Gaming as a Commodity

By Andrew MacDonald and William R. Eadington.

Thinking of gaming as an entertainment service.

It is not unusual to hear casino executives speak of gaming as a unique and mysterious product. This notion also manifests itself in how casino managers think about the business of gaming. Unique, mysterious, unlike any other - these are the words often associated with the gaming business that are uttered by long-term casino managers. This is consistent with the belief that the only way to learn the business is to live the business and see all of the unusual things that can happen on the casino floor and in the executive offices.

In reality though, gaming is just a business like most others - one that can benefit from analysis of its fundamental economic characteristics, and by drawing from, and applying, principles and experiences from other businesses.

How should one look at the business and products of gaming? Whether it be a table game, a slot machine, a sports bet or a lottery - what is it that is being sold? Referring to gaming as a leisure or entertainment product is certainly a reasonable general description and a good starting point. Casinos and other gaming operations sell "fun and entertainment" to the majority of their customers. More dramatic or superstitious customers may view casino games as an opportunity to "meet destiny," to "test fate" or to determine if "God is smiling upon them."

Some customers are attracted by the hope of "winning a lot for a little" or are chasing the "dream of a life changing event." Others view gambling as an investment of time and energy into a hobby where they believe - rightly or wrongly - that their knowledge and experience at the games and understanding of the odds provides them with a better chance of winning than others. And some customers consider their encounters in a casino as "buying time on the machines or the tables."

Before venturing further into descriptions, it is useful to define the gambling activity versus the business of gambling, and gambling versus investment. Casino customers gamble, whereas casino operators are in the business of gambling in the short run, and are investors in the long run. A simple definition of gambling is where the player's long-term mathematical expectation from participation is less than zero, and the activity is freely entered into. (Jumping out of a window of a burning high-rise building also involves a negative expectation, but the lack of choice pushes it away from the category of a gamble.)

Operators in the business of gambling have a positive expectation on the monetary amounts they put at risk. In casino games, the operator derives a positive expectation from the games offered, and the house is selling a product at a positive price (the "house advantage") whereas the customer is a gambler, paying the house advantage for the opportunity to gamble. Casino games are "zero-sum" games, so the positive expectation for the house is a mirror reflection of the negative expectation for the customer.

There are, of course, situations where the customer can alter this equation through "advantage play" techniques of various kinds - such as professional poker players, card counters, slot jackpot teams and professional sports bettors and odds takers. However, in general the casino should always view itself as the purveyor of a service rather than as a gambler. "We are in the gambling business - not in the business of gambling." This should be a mantra for every gaming executive and one learned early on in one's career.

Organizations in the gambling business are going to evaluate their capital outlays in terms of the expected return on invested capital, and such expectations have to be positive, and exceed some risk-adjusted minimum hurdle rate. In this context, one can invest in the gambling business. With the exception of advantage players, there are no investors among gamblers; in the long run, they all will lose.

Thus, gaming can be conceptualized as a generic entertainment and leisure product. Furthermore, gambling is an intangible product, which like many other intangibles, is one where what is being purchased cannot be touched or held. It can also be described as an "experience good" where the consumer does not know how pleasurable - or unattractive - the product will be until after the act of consumption has taken place. (Indeed, as many gamblers will attest, the experience on any given outing can be pretty ugly.)

Other easily identifiable experience goods among leisure and entertainment commodities include movies, books, sporting events, concerts, visits to art galleries, and participatory adventure sports. With these products, customers are purchasing an experience and a "memory" of an event as well as the thrill, satisfaction, uncertainty, or adrenaline associated with the activity at the time. They are also purchasing the "anticipation" of consumption, which is often an important ingredient in the decision-making process. Anticipation plays a role for a gambling adventure similar to that experienced in advance of seeing one's favorite football or basketball team play.

For casino managers, it is important to view the gambling product in this light. If they consider themselves as purveyors running a business that provides entertainment and leisure services, they can better conceptualize the economic dimensions of the offers they are making to their customers. In general, consumers purchase commodities in various quantities, depending on prices, product attributes, consumers' levels of discretionary income and time available, and various other important parameters.

For gaming products, the price of the service can best be defined as the house advantage associated with the specific games. The house advantage is simply the long run average amount won per unit of wager by the casino. More rigorous definitions can be found in various places1, but the essence of house advantage is that it is the amount a gambler loses ("pays") per dollar wagered to participate in a game.

