Table Games RM


Historically, table games departments have been one of the hearts of a casino, especially in Asia. In places like Macau, Singapore, and the Philippines, the table games/slot ratio is closer to 80/20, so table games are huge revenue generators in Asia.

Since the highest-betting gamblers are estimated to be worth up to 50 times more than their lower-betting counterparts, casinos want to ensure that these high-rollers always have a seat at the table, even if that freezes out some lower-betting players. With so much money at stake, it is surprising that any casino bases its table game minimums on the judgment of human floor managers.

Bill Zender warns in his article Table Game Management for the Small Casino:

“I can’t emphasize enough how important game pace is to maximize an operation’s revenue potential. The more hands you deal, the more decisions you achieve. The more decisions you achieve, the more revenue you earn. It’s as simple as that. Many executives seem to focus on outcomes. I’ve worked for executives who believed in dealing more slowly when you were losing. This theory is so far off base it’s not even funny. Even in a smaller table games operation, if you can achieve one more round per hour on every open table game, just one more round, you can increase your table game revenue by at least $50,000 annually.”

Zender’s main point is that:

“The revenue potential of a blackjack game based on several variables: average bet per wagered hand; hands wagered per round; mathematical house advantage based on decks, rules, and player error in percentage; rounds dealt per hour adjusted for the number of wagering positions on the table; and hourly labor expense estimated by adding the dealer’s hourly wage and benefits cost with one-fourth of the hourly cost for the floor supervisor.”

These variables are used to determine hourly revenue potential known as theoretical win (T-Win) and net return, also known as hourly profit. The net return is calculated before additional operating costs, such as cost of equipment, complimentary table service, table game promotions and customer reinvestments (comps).

The results are quite stark, only if you have table minimums in the range of $6-$8, with full tables will the casino start making money. As Zender argues, “Optimally, your game needs to generate an average bet of $8 per player before you can expect to overcome your labor cost and start paying for any complimentary service and player reinvestment. Heaven help the dead games.”v

Several other studies have looked at the TGRM problem, including Daniel Boykin’s Table Games Revenue Management: A Bayesian Approach[vi], Chen et al.’s A revenue management model for casino table games[vii], Haley & Inge’s Revenue Management — It Really Should Be Called Profit Management[viii] and Clayton Peister’s Table-games revenue management.[ix]  

For Boykin, “Revenue management (RM) is a complex process for optimizing revenue from a fixed inventory which has applications in various industries. It has its origins in the airline industry. By looking at the common practices of RM in other industries, it is possible to develop a RM system that is applicable to a table games department.”vi

As Haley and Inge explain, “Affinia Hospitality saw revenues increase 17 percent over the prior year in the first month after implementing manual RM processes in a new central reservations office. The Millennium Bostonian Hotel paid back all of their start-up costs and more in the first month after converting from manual RM processes to an ASP-based service. Harrah’s Entertainment credited its RM system (installed in 2001) with increasing room and gaming revenues 13 percent for the year in 2002.”viii This is real money and a highly quantifiable ROI.

Haley and Inge also note that, “Anyone selling a perishable product knows that you need to flex your pricing in accordance with demand, lead time, competitors and a host of other factors. Hotel rooms, airplane seats, advertising time, fresh produce and winter clothing are all subject to revenue management tactics.”viii Table game seats fit well within this paradigm.

Boykin states that, for any RM system, there must be three set conditionsvi:

1.       Differences in customers.

2.       Variation in demand.

3.       Product perishability and a fixed production.

“If all the customers of a business or industry are uniform then there is very little to maximize,” Boykin explains. “The airlines utilize price differencing between business travelers and recreational travelers. This includes price differencing for days of the week, time of the year, even time of day. Hotels also take advantage of variations among customers,” adds Casinos should be able to as well. Besides the “variations between businesses vs. recreational travelers, even within these broad groupings there are a significant number of variations based upon demographics.”vi Boykin argues that, “In areas where you have greater variations, there is a greater potential to exploit that variation and therefore a greater potential to maximize revenues.”vi

TGRM issues include:

·       The problem of which tables to open on the casino floor, and for each table what bet minimums and bet maximums to assign.

