v OWL RESEARCH v

Optimal Slot Machine Mix: Statement of Work

Prepared by: Geoffrey Knight

Prepared for: Lucky Duck Entertainment Date: February 20, 2013

OWL RESEARCH LUCKY DUCK ENTERTAINMENT Geoffrey Knight Optimal Slot Machine Mix: Statement of Work

Executive Summary Lucky Duck Entertainment (LDE) is faced with a problem of maximizing the profitability of slot machines at each of their eight Nevada locations. The number of possible machine mixes is too great to rely on ad-hoc optimization. For that reason, Owl Research (OR) proposes an analytics approach to this problem. First, all machines will be grouped by profit level and demand. This will make the problem more tractable, by reducing the number of possible combinations. Second, an Excel based forecasting tool will be developed, to predict the performance of a given machine mix. This is essential for comparing any proposed changes to the performance of the current mix. Finally, a mathematical optimization problem will be formulated and solved to find the optimal machine mix, given capacity and management constraints. After the optimal mix is verified with the forecasting tool, it will provide a clear implementation strategy for each casino manager. The rest of this document provides high-level description of the projects methodology, data and other requirements.

1.0 System Environment For this project, a number of analytical tools will be used. In particular, to categorize the machines, a large amount of data will need to be processed. SAS will be used for this purpose, as it provides a platform to format the data and to perform the necessary analysis. Owl Research has a fully licensed version of SAS installed on an in-house server. No investment by LDE is required at this stage. Monte Carlo Simulation will be employed in forecasting. A combination of VBA and Microsoft Excel will be used for this purpose. Since VBA is built into Excel, LDE simply requires a recent, licensed copy of Microsoft Office. Finally, depending on the size of the final problem, either Open Solver or AMPL will be used. OR has both of these installed locally. AMPL and its packages are available for commercial use for a fee. The necessity of AMPL will become evident after machine categorization.

2.0 Project Description This section contains information regarding the resources required to complete the project, the final deliverables, and the overview of the analytical approach.

2.1 Information Flow

To provide final recommendations to LDE, Owl Research will require accurate data. First, available historical transaction records, going back at least one year, will be necessary to complete categorization and forecasting. Separate data sets for overall and cardholder-only transactions will benefit the analysis. At the optimization stage, approximate data regarding cost of installation and decommissioning of each machine will be necessary. Ms. de la Luz shall be the primary point of contact to provide technical data to OR. Lastly, since management preferences play an important role in casinos performance, optimization cannot be completed without it. A survey will be sufficient to gather these preferences. This survey will be compiled by OR and administered by LDE. OR will collect back the survey, organize the data, and use it for modeling.

OWL RESEARCH LUCKY DUCK ENTERTAINMENT Geoffrey Knight Optimal Slot Machine Mix: Statement of Work 2.2 Analytical Component

This project is broken down into three parts: machine categorization, performance forecasting, and machine mix optimization. All three parts of the project depend on one another, and will be completed in the following order.

2.2.1 Machine Categorization Currently there are hundreds of machine types, each to one of six denominations, among four distinct locations, within each of eight casinos. If no further categorization were to be performed, this would result in a problem with hundreds of thousands of variables. While it is not infeasible to solve such large problems, it is problematic to collect valid data for them. Therefore, it will be necessary to break down the machine types into a manageable number of categories. Most of the effort will be directed to understanding which games and models can be grouped together, as there are hundreds of these combinations. Preliminary goal is to have no more than 20 machine groups. This will allow managers to have a great deal of flexibility in terms of what games and themes they employ, as long as these machine adjustments do not cross group boundaries. The process of grouping will be profit and demand driven. First, each machine group will have certain profit range associated with it. This profit range will be derived from the historical performance for all machines of the given group. Furthermore, the profit range will vary according to casino, location within that casino, denomination setting, and time of year. If any of these parameters are found to be persistent in a group, the parameter may be excluded after further analysis. This is why historical data is more precise, in this case, than vendors estimates. Second, each machine group will be examined based on its player demographic. This will require analyzing cardholder transaction data to determine how it differs (if at all) from the overall player behavior. If significant difference is found, a number of machine groups can be established for cardholders benefit. OR will provide a document that arranges all machines into a small number of categories, along with the explanation as to why these categories are practical.

2.2.2 Performance Forecasting Forecasting performance of a machine mix will be an important component of the project. It will be a management tool, and could be used to test the final recommendations against the current mix performance. Therefore, the model will have to be rigorously verified and validated. After the deliverable of machine categorization is completed, the work on the forecasting will begin. OR will build a Monte Carlo simulation model, which evaluates the performance of a particular machine mix. The model will have a variable time-horizon cycle: from one week to a year (shorter or longer forecasts will be increasingly inaccurate). The mechanics of a Monte Carlo model are simple. First, the profit range for each machine group, location and denomination will be entered into the model. Next, the model will draw normally distributed random numbers from each profit range that

OWL RESEARCH LUCKY DUCK ENTERTAINMENT Geoffrey Knight Optimal Slot Machine Mix: Statement of Work corresponds to a given machine mix. If there is more than one machine in the group, a random number will be drawn for each machine. The sum of all these numbers will estimate the profit for one cycle. Repeating this procedure a sufficient number of times (determined analytically) will allow the construction of a confidence interval (of desired width) that can be used as a forecast of the given machine mix performance. In order to validate the forecasting model, and simultaneously validate the categorization parameters, a performance forecast of a quarter of a year will be completed. The output will be compared to the actual performance derived from the data for the corresponding period. Additional precautions will be taken to negate the effects of seasonal outliers.