For example, the house advantage on a single number wager at single zero roulette is 2.70%. This is a weighted average of the proportion of times the player will win in the long run times the amount to be lost to the player by the casino, and the proportion of times the player will lose times the amount to be won from the player by the casino. The weights for winning and losing are the respective probabilities (1/37 and 36/37) and the amounts to be lost and won by the casino are -$35 and +$1, respectively. Thus, the arithmetic is: HA = 1/37*(-35) +36/37*(+1) = 2.70%.

This result is positive when viewed from the casino's perspective and of equal magnitude but negative from the player's view. For every $1 of single zero roulette purchased, the player can expect (mathematically) to lose 2.7 cents, and the house stands to win 2.7 cents. All gaming events have a similar price associated with them. Some other simple examples are craps (pass line bet) at 1.41%, baccarat (Player bet) at 1.36%, keno (depending on pay scale) at around 28%, slot machines at between 3% and 15% and blackjack (with a player of average skill) at about 2%.

The quantity of gambling services that customers will purchase in a given period is measured by the "handle," the amount of money wagered. The amount of product sold, the handle, is determined by several factors. First are aggregate economic factors that might reflect the general purchasing power of the potential customer market. Such variables include aggregate personal income, changes in levels of income, prices of competing commodities (i.e. other entertainment and leisure activities), and prices and availability of complementary activities (i.e. gasoline prices, hotel accommodation prices, air fares, etc.) There are also attributes which are specific to the various games that affect handle: each game's inherent house advantage, minimum and maximum betting limits, and game speed, as well as players' preferences and gambling behaviors.

Because many consumers are buying entertainment at the casino games with the thought of buying "time at the table" or "time on the machine," it is useful to estimate an expected cost of playing per hour, which to some extent can be controlled by the consumer. This can also be useful to the casino manager in understanding the returns generated when selling various gaming products. For example, consider a $2 minimum blackjack table with six players of average skill and a dealer who deals at a rate of 50 rounds of hands an hour. If all of the players make their wagers at the table minimum and the House Advantage for each player averages 2%, then in an hour the average player can expect to lose $2, which is the casino's expected win. (Each player has purchased 50 hands of Blackjack at $2 per hand where the price per hand is 2% of the handle, or 4 cents). Thus, for the entire table, the casino can expect to win (only) $12 per hour.

When viewed in this light, casino managers can estimate the "rents" they are charging for chairs at the blackjack table or the space in front of a slot machine. Is $2 an hour for a chair at the blackjack table reasonable? The same consumer who pays $9 for a movie ticket for a 90 minute feature film at the local cinema is paying $6 per hour; the sports fan who pays $100 for his ticket to a three-hour NFL game is paying $33 per hour. Taken in this perspective, it is no wonder that $2 blackjack minimums, and even $5 minimums, are rapidly disappearing.

The same approach can be taken for evaluating slot machines. Consider, for example, a penny (1 cent) slot machine with a 10% house advantage. For each $1 of handle, the average price is 10 cents. The player who purchases 300 spins an hour (5 spins a minute) with an average bet of 40 cents per spin will have purchased $120 in handle (quantity) at a price of 10 cents per dollar wagered for an expected cost for the hour of $12. Thus, the player has purchased - and the casino has sold - an hour's worth of the entertainment service for $12. How might casino managers influence the rents they are charging to the casino's customers? The House Advantage (or price) of a particular game or device is dictated by the underlying probability structure and the various payouts for player wins; this is true for table games as well as slot machines. House Advantage can be altered by changing the game's rules, changes in the probabilities of winning and losing outcomes, or changes in the payout structure for winning and losing outcomes.

Several nuances arise when using this methodology for calculating price and quantity for gaming products. Quantities are typically bought in single units with a fixed price per unit associated with the game's outcomes and the prizes awarded. It is not really possible to sell the products in discrete blocks - although IGT and Walker Digital's Guaranteed Play™ product2 is an attempt to overcome this to some extent. Players are generally not forced to play at a given rate over a period of time, with the exception of minimum wagers and sometimes the dictated speed of the game. A player on a slot machine could choose to hit the spin button rapidly, or alternatively, might idly chat with neighbors between spins. Thus, in the same one hour period, two customers playing exactly the same game could be purchasing very different quantities. The same is true at table games where some players might take longer to make required decisions or sit out certain events, thus not making a play every time the event is offered. Skill levels on certain games may also have an effect where the player's skill level can impact price.