·       The tradeoff is between having limits that are too high, thus excluding some customers who would otherwise have bet, and limits that are too low, thus leaving some money in the customer’s pocket.

·       The optimization problem is a simple maximization of revenue, given knowledge of the demand for each bet size.

·       Labor management needs must be added to the model to understand dealer needs.

For an IR, customers can be divided into gaming play segments, i.e., type of game, style of play, and minimum price per hand play. Boykin explains, “Variations in demand is evident through observation over a period. The limited demand and perishability of the product is inherent to the nature of a game.”vi

The second condition — a variation in demand — certainly affects the casino industry just as it does the airline and hotel “If the amount of demand is known, accurately and consistently, then there is no need for a sophisticated tool to maximize the revenue from that demand,” but unknown demand provides RM opportunity. Just like the airline industry, the casino industry is dependent on fluctuating seasonal and sometimes even daily “The greater the inability to forecast demand accurately, the larger the risk of management not maximizing revenues,” says

The third condition — product perishability and fixed production — is certainly true about the casino industry, as it cannot simply add new tables or double book a seat to satisfy excessive Likewise, the perishability of the “product”, e.g., one poker hand, one dice roll, or one spin of a roulette wheel, is obvious as Once the event occurs, there is no opportunity to recover the bet that was not placed.ix

Boykin states that, “The aspects of table games that call for the use of a revenue management system are the variable demand of the games and the variable betting threshold of each player.”vi Previous research has also looked at other variables such as win per available seat hour, or length of each play session; the Chen et alvii and Peisterix studies looked into the development of table games revenue management systems, but neither used the existing counts and player database to determine the

Boykin argues that “By predicting the next time period’s expected demand in terms of head count, then applying the percentage of players at each average bet level, the number of players expected at each betting level can be predicted. After optimizing and considering overall house advantage, we can maximize profit for the next time period in a proactive manner.”vi

As Peister sees it, “Since table games generate revenue through a house advantage built into the game itself on each wager placed, maximizing the wagers placed in an hour is a critical component of any revenue management system for table games.”ix

In his paper, Peister established the win per available seat hour (WPASH) concept, and looked to maximize casino win per seat hour.ix By manipulating the table minimums and number of open games, Peister created a distribution that sacrifices a few seats to increase the number of hands dealt at a table, while maximizing the casino win.ix

Peister also identified a major data issue for any potential revenue manager — actual demand is censored because when demand exceeds capacity it is impossible to tell how many players want to play and, therefore, how much money the casino loses due to a player’s inability to find a seat.ix By utilizing the Cox survival regression, Peister was able to predict the survival of each seat per hour, i.e., the likelihood of it remaining vacant throughout the entire hour.ix

The main weakness of Peister’s model was that the mathematical calculations were complicated and would prove difficult to anyone who didn’t have extensive mathematical and statistical Peister acknowledged and accepted these limitations, but argued that one of the primary reasons to use the Cox Regression model was because of the unknown underlying distribution of the  

Chen et al. took a different approach, choosing to measure Theo win rather than gross win and they utilized Croston’s method instead of Cox Regression.vii With this method, Chen et al. were able to forecast intermittent demand.vii The authors differed from Peister in that they compared their simulated results to actual revenue numbers from a casino.vii Then they estimated game demand at any given hour through a ratio of the two equations.vii Once demand was determined, a maximization equation was then applied “to determine the maximum house advantage for the given demand by adjusting the spots per table, minimum bet, average wager, and table limit.”vi A table-opening plan for the shift manager was developed from this, which was based upon the forecasted demand, for the maximization of house In the Chen et al. study, the casino could potentially bring in more than sixteen thousand dollars in theoretical incremental revenue at the blackjack tables on any given day, which would represent a considerable increase in potential revenue.vii

