In my last entrys, I discussed the shortcomings of measuring coin-in. I will next take aim at the sacred theoretical win metric, which I believe is one of the most common measurements used by casino marketing departments to segment customers.
Theoretical Win = Σ Coin-in * Hold Percentage (Par or expected win) for the device.
Because theoretical win for slots is derived from coin-in, it is subject to all of the problems I pointed out in my last discussion, which I need not repeat here. The second major component of theoretical win, the hold percentage, is also quite problematic.
1. The Hold Percentage for a slot machine varies greatly depending on how a machine is played and the amount beton a particular game. Casino management systems (CMS) typically allow for a few blended hold percentages to be entered for a particular slot. Of course the blended percentage does not reflect how an individual machine or player has played. But, this number is used to calculate an individual players total theoretical win for a period.
2. The hold percentages used to by the CMS may not take into account progressive jackpots, side bets, or bonuses available to the player while playing (sometimes these awards vary based on time and behavior).
3. Hold percentages are calculated based on the random number generator used by the slot machine’s cycle—e.g., a machine is expected to hold X% of all wagers made for Y number of games played. With today’s sophisticated slots, Y could be a 7-figure number. This is important because in some cases, if the average daily theoretical win for a short period (e.g., a 2 day trip) is being used to make marketing decisions (a very common metric), the player has likely been subject to a miniscule percentage of the cycle for which the hold percentage is based—allowing the possibility of the calculation being highly skewed.
More fun complications with the numbers we literally take to the bank ...
Stay tuned for my suggested solutions.
Comments
You are absolutely right! As
You are absolutely right! As a matter of fact, the win metric has always been one of the most significant measurements used to segment people by the marketing departments of casino. One thing we need to take into account is the fact that theoretical success seems to be inside the bloodline of casino markets and there is no denying that fact. The Hold percentage is clearly an example of that and nobody can argue against that!
pick up line
Theoretical Win
As the title states, it is all 'Theoretical'. All theories have basic flaws because they are assumptions. There can exist no true model that addresses all variable. Good points!
interesting article!
interesting article!
Really nice post Thanks a lot
Really nice post Thanks a lot for sharing...
Nice post !! I m very
Nice post !!
I m very impressed with this and I expect the theoretical-win from these areas to be dramatically higher than the balance of the gaming floor. When looking at the performance of individual games it creates distortions in the analysis if we include the high limit slots in the average figure.
Great job
RFM Analysis
It seems that casino marketers have theoretical win in their DNA. This is because they are also likely to have, as marketers in many industries have, the recency, frequency and monetary value (RFM) gene.
Calculating the recency and frequency elements is fairly intuitive. A recency score for an individual, for instance, could be calculated by looking at the number of days it has been since their last gambling trip. A frequency score for an individual could be calculated by looking at how many trips they made to the establishment during a particular time period. Though the definitions of a trip, the length of the period, whether or not averages or other factors should be used are subject to debate, in the end, a fairly straightforward and accurate measurement will be used.
Establishing a metric for measuring the monetary value of a customer for gambling activity, however, is not as clear-cut. In other industries, this factor is more or less an accounting exercise—add the revenue gained from purchases less the cost. Theoretical win, the most common monetary value measurement for individual players in the gaming industry, though it has been used a long time and is an excellent notion, is subject to subjective elements and measurement errors that significantly degrade its effectiveness for this purpose. Understanding the biases that this measurement contains is a critical component of optimizing our due back programs.
---Andrew Cardno (From upcoming CEM article with Bart Lewin and Ashok Singh)
The fastest players
When looking at theoretical-win one of the most interesting lists to pull is the fastest players in the property. It is especially interesting to analyze these fast players in terms of, luck (or have they been unlucky), frequency and time of day of play.
One business performance driver that helps to understand the rate of play is theoretical-win per hour per customer (TWPHPC). Using TWPHPC we might change the promotions such that higher rate players are more likely to gain access to the products they prefer when they prefer to play.
More to come on theoretical-win optimization.
---Andrew Cardno
Using Optimization Models to De-Averaging Theoretical-Win
The airline industry is a great example of how optimization models can be applied to "de-average" the customer. Before yield management airline prices were set using comparatively simple mechanisms, after yield management the prices one pays for an airline ticket can vary wildly, this price is largely determined by the yield management software.
Gaming machine optimization has two key aspects; firstly maximizing the peaks and secondly managing the incentive offers. When looking at theoretical-win per player or per machine per day we must also consider the rate of spend and the time of spend against yield management issues.
The key question is what are the levers that can be used to alter the behavioural characteristics such to maximize our yield.
I have seen dramatic results from optimization, done well these models join the player and product with specific incentives. While the results can be measured in theoretical-win per day the analysis moves far beyond this.
More to come on theoretical-win gaming optimization.
---Andrew Cardno
Average Theo Win: Another Sacred Cow!
Averages and totals are an accurate measure for the purpose of determination of overall results. For example when looking at the end of year results it is quite normal to look at the total theoretical-win of the property or the total theoretical-win per slot per day.