Multiple betting options on some games can also change the average price. For example, in the game of baccarat (known as punto banco in the UK) there are in fact three different betting options - "player," "banker" and "tie" and each has a specific price. A customer betting $100 on "player" and $10 on "tie" on the same round of play will effectively be purchasing $110 of the entertainment service at an expected price of $2.78 for that event. Another customer on the same game of baccarat with $110 wagered on "banker" is also purchasing $110 in quantity but at an expected price of $1.29. Thus, even on the same game, purchases of the same quantity (handle) can have very different expected prices.

In spite of such complications, it is still useful to think of gaming as an entertainment service and to estimate an expected or theoretical spend per hour per gaming position on the casino floor. For "back of the envelope" analysis, one can use average prices for games and average quantities purchased by customers based on historical experience. Consider a $5 minimum table limit blackjack game where the average bet is $10 and where the average rounds played per hour is 50. This implies the expected quantity to be sold per player per hour is $500. If the price that the average Blackjack player pays - based on game rules and skill level - is 2% then the expected spend per player per hour is $10. In other words, the casino is providing its blackjack entertainment services to such players at an expected price of $10 per hour.

Making such calculations for each important type of game within the casino, it is possible to map out a pricing structure for the entire casino floor at the property level. This allows management to go to the next level: to conceptualize a pricing strategy that maximizes the casino's contributions to profits, for the casino floor. This leads to proper conceptualizing of the potential income generating capacity of each gaming position, or each square foot of allocatable gaming space. A guideline for optimizing contributions to profit for the casino floor is to equalize incremental profit per square foot over all categories of games. For example, if a casino floor would yield incremental profit of $100 per hour from adding one more blackjack table (requiring 150 square feet of casino space) versus $25 per gaming device (requiring 25 square feet per device), management will do better by increasing the number of gaming devices and reducing (by at least one) the number of blackjack tables, and to continue to do so as long as the contribution per square feet were out of balance.

The above discussion concentrates on average theoretical prices and purchased quantities of the services offered based on the games and player behaviors. However, this is indeed gambling so "luck" - defined as statistical variation from the theoretical price - plays an integral part for each consumer's (short-term) experience. As with house advantage, the volatility of a game or gaming device can also be measured and used to predict the variations between expected performance and actual performance that can and will occur. For any particular game (with well-defined rules, pay-offs, and consumer skill levels and betting patterns), standard deviation measures can be computed. Statistical theory suggests that about ninety-five percent of results will fall within two standard deviations of the expected outcome. For example, for a baccarat player playing for two hours at 50 decisions per hour and $100,000 per play, and playing only the "player" bet, it is possible to calculate not only the expected outcome but also a probability distribution for the entire range of possible outcomes. In two hours the baccarat player generates handle (purchases quantity) of $10 million, at an expected price of 1.36% for an expected loss of $136,000. However, the standard deviation of the two hours of play is about $1 million, so there is a 95% probability the actual outcome for this foray at the table will yield a result between a $1.1 million win and a $900,000 loss for the casino. There is also about one chance in 40 the player will win $1 million or more, and about one chance in 40 the casino will win $1.2 million or more.

Clearly there is a very significant disparity between what the expected cost is to the player in the above example, and what they will likely actually experience on an individual basis in the short-term. In the long-term, volatility gets overwhelmed by the expected price, so "luck" disappears and the standard deviation becomes insignificant compared to the house advantage. However, in some circumstances, a casino may not have enough handle to get to the long run before very bad things happen 3.

For a casino with hundreds or thousands of slot machines, there is virtually no volatility experienced by the casino over those devices even in relatively short periods of time; there is so much handle generated every day that, even though individual customers might be particularly lucky or unlucky, the casino as a whole will win very close to the amount of revenue that would be predicted by computing a properly weighted summation of (house advantage times handle) over all relevant gaming device categories. The same is true for grind play at the table games. The only exceptions occur with games that will not get to the long run quickly, i.e. the whale playing very high stakes baccarat (much higher than other big players for the casino) or the super jackpot that is only rarely hit.