Like Peister’s method, Chen et al.’s study also had some drawbacks and Primarily, in their simulations, Chen et al. assumed uniform distribution of betting between table minimum and table maximumvii, which would rarely, if ever, happen in real “In fact, most shift managers would look upon results based on this assumption as highly suspicious,” Boykin Another drawback is that Chen et al.’s method would require extensive data collection and it would be labor intensive. Boykin argues that, “Even though this is a simpler method, this weakness still leaves room for improvement in a table games revenue management system.”vi

For Boykin, analysis of the data begins with the analysis of “Hourly demand data is inherently a time series collection issue, Boykin states, arguing that, “a time series analysis would be a logical plan for forecasting demand.”vi “However, after looking at the data, the realization that the miscellaneous variables to produce a reliable enough prediction model through time series analysis would be cumbersome and limited in scope,” warns Boykin. “This would not suit the needs of creating an operationally efficient model, which would require the ability to update quickly and with flexibility. Additionally, time series regression requires data to be consecutive.”vi “This either requires the casino to start tracking hourly head counts or have a large block of consecutive hourly head counts in a recent time period.”vi Tracking head counts would actually be a good idea and it is certainly a possibility with video analytics technology, but that option wasn’t available to Boykin so he chose an alternative

Boykin argues that, “A Bayesian approach allows one to utilize expert opinion and prior knowledge of a system, and is quickly and easily adaptable by using historical data and prior information to predict the demand for the next time period and each subsequent observation, updating the model and prediction using the next set of observed According to Boykin, “This allows for a very flexible model that would adapt itself based on recent observations.”vi

The model itself was set to predict expected demand for each part of the day in conjunction with player distribution. As Boykin explainsvi:

“Once the player betting data is segmented, the percentage of players in each player cluster is then calculated. Since this is representative of the entire population of players for the casino, the assumption is that any random sample of sufficient size would have the same player distribution. Therefore, the percentages in each cluster can be applied to the expected number of players for each day part. This would give the Shift Manager the expected number of players for each betting level at each day part. The Shift Manager could then determine if tables would need to be opened to accommodate future players, and at what level the table minimums should be set.”

Boykin concluded that, “By using Bayesian techniques, it is possible to develop a revenue management system that would reduce uncertainty in the Shift Manager’s estimations of future business. By reducing this uncertainty, the department can maximize revenues in a proactive manner, and the system can be used as a tool to assist casino managers in the better management of the table games department.”vi

The revenue management model could also be improved “by using observational data gathered by observing players as they enter the property and noting what attracts certain players to certain games. This could be incorporated into the database so the model could then classify players to each game type,” recommends

[i] Lucas, A. F., & Kilby, J. (2012). Introduction to casino management (1st ed.). Escondido, CA: Okie International, Inc.
[ii] Schwartz, D. G. (2013). Nevada gaming revenues: Long-term trends. Retrieved From: University of Nevada Las Vegas; Center for Gaming Research.
[iv] Ferguson, Mark E., Richard Metters, and Carolyn R. Crystal. 2008. The “killer application” of revenue management: Harrah’s Cherokee Casino & Hotel. March 13, 2009.
[v] Zender, Bill. 2013. Table Game Management for the Small Casino.
[vi] Boykin, Daryl. Table Games Revenue Management: A Bayesian Approach. May 1, 2014. UNLV Theses. 
[vii] Chen, M., Tsai, H., & McCain, S. C. (2012). A revenue management model for casino table games. Cornell Hospitality Quarterly, 53(2), 144-153.
[viii] Haley, M. & Inge, Jon. 2004. Revenue Management - It Really Should Be Called Profit Management. Hospitality Upgrade.  
[ix] Peister, C. (2007). Table-games revenue management. Cornell Hotel & Restaurant Administration Quarterly, 48(1), 70-87.


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