When it comes to looking at the relative performance of a slot machines or customers averages are often quite misleading, especially if different groups have different distributions (for example the distribution is bimodal). For the performance analysis when we apply averages to these quite different distributions we are hiding the true nature of the underlying of the data.
The canonical example is to consider the high limits slots and their players. We expect the theoretical-win from these areas to be dramatically higher than the balance of the gaming floor. When looking at the performance of individual games it creates distortions in the analysis if we include the high limit slots in the average figure.
There are a number of quite good approaches to the analysis of theoretical win, but we first must accept the basic measurement is has its limitations.
---Andrew Cardno
"theoretical win is not wrong it is just allocated with bias"
Good to see various vantage points, thanks.
T-Win is very much a direct product of a player's total turnover; i,.e. recycling of credits won and bankroll. IMO, the "averaging" of behavior produces the most reliable predictability; knowing full well that predictability doesn't guarantee any specific result.
Of course it's with bias - isn't that what odds are all about?
As for optimally evalualting a player's overall value - gaming is but one component.
Actual Theoretical Win
One option I have put to good use is to calculate the actual-theoretical (ActualTheo) win of players.
I think the best way of doing the ActualTheo calculation is to measure the actual plays by the patron (information that is not generally available). However in the absence of this information we can start with simple categorization, for example categorize the players on slots who play the optimum mix of jackpots (often max-bet) as having a different theo-hold to non optimum players.
In the examples where I have done this analysis I have found that the distribution is bimodal (http://en.wikipedia.org/wiki/Bimodal_distribution). Thus the simple approach of separating out two groups often provides a more accurate model of customer behaviour.
One issue with this method is handling the effects of jackpots. Specifically when the player wins a jackpot and then reinvests the jackpot into the game their Actual and TheoWin skyrocket.
There are other methods to follow but this is a fun one to start with.
---Andrew Cardno
www.andrewcardno.com
Sacred Cow
Both ED and CH look at theoretical win to determine "reinvestment value," and "what the player could or should have received for X amount of play." My thinking is it might be more fruitful to segment your customers based on behavioral factors (e.g., how far they travel, the games they play, length of visit, service purchased, etc.), and create offers based on these instead of price based offers (e.g., giveaways or discounts)--using the aggregated actuals for the segment to determine the value of the giveaway and ROI for the offer. This is a much more traditional approach for service industries. The aggregated actuals for the segment will naturally take into account the theoretical win. What do you think?
Bart A. Lewin
Often analysts have said to
Often analysts have said to me that their theoretical win balances in the long term and of course they are right.
The question is *how* does it balance?
To start with lets consider one critical flaw, the max-coin effect: on may games there is an extra bonus for playing max-coin. So players playing following this max-coin pattern are playing an effectively looser game than those who are not.
When one considers Video Poker where the skill of the player truly effects the outcome then we are creating true bias in out customer classifications if we simply rely on theoretical win.
These and other effects such as I mentioned in the initial blog create a situation where the "skilled" player is playing in a more generous gaming environment.
In most of the gaming environments I have looked at the aggregate theoretical win does balance to actual win over a long time. The issue is one of allocation to both players and games not the correct aggregation.
In summary: typically theoretical win is not wrong it is just allocated with bias.
These *fun* issues truly come to light when you look at your most "skilled" versus most "unskilled" players and then look at the profitability. In my experience it can cause minor riots between finance and marketing.
Maybe is there is no true measure of a gaming customer.
If you are reading this and your marketing is based on theoretical win stay tuned for some ideas on how to build different kinds of analytical models.
--Andrew Cardno
Sacred Cow - Comment
AC - when evaluating tens of thousands of slot players over a period of months for the express purpose of determining reinvestment values, the TW factor works just fine. It's not a perfect science, but it sure provides most managers a better than wholesale method of making effective decisions. Like CH, always interested in learning new viewpoints.
eileen d
Sacred Cow
Certainly the hold percentage can vary for the player as you mentioned. However the theoretical win doesn't really vary. We are taking a snapshot of what the player could or should have received for X amount of play. I would agree that if we were looking at ACTUAL win, then the vagaries of the minuscule percentage of the cycle of the game would come into play and it would vary greatly with the high volatility of today's games. However Theo is the best way to look at what the player would experience over time. You could get more complicated and look at average bet X handle pulls or come up with something perhaps more representative, but theo works pretty well as a predictor of value. We all know players who couldn't win on a game if we gave them the keys to the machine. No matter what they do - what they win - they will walk out losing XXX amount of dollars. I tend to look at them in terms of average loss per visit. I know that I will get XXX dollars from them every day that they come. There are some players that you could predict almost to the penny their daily average loss. I think Theo is much better than actual and barring any other convoluted method of calculating, I don't see much that is better. At least theo takes the volatility out of using actual. I do agree that comparing average coin in per game is only useful when comparing similar games in similar locations and of course combined with the return percentage of the game can often be misleading.
Can't wait to hear your suggested solutions, though. Always interested in hearing better ways to evaluate play.
chuck hickey
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