U.S. patent application number 13/946216 was filed with the patent office on 2013-11-14 for method for optimizing revenue or profit of a gambling enterprise.
The applicant listed for this patent is JENNIFER KUTCHER LENDLER. Invention is credited to JENNIFER KUTCHER LENDLER.
Application Number | 20130303271 13/946216 |
Document ID | / |
Family ID | 48952238 |
Filed Date | 2013-11-14 |
United States Patent
Application |
20130303271 |
Kind Code |
A1 |
LENDLER; JENNIFER KUTCHER |
November 14, 2013 |
METHOD FOR OPTIMIZING REVENUE OR PROFIT OF A GAMBLING
ENTERPRISE
Abstract
A method optimizes revenue or profit for a gambling enterprise,
such as a casino. The method employs a plurality of different
gaming units, such as table games and electronic gaming devices, in
the gambling enterprise. A plurality of counts is employed, one of
the counts for each of the different gaming units. A plurality of
decision functions is employed, with at least one of the decision
functions for each of the different gaming units. Revenue or profit
optimization is employed as an objective function. Optimal values
for the counts for each of the different gaming units are
determined from the decision functions and a plurality of
constraints in order to optimize the objective function.
Inventors: |
LENDLER; JENNIFER KUTCHER;
(PHILADELPHIA, PA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LENDLER; JENNIFER KUTCHER |
PHILADELPHIA |
PA |
US |
|
|
Family ID: |
48952238 |
Appl. No.: |
13/946216 |
Filed: |
July 19, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10767377 |
Jan 29, 2004 |
8515789 |
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13946216 |
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Current U.S.
Class: |
463/25 |
Current CPC
Class: |
G06Q 10/067 20130101;
G07F 17/3227 20130101 |
Class at
Publication: |
463/25 |
International
Class: |
G07F 17/32 20060101
G07F017/32 |
Claims
1. A method for optimizing revenue or profit for a gambling
enterprise, said method comprising: employing a plurality of
different gaming units in said gambling enterprise; employing a
plurality of counts, one of said counts for each of said different
gaming units; employing a plurality of decision functions, at least
one of said decision functions for each of said different gaming
units; employing revenue or profit optimization as an objective
function; determining with a processor optimal values for said
counts for each of said different gaming units from said decision
functions in order to optimize said objective function; and
adjusting said counts for each of said different gaming units to be
said optimal values for said counts in said gambling
enterprise.
2. The method of claim 1 further comprising: employing revenue
optimization as said objective function; employing at least one
constraint for at least some of said different gaming units as one
of said decision functions; determining time series revenue data
for said different gaming units and determining a plurality of
demand functions, one of said demand functions for each of said
different gaming units; employing said demand functions as some of
said decision functions; and determining said optimal values from
said at least one constraint and said demand functions.
3. A method for optimizing revenue for a gambling enterprise, said
method comprising: identifying a plurality of different classes of
gaming units in said gambling enterprise; employing a plurality of
counts, one of said counts for each of said different classes;
employing at least one decision function for said different
classes; employing revenue optimization as an objective function;
determining time series revenue data for said different classes and
determining a plurality of demand functions, one of said demand
functions for each of said different classes; determining with a
processor optimal values for said counts for each of said different
classes from said at least one decision function and said demand
functions, in order to optimize said objective function and
optimize revenue from said different classes of gaming units; and
adjusting said counts for each of said different classes to be said
optimal values for said counts in said gambling enterprise.
4. The method of claim 3 further comprising: employing a
predetermined time period of greater than one year for said time
series revenue data and said demand functions.
5. The method of claim 3 further comprising: employing one of
linear programming and non-linear programming to determine said
optimal values for said counts.
6. The method of claim 3 further comprising: employing a plurality
of constraints associated with said different classes of gaming
units; translating said constraints to a plurality of mathematical
expressions; employing said mathematical expressions as said at
least one decision function; and employing said demand functions
and said mathematical expressions to determine said optimal values
for said counts.
7. The method of claim 6 further comprising: employing one of
linear programming and non-linear programming to determine said
optimal values for said counts.