Besides such exceptions, what happens is that the "law of large numbers" takes effect as hundreds or thousands of customers make thousands or millions of wagers. Each wager's outcome has only a miniscule impact on aggregate winnings for the month or week or day in the casino. All the volatility - all the "luck" - washes out.

Some other observations can be made with respect to pricing strategies and volatility risk in casinos. Tourist casinos (such as those found on the Las Vegas Strip) cater to players who have more money than time, whereas locals' casinos (found in most casino markets) have a preponderance of their customers with more time than money. In the jargon of economics, demand is less price elastic for tourists than for locals. As a result, pricing is higher in tourist oriented casinos than in locals' casinos. In a similar manner, pricing is higher in a monopoly casino than among casinos that must compete against one another for the same player markets.

At locals' casinos, we can identify certain classes of players who are effectively buying time at slot machines. One relevant aspect of this discussion and analysis is the logic used in setting prices for slot games. Old-time casino managers often claim that players will react quickly and negatively to any increase in price. As a result, they keep prices low. That may have some validity with video poker game players, especially in locals' markets; video poker has relatively transparent pricing. However, it seems much less likely that a modern day (tourist) customer playing on multi-line slot machines with multiplier features would notice marginal increases in pricing. The slot machine game designer can amend the probabilitypayoff math model in such as a way as to increase the variance and effectively mask the price increase. This has been particularly evident with the success of penny video slots in markets like Australia and North America - and has led companies like Harrah's and others to experiment with optimal pricing models for slot games across their estate. It has also resulted in gaming machine manufacturers such as IGT, WMS, Aristocrat, and Bally's to recognize the importance of math models in their game design. Creating hit games is partly art and partly science, but game pricing and the math models involved are a highly relevant portion of the science.

Once we have established and measured prices for our gaming entertainment services and are able to monitor the relative quantities that players consume in given periods, we can then explore ways to enhance or modify the offerings. This might be accomplished by discounting the price through such things as loyalty program rewards, rolling chip commissions, rebates on loss, or through complimentary offers of free food and beverage while playing. Coupons are an early version of such price discounting. Such discounting can be justified for bulk purchasers. As long as the cost of providing the service is relatively fixed, then bulk purchasers can be offered discounts because of the low marginal cost of increased production. For example, if a casino could increase the average wager at blackjack from $10 to $20 with no other changes, then incremental costs of offering the game would be near zero; if the costs of discounts were less than the incremental revenues from the increased quantity sold, such a move would be beneficial to the bottom line.

Server-based gaming or server-supported gaming are both new forms of slot machine systems that offer the potential to permit greater yield management on gaming floors in similar manners to the way hotels are managed. Higher prices should be charged in a casino at times of greater demand (weekends, holiday periods, Super Bowl weekend, etc.) New technologies, along with regulatory approvals, may allow more refined and sophisticated pricing variations in casino operations.

Thinking about gaming as an entertainment service with specific prices and consumption patterns is indeed a useful exercise and business strategy. With greater confidence in understanding the product - as a legitimate and popular entertainment offering - managers should be better able to determine what to charge for their offerings and what common business and marketing tools can be used to modify purchase behavior. Gaming is not so unique that we cannot learn from airlines, hotels, cinemas, software companies and the like - but to do so we have to establish pricing models and be prepared to experiment and seek to optimize returns.

1 See, for example, Robert Hannum and Anthony Cabot, PRACTICAL CASINO MATH (2nd edition, 2005), Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno

2 Guaranteed Play borrows from Walker's PriceLine™ concepts to allow the player to specify how many plays at a gaming device he will be able to play in a particular session, in effect by reducing the volatility of payouts. The concept is to allow a player to avoid the disappointment of particularly unlucky short-term runs where their stake is exhausted far more quickly than their expectations and desires would have wanted. Of course, such a reduction in downside volatility implies upward swings in performance must also be dampened.

3 A single player making extremely large wagers and getting lucky might break the bank, or at least cost management their jobs, before the long run comes into play. A particularly famous example of this occurred in 1995 when Australian billionaire Kerry Packer won $20 million over a weekend from MGM Grand in Las Vegas. See John L. Smith, Sharks in the Desert (2005) for a description of this incident.