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
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
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
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.