8. The method of claim 6 further comprising: determining whether
said optimal values for said counts are reasonable values based
upon said optimal values for said counts for each of said different
classes resulting in a floor space of the different classes of the
gaming units in said gambling enterprise being less than a
predetermined value; responsively adjusting said constraints;
translating said adjusted constraints to a plurality of
corresponding mathematical expressions; and re-determining optimal
values for said counts for each of said different classes from said
demand functions and said corresponding mathematical expressions,
in order to optimize said objective function and optimize revenue
from said different classes of gaming units.
9. The method of claim 6 further comprising: employing as one of
said constraints a minimum count and a maximum count of a
corresponding one of said different classes of gaming units.
10. The method of claim 3 further comprising: employing as said
different classes of gaming units in said gambling enterprise a
plurality of different classes of table games and a plurality of
different classes of electronic gaming devices.
11. The method of claim 10 further comprising: differentiating said
different classes of electronic gaming devices by denomination of
wager; and differentiating said different classes of table games by
type of game.
12. The method of claim 3 further comprising: determining said time
series revenue data from a user interface of a financial reporting
system.
13. The method of claim 3 further comprising: employing regression
analysis to convert each of said time series revenue data for said
different classes to a mathematical expression for a corresponding
one of said demand functions.
14. The method of claim 13 further comprising: for one of said time
series revenue data for a corresponding one of said different
classes, employing as said mathematical expression for a
corresponding one of said demand functions a first type of
mathematical expression; selecting a different second type of
mathematical expression; employing regression analysis to convert
said one of said time series revenue data for the corresponding one
of said different classes to said different second type of
mathematical expression for the corresponding one of said demand
functions; and employing one of said first type of mathematical
expression and said second type of mathematical expression which
provides a better fit of said one of said time series revenue
data.
15. The method of claim 13 further comprising: analyzing said
mathematical expression for each of said demand functions and
selecting one of linear programming and non-linear programming to
determine said optimal values for said counts for each of said
different classes.
16. The method of claim 3 further comprising: employing a
predetermined time period and a predetermined count of samples for
said time series revenue data and said demand functions; and
including with said time series revenue data a revenue value and a
count of said different classes of gaming units for each of said
samples.
17. The method of claim 3 further comprising: employing at least
one constraint associated with said different classes of gaming
units; translating said at least one constraint to at least one
mathematical expression; employing said at least one mathematical
expression as said at least one decision function; translating said
demand functions to a plurality of polynomial equations; and
determining said optimal values from said at least one mathematical
expression and said polynomial equations, in order to optimize said
objective function.
18. The method of claim 3 further comprising: displaying said
optimal values.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/767,377, filed Jan. 29, 2004, the entire
contents of which are hereby incorporated by reference herein.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] This invention pertains generally to methods for optimizing
revenue or profit of a gambling enterprise and, more particularly,
to such methods for optimizing revenue or profit generated by
gaming units on a casino floor.
[0004] 2. Background Information
[0005] Gambling enterprises, such as casinos, generate gaming
revenue in many ways and from many sources. These can include, but
are not limited to, the operation of table games, electronic gaming
devices (EGDs) such as slot machines, video lottery terminals
(VLTs), video poker machines, keno, bingo, pulltabs, race and
sports wagers, as well as other forms of gaming that occur on the
casino floor. However, table games and EGDs produce the largest
percentage of gaming revenue and profit for most casinos and are
areas of particular interest and scrutiny by casino managers.
[0006] Additionally, the size of a casino floor is generally
constrained either by direct regulation, which restricts total
space, or practical or monetary considerations on the part of the
operator. The amount of space available to a casino operator within
which to generate revenue and profit is therefore finite. Casino
operators thus wish to strive to optimize revenue and profit in
gaming operations given this limited available floor space.
[0007] Gambling enterprises use various types of casino management
systems (CMSs) to provide information on activity generated from
gaming activities. A CMS gathers data on money wagered at gaming
units throughout the casino, with information available generally
on a daily basis, although some CMSs provide information of even
greater detail (e.g., by hour; by shift).