2.2.3 Optimal Machine Mix Optimization component of this project will begin as soon as machine categorization is completed. There are two tasks in this section: gathering constraint data and solving the optimization problem. An optimization problem consists of variables, objective function and constraints. Variables, in this case, are the numbers of machines of a particular group, at some casino location, with a certain denomination. The objective is to maximize the profit generated by all machines in some timeframe. The only constraints of this problem are the managerial preferences at each casino location and integral constraint on the variables. Before discussing solving the problem, one must be formulated. LDE will pursue two approaches here. The first will rely on deterministic assumption. With this approach, it is assumed that all data regarding revenue is known with certainty (average values will be used). The solution will be crude, as it does not take into account variability. However, it will at least provide a basic benchmark for any additional optimization. Furthermore, the optimal mix solution under the deterministic assumption can be used to test the forecasting model described in section 2.2.2. Second approach will use stochastic optimization. This procedure assumes that the revenue is variable (a random variable). Depending on the data analysis and desired time horizon, stochastic model may include seasonal effects and cost variability. Both approaches will have similar problem statements, but the stochastic method will have a more complex objective function. There is a number of ways to compute the total profit mentioned above. One way is to consider how much revenue a machine group generates per unit time. This is practical, since machines are often relocated within each casino, and different locations lead to different revenues. It will be straightforward to compute these parameters based on the transaction data. From these profits, costs will be subtracted. Costs are associated with moving and setting up of machines. If it is established that set-up costs are low, compared to revenues, they may be excluded from the model. To quantify the management constraints, a survey, that is to be distributed among LDEs casino managers, will be prepared by OR. This survey will contain the information on the categorization effort and instructions on how to perform inventory according to this

OWL RESEARCH LUCKY DUCK ENTERTAINMENT Geoffrey Knight Optimal Slot Machine Mix: Statement of Work categorization. Additionally, each manager will be asked to provide an upper and a lower bound on the number of machines in each group that the manager is willing to have at that location. It is important to note that the amount of change at each location is completely up to the manager and is very flexible. Knowing the current machine mix, a manager can set such upper and lower bounds that only a minimal change to the mix is allowed. Moreover, since the machine groups will be broad, managers will be free to mix games and models within each group. The completion of the optimization part of the project culminates in a report that recommends an optimal machine mix along with its analysis and comparison to the current mix. This comparison will be performed using the forecasting tool, which will be completed before this deliverable.

Input Data Structure

For machine categorization, the overall transaction data and cardholder transaction data is necessary. The overall aggregate transaction data should contain the following fields: machine name, casino, section, denomination, manufacturer, model, period of record, realized gross revenue for the period, number of plays for the period. For simplicity, the above fields can be separate for each type of machine. Transaction data for cardholders can be provided in the following format: cardholder id, age, locality, section, casino, machine name, denomination, period of record, gross revenue and number of plays. Complete data sets should include as many records as there are available (going at least one year back). Additional data may be required, but LDE will be notified in advance of any such possibility. Forecasting model will be based on categorization data set (see next section). No input is required from LDE. At optimization stage, cost data is necessary. These data can be in the following format: machine name, manufacturer, model, casino, section, decommissioning cost, procurement cost. Note that if a particular model is already available at a given casino section, its procurement cost is zero. Otherwise, if a machine is not available, the cheapest procurement cost is to be used. Costs may be estimates and same numbers can be provided for machine of similar types. Output Data Structure

A deliverable of categorization component of the project will be a data set where each machine is listed under some group. Every machine group will have associated with it a profit range (2 fields), depending on casino location, position within casino, denomination, and time of year. For example, one group of machines may have a profit range between 20,000 and 30,000 in 3rd quarter, given they are at Aries casino, in the interior, and with denomination setting of $0.01. Majority of groups will not have overlapping machine types. However, based on demographics analysis, a group may be created to recognize the preferences of cardholders. This group will contain overlapping

OWL RESEARCH LUCKY DUCK ENTERTAINMENT Geoffrey Knight Optimal Slot Machine Mix: Statement of Work entries with other groups. This data set will lay the groundwork for both forecasting and optimization components. Given a machine mix, grouped based on the above categorization, the output of running the forecasting model is an average and a 95%-confidence interval for profits due to the mix. The profits will be broken down by casino and section, as that is more meaningful from management perspective. Solution of the optimization problem will give an optimal machine mix. That is, how many machines from each group are to be placed at each location, and at what denomination. Solution to stochastic problem will also include a schedule that reflects how the mix should be adjusted in different periods. To make the result more readable, the final report will contain a breakdown of machine groups by casinos and sections.

Assumptions As the project is in early stages, a number of assumptions have to be made. Some of these will be verified or rejected as the project progresses, while others will remain. First and foremost, OR assumes that the transaction data provided by LDE is accurate. A tolerable amount of data may be missing, in which case one of two tactics will be used. If the missing data is not essential, it can be ignored. Otherwise, missing data will be collected through expert opinion and estimation. OR expects that machines generate different revenues depending on the section of the casino they are in. Therefore, transaction data should reflect this level of detail. Second, it is assumed that operating cost is approximately the same for all machine types. This simplification allows the optimization model to be simplified by excluding the operating cost from the objective function. The goal is to maximize machine performance, which is independent of operating cost. Third, linear optimization assumptions of proportionality and additivity hold. That is, if a machine generates certain amount of revenue per day, then using two such machines will generate double the amount on the same day. Similarly, if one machine has revenue 10,000 and other has revenue 30,000, then using them together generates revenue 40,000. While these may not reflect reality perfectly, as demand may be dependent on machine mix, high traffic of customers and stochastic optimization will smooth the covariance effects.