then the theo hold will be lower than the arithmetic hold, and operator attempts to raise the theo hold may be met with customer resistance.
Finally, we have Lady Luck and her influence on actual hold to consider. Actual hold is actual win divided by coin-in, and as such, it is highly influenced by the volatility of gaming outcomes. And no matter what the operators set the arithmetic hold to be, no matter which customer choices drive the theo hold, in the end Lady Luck will have a significant influence on the actual hold.
We tackled this issue in great detail in our April 2011 CEM article “Hold a Sacred Cow.”1 Basically, as it turns out, the hold percentage of the casino floor is a nearly meaningless number.
At a machine level, hold percentage is an important metric, and we will see later that it is one of three metrics that influence customer perception of the price of a game. Plus, changes to hold percentage for a single machine will have wide-ranging consequences to the overall performance of that machine. Raising hold may not have too negative of an impact on volume, in which case the game will produce more theo win. Alternatively, it could significantly reduce volume, in which case the theo win will decline.
However, as we add more games into the analysis, the relevance of hold percentage declines exponentially. Once the casino floor is being considered in its entirety, hold percentage is nearly irrelevant.
What is the Price?
But if hold percentage is not the price of a game (or of our floor), what is a good measure of price?
Let’s start by asking a customer about his experience on our gaming floor. “Bob” has just completed a session on our floor. If we walk up to Bob and ask, “How did it go today?” Bob is not very likely at all to say, “Well, your casino held 8.5 percent against me.”
Bob is far more likely to respond with one of the following lines:
• “I won!”
• “It was terrible. I lost $100 in 15 minutes.”
• “Great! I broke even but got to play for two hours.”
In all three situations, Bob is referring to his time played and/or money won or lost. Thus, the price of the game should be a measure of money won/lost over a time of play: Price = Win per Hour of Play.
Now, whether to use theo or actual win here depends on the situation, but for the remainder of this article, we will use theo win: Price = Theo Win per Hour of Play.
What is the Volume?
Every CFO is focused on revenues, and in the end, the CFO’s goal is to maximize revenues while minimizing costs. By looking at hold percentages, CFOs are hoping to leverage the formula Revenue = Volume x Price, and are attempting to use coin-in as volume and hold percentage as price. As we just discussed, however, theo win per hour is a better metric of price. But then what metric best represents volume in this formula?
Let’s go back to Bob. We already know Bob sees time-on-play as important. Another factor that may come into light when talking to Bob is his ability to get on a game. For example, perhaps Bob will make one of these comments when asked about his gaming day:
• “It was great. I walked in and sat right down at my game!”
• “It was very frustrating. My favorite game was occupied, and the person playing it stayed on it for an hour.”
Clearly, Bob is able to feel the impact of occupancy, defined as the percentage of time that a game is being played. Furthermore, our CFO will appreciate occupancy as it can be used as volume in our formula, due to the fact that Revenues = Occupancy x Theo Win per Hour of Play x Number of Hours x Number of Machines.
So now we have two metrics to present to our CFO to help him or her better understand our revenues as a function of occupancy and theo win per hour. But how should we present this data, and how does this data change over time?
Segment the Revenues
In this section, we present anonymized data from Grand Casino Mille Lacs—and again thank Robbie Sawyer for his assistance in interpreting these results. While this is not the real data set and not the real conclusions for Grand Casino, we are still able to understand the concepts by examining this anonymous data.
In Figure 1, we see the overall results (over an unspecified time period). We see $5.5 million in theo win across 1,873 machines. The average occupancy for these games is 29, and the average theo win per hour is $33.
Now let’s dig deeper by segmenting the revenues using a Quartal technique (see Figure 2). With this technique we can create a “balanced scatterplot” of each machine’s performance. We use the x-axis to arrange the games by occupancy and the y-axis to arrange the games by theo win per hour. Then the Quartal technique balances the revenues, creating four groups of games on the scatterplot, each containing the same amount of revenue per group.
As an example, in the upper left corner of Figure 2, we can see that roughly 25 percent of the revenue is coming from 423 machines that average only 17 percent occupancy but $61 theo win per hour. In the lower right, we can see another 25 percent of revenues is coming from 398 games that have a much higher average occupancy of 42 percent but a much lower theo win per hour of only $20. Think of the upper left as our “Tiffany” games and the lower right as our “Walmart” games. In most gaming markets, we need to provide both types of products.
Now let’s take our Quartal technique one level deeper, down to the 1/16th (or 6.25 percent) of revenues (see Figure 3).
Here we see a wide range of game performance groups. From the 98 games with a $114 theo win per hour and an 11 percent occupancy in the upper left, to the 101 games with a 57 percent occupancy and a $15 theo win per hour in the lower right. Armed with this robust data, we can begin to identify and analyze our gaming floor from this perspective of volume and price.
Over time, we will collect multiple pictures of our gaming floor through this lens, and it is important to understand the changes over times by doing variance analysis.
Now that we have a very detailed picture of our casino floor from the perspective of two customer-facing metrics that combine to give us the price-volume formula for revenues, we can leverage this new picture of our data to optimize game changes and measure the impact of these changes.
At a high level, we can leverage the price-volume formulas for variance analysis:
• Volume effect = (new volume – old volume) x original price
• Price effect = (new price – old price) x new volume2
At a deeper level, our slot operators can now begin the process of optimizing each of the revenue segments created by our Quartal process above. Selecting one of the revenue segments and optimizing those games, our slot operator can return in three or six months and see the impact of his or her game changes. Did the segment that was optimized increase its revenues? Did any other segment of games become cannibalized and demonstrate decreased revenues as a result?