[0008] Additionally, casinos utilize various financial reporting
systems (FRSs). Information from the CMS is often used by the FRS
in developing financial statements and creating financial reports
on gaming departments. These statements and reports provide casino
managers with information on the overall revenue performance
("win") from gaming and other sources at the casino property, as
well as costs associated with operating these departments, since
the FRS is also often the primary repository of information on
expenses throughout the property. Information is often provided
grouped by broad category (e.g., casino; hotel; food) as well as by
sub-category or department (e.g., table games; EGDs; casino cage
(e.g., an area on the casino floor where financial transactions are
completed to serve the needs of the patrons on the gaming floor as
well as to provide cash, coin, and chip resources to the gaming
units in operation on the gaming floor; patrons may, for example,
cash checks, change currency for coin or redeem chips won at a
table game at the casino cage); rooms; food outlet A; food outlet
B).
[0009] Aside from preparing financial statements, data from
activities on the gaming floor are also collected to assist the
marketing department in performing various analyses. It is standard
practice in the industry to establish systems for collecting and
tracking customer activity at casinos for use in customer
recognition and marketing programs, the goal of which is to attempt
to generate as much customer visitation as possible. The
presumption is that more customer visits will tend to generate more
gaming time and will increase gaming revenue. Thus, casino
operators have tended to focus their effects on determining ways to
increase visitation through loyalty programs or promotions to
selected higher worth customers, as determined by a customer
database analysis. See, for example, U.S. Pat. No. 6,003,013.
[0010] It is known to control the cost of playing an individual
electronic gaming device (e.g., slot machine; video poker machine)
by configuring game speed, payback percentage, and game appearance.
See U.S. Pat. No. 6,254,483.
[0011] It is also known to allocate different games to various game
machines based upon time periods, dates, type of players or the
traffic line of players, without the replacement of the game
machines. See U.S. Pat. No. 6,354,943.
[0012] It is further known to manage gaming tables in a gaming
facility by determining the performance of dealers and by
estimating the revenue for each gaming table. See U.S. Pat. No.
6,446,864.
[0013] It is also known to employ a casino drawing/lottery game to
attempt to maximize gaming revenues by influencing which kind of
games players play. See U.S. Pat. No. 5,129,652.
[0014] It is further known to increase revenues by offering a
relatively more attractive loss ratio, while incurring essentially
the same fixed costs for a gambling operation. See U.S. Pat. No.
6,500,066.
[0015] There is room for improvement in methods for optimizing
revenue or profit of a gambling enterprise.
SUMMARY OF THE INVENTION
[0016] These needs and others are met by the present invention,
which provides a method for optimizing profit or revenue of a
gambling enterprise.
[0017] It is believed that known prior attempts to increase revenue
or to increase profit from gambling enterprises, such as casinos,
have not been optimal and have not employed techniques to optimize
revenue or profit by analyzing data on past gaming activity to
determine demand functions of gaming units employed, and for the
optimization of profit by also analyzing the cost structure in
place to service the gaming units employed, in order to determine
through such analysis the optimal solution set of gaming units to
employ to reach optimal revenue or profit.
[0018] It is believed that no prior attempt has been made to
optimize revenue from gaming units on a casino floor by determining
the key characteristics of the gaming units, defining these key
characteristics as decision variables, analyzing demand functions
for each of these decision variables, determining reasonable
constraints, and applying linear or non-linear programming
techniques to optimize the revenue.
[0019] Furthermore, it is believed that no prior attempt has been
made to optimize profit from gaming units on a casino floor by
determining their key characteristics, defining these key
characteristics as decision variables, analyzing demand functions
for each of these decision variables, analyzing fixed and variable
cost functions for each of the related casino departments,
determining reasonable constraints, and applying linear or
non-linear programming techniques to optimize the profit.
[0020] The present invention optimizes revenue or profit of a
gambling enterprise, such as a casino or casino floor, by, for
example, determining the mix of gaming units, such as table games
and electronic gaming devices, such as slot machines, on the casino
floor. The present invention thus provides a method for optimizing
revenue or profit generated from gaming units on the casino
floor.
[0021] In accordance with one aspect of the invention, a method for
optimizing revenue or profit for a gambling enterprise comprises:
employing a plurality of different gaming units in the gambling
enterprise; employing a plurality of counts, one of the counts for
each of the different gaming units; employing a plurality of
decision functions, at least one of the decision functions for each
of the different gaming units; employing revenue or profit
optimization as an objective function; and determining optimal
values for the counts for each of the different gaming units from
the decision functions in order to optimize the objective
function.
[0022] The method may include employing a casino floor having a
physical area as the gambling enterprise; employing a physical area
associated with each of the different gaming units; employing a
plurality of different electronic gaming devices and a plurality of
different table games as some of the different gaming units; and
employing a constraint to require the physical area of the
different electronic gaming devices and the physical area of the
different table games to be less than or equal to the physical area
of the casino floor when the optimal values are determined for the
counts for each of the different gaming units.
[0023] The method may include employing a predetermined time period
for at least some of the decision functions; and including current
and historical time series revenue data and current and historical
time series cost data in the predetermined time period for the at
least some of the decision functions.
[0024] The method may include employing revenue optimization as the
objective function; employing at least one constraint for at least
some of the different gaming units as one of the decision
functions; determining time series revenue data for the different
gaming units and determining a plurality of demand functions, one
of the demand functions for each of the different gaming units;
employing the demand functions as some of the decision functions;
and determining the optimal values from the at least one constraint
and the demand functions.
[0025] The method may include employing profit optimization as the
objective function; employing at least one constraint for at least
some of the different gaming units as one of the decision
functions; determining time series revenue data for the different
gaming units and determining a demand function for each of the
different gaming units; determining time series cost data for the
different gaming units and determining a cost function for the
different gaming units; employing the demand function for each of
the different gaming units and the cost function for the different
gaming units as some of the decision functions; and determining the
optimal values from the at least one constraint, the demand
function for each of the different gaming units and the cost
function for the different gaming units.
[0026] As another aspect of the invention, a method for optimizing
revenue for a gambling enterprise comprises: identifying a
plurality of different classes of gaming units in the gambling
enterprise; employing a plurality of counts, one of the counts for
each of the different classes; employing at least one decision
function for the different classes; employing revenue optimization
as an objective function; determining time series revenue data for
the different classes and determining a plurality of demand
functions, one of the demand functions for each of the different
classes; and determining optimal values for the counts for each of
the different classes from the at least one decision function and
the demand functions, in order to optimize the objective function
and optimize revenue from the different classes of gaming
units.
[0027] The method may include employing a plurality of constraints
associated with the different classes of gaming units; translating
the constraints to a plurality of mathematical expressions;
employing the mathematical expressions as the at least one decision
function; and employing the demand functions and the mathematical
expressions to determine the optimal values for the counts.
[0028] The method may include determining whether the optimal
values for the counts are reasonable values; responsively adjusting
the constraints; translating the adjusted constraints to a
plurality of corresponding mathematical expressions; and
re-determining optimal values for the counts for each of the
different classes from the demand functions and the corresponding
mathematical expressions, in order to optimize the objective
function and optimize revenue from the different classes of gaming
units.
[0029] The method may include employing at least one constraint
associated with the different classes of gaming units; translating
the at least one constraint to at least one mathematical
expression; employing the at least one mathematical expression as
the at least one decision function; translating the demand
functions to a plurality of polynomial equations; and determining
the optimal values from the at least one mathematical expression
and the polynomial equations, in order to optimize the objective
function.
[0030] As another aspect of the invention, a method for optimizing
profit for a gambling enterprise comprises: identifying a plurality
of different classes of gaming units in the gambling enterprise;
employing a count for each of the different classes; employing at
least one decision function for the different classes; employing
profit optimization as an objective function; determining time
series revenue data for the different classes and determining a
demand function for each of the different classes; determining time
series cost data for the different classes and determining a cost
function for the different classes; and determining optimal values
for the counts for each of the different classes from the at least
one decision function, the demand function for each of the
different classes and the cost function for the different classes,
in order to optimize the objective function.
[0031] The method may include employing a plurality of constraints
associated with the different classes of gaming units; translating
the constraints to mathematical expressions; employing the
mathematical expressions as the at least one decision function; and
employing the demand functions, the cost functions and the
mathematical expressions to determine the optimal values for the
counts.
[0032] The method may include identifying a plurality of gaming
departments associated with the plurality of different classes of
gaming units; determining historical fixed costs and historical
variable costs for each of the gaming departments; and determining
an historical fixed cost function and an historical variable cost
function for each of the gaming departments from the historical
fixed costs and the historical variable costs, respectively.