Note that each of these revenue segments is very different, and each will have a different optimization strategy. For low occupancy but high theo win per hour games, our strategy may be to extend time on device by improving customer service. For high occupancy but low theo win per hour games we may want to look at ways to increase the price, perhaps by raising the minimum bet or lowering the maximum bet to encourage more max betters—or possibly even raising hold percentage after all.
This process of optimizing one revenue segment at a time, and examining the profitability of these optimization efforts by looking to other revenue segments to see if cannibalization occurred, can be applied repeatedly as a continuous improvement process.
Change the Conversation
Ultimately, we can give our CFOs much more information than in the past, such as:
1. We are currently pricing our games at x theo win per hour and seeing volumes of y occupancy.
2. This result has changed, and we can show you the changes in terms of the volume effect and the price effect.
3. We have optimized a number of revenue segments, and these are the results (hopefully positive!) we are seeing.
These three statements bring us to a special place where, with real data on the price of the game and real data on the results of price, changing hold percentage is no longer relevant and we are able to discuss the actual price of the game.
2 Further details can be found in the Treadwell Media Group blog: http://blog.treadwellmedia.com/archives/13.
Andrew Cardno has more than 16 years of experience in analytics ranging from modeling health-care drive times to gaming floor analytics. He presents on the future of analytics and is living in the U.S. and works with worldwide corporations. He serves as the chief technology officer of VizExplorer. He can be reached at andrew.cardno[at]vizexplorer.com.
Dr. Ralph Thomas, chief data scientist and vice president, gaming division, VizExplorer. During his 10 years in the casino industry, Thomas has focused on maximizing profitability by applying statistical analysis to company databases. Previously, Thomas spent 15 years in academia, as both a student and a lecturer of mathematics. He can be reached at ralph.thomas[at]vizexplorer.com.
Robbie Sawyer brings nearly two decades gaming experience to his role as Vice President of Slot Operations at Grand Casino Mille Lacs. He is responsible for all aspects of a slot department with over 1900 gaming machines and 61,000 square feet of total gaming space. Robbie was instrumental with the creation of Play Pulse®, Grand Casino’s slot volatility marketing campaign.
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Never spent a day of my life in anonymity
Submitted by Anonymous on Mon, 06/01/2015 – 12:10.
Aside from AA, I’m not one to write letters or post anonymously. Hi, my name is Rex Stock, and I wrote the reply to Andrew and Ralph’s piece.
So no one gets the wrong idea, please know that I think Andrew Cardno is brilliant and I like his products very much. I introduced a lot of operators ((Cannery Casinos, Station Casinos, Atlantis Resort in Reno and their Colorado Property, Gila River, Desert Diamond, Delaware North) to what was then BIS2 and asked those operators to invest in his product, which they did…
Ralph Thomas is one of the industry’s great thinkers, mathematicians, and analyst, and anyone who thinks Ralph isn’t capable of improving their slot floor is sadly mistaken. He’s the best.
However, I disagree with this notion that hold percentages don’t matter, and I spent a lot of time working in operations and the supplier side with more than simple anecdotal/mythology to support my observations.
And, in my travels, players can tell the difference between a tight machine and one that is set at reasonable payback percentages.
On the other hand, it may be true that players cannot properly discern when a game is set too liberally (video poker excepted) but that seems to be more an outcome of basic variable reinforcement psychology and to think either side of that equation is equal, I believe, is a mistake made all too often by those–as Cardno and Thomas so adeptly point out–looking for easy answers to a very complex world…
Where Theory and Reality Meet
Submitted by Anonymous on Mon, 06/01/2015 – 10:37.
Anyone that has run a slot floor or talked with players or spent any amount of time watching the dynamics of slot play will tell you that while it’s nice to talk about theoretical win to figure out comp levels, there’s no doubt that a player can tell the difference between the play of 93% game versus one that is 88%, or even games that are set at 98%.
For the sake of this article I’ll keep my comments to high hit frequency games that are quite common in most markets (especially Minnesota) but just know that there’s still a class of games in markets that use stepper technology with games that have a hit frequency of 20% on a good day.
And, certainly, this was proven time and again up in Minnesota (where Grand Casino Mille Lacs is located) when video gaming machines that utilize multi-line/multi-coin high-hit frequency games were first introduced in the early 90’s.
Back then we did lots and lots of data crunching and without a doubt there was negative ramifications moving a game to a ‘tighter’ hold of 88% while increasing it to 96% did nothing to increase coin in–it simply allowed a few more players per month to win the top award.
Here’s a comment in the piece that should prove useful and raise suspicion of the premise of this article:
“Note that each of these revenue segments is very different, and each will have a different optimization strategy. For low occupancy but high theo win per hour games, our strategy may be to extend time on device by improving customer service. For high occupancy but low theo win per hour games we may want to look at ways to increase the price, perhaps by raising the minimum bet or lowering the maximum bet to encourage more max betters—or possibly even raising hold percentage after all.”
The question needs to be asked why the games are low or high occupancy?
Location of the game, overall occupancy of the casino, AND hold percentage are all variables in that outcome. The notion of extending time on device by ‘improving customer service’ is almost laughable–players will sit and play if their having fun with or without customer service (gone are the concerns about hopper fills and such so that’s not really an issue) and they certainly aren’t going to sit around and lose their ass for extended periods of time just because a host is checking in on them…
When the CFO comes and tells the slot director that they need more money so “tighten up the games”, especially in a place where it is all local/repeat visitors, fight them with all you’ve got.
And while one can always hear the battle cry of the slot player that “the machines are tight, and I can’t win” sometimes there’s more truth to that than this article would have you believe.