[0033] The method may include determining an historical fixed cost
function and an historical variable cost function for each of the
different classes of gaming units.
BRIEF DESCRIPTION OF THE DRAWINGS
[0034] A full understanding of the invention can be gained from the
following description of the preferred embodiments when read in
conjunction with the accompanying drawings in which:
[0035] FIG. 1 is a block diagram of data gathering systems for a
casino operation and an optimization procedure in accordance with
the present invention.
[0036] FIG. 2 is a flowchart of revenue or profit optimization
steps in accordance with the present invention.
[0037] FIG. 3 is a flowchart of revenue optimization steps in
accordance with another embodiment of the invention.
[0038] FIG. 4 is a flowchart of profit optimization steps in
accordance with another embodiment of the invention.
[0039] FIGS. 5A-5B are a flowchart of revenue and profit
optimization steps in accordance with another embodiment of the
invention.
[0040] FIG. 6 is a block diagram of a personal computer as employed
with the optimization procedure of FIGS. 5A-5B.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0041] As employed herein, the term "gambling enterprise" shall
expressly include, but not be limited by, a casino, a casino floor,
a slot parlor, a video lottery terminal (VLT) parlor, a "racino",
or any enterprise where patrons engage in gambling activity.
[0042] As employed herein, the term "table games" shall expressly
include, but not be limited by, table gambling games such as, for
example, Blackjack ("21"), Craps ("Dice"), Roulette, Caribbean Stud
Poker, Pai Gow, Pai Gow Poker, Let it Ride, 3 Card Poker, Baccarat,
Mini-Baccarat, and Sic Bo.
[0043] As employed herein, the term "electronic gaming device" or
"EGD" shall expressly include, but not be limited by, any
coin-activated, currency-activated, debit-activated or
credit-activated game on which a player may place a wager. Some
non-limiting examples of EGDs include video poker; video blackjack;
video keno; slot machines; video roulette; craps machines; EGDs by
denomination (e.g., Penny; Nickel; Dime; Quarter; Half Dollar;
Dollar; Five Dollar; Ten Dollar; Twenty-five dollar; Hundred
Dollar; Multi-denominational); EGDs by type (e.g., Reel; Video
reel; Video poker; Proprietary or Participation; Progressive); EGDs
by "personality" or theme associated with the game (e.g., Double
Diamonds; Blazing 7s; Wheel of Fortune); and EGDs made by different
manufacturers (e.g., Bally Gaming Systems; International Game
Technology; WMS Industries; Aristocrat; AC Coin & Slot;
Alliance Gaming; Atronic; Mikohn Gaming; Shuffle Master
Gaming).
[0044] As employed herein, the term "games" or "gaming" shall
expressly include, but not be limited by, table games, EGDs, Race
and sports book, Poker, Keno, Bingo, and Pulltabs.
[0045] As employed herein, the term "denomination" is a specific
monetary amount of a coin or token. Some common denominations
include, for example, pennies, nickels, quarters and dollars,
although larger denominations are available as well.
[0046] As employed herein, the term "progressive" as applied to an
EGD, such as a slot machine, provides a progressive slot machine,
which takes a percentage of all coins that are played and adds it
to a jackpot that increases in value. Players hitting the winning
jackpot symbols win the total accumulated jackpot.
[0047] As employed herein, the term "proprietary" or
"participation" games include slot machines or other games where
the equipment supplier retains ownership of the machine and leases
it to the casino, thus "participating" in the machine's revenue
stream.
[0048] The present invention is described in association with
optimizing revenue or profit generated by gaming units on the
casino floor. It will be appreciated, however, that the present
invention is applicable to a wide range of gambling
enterprises.
[0049] FIG. 1 shows data gathering systems 2,4 for a casino
operation including a casino floor 6. The casino floor 6 includes a
plurality of gaming units 8, which, in turn, include a plurality of
table games 10, a plurality of electronic gaming devices (EGDs) 12
and other gambling games 14. As will be disclosed, data is
generated from queries to the casino management system (CMS) 2 to
provide information on activity generated from gaming activities,
and from the financial reporting system (FRS) 4. Typically, the FRS
4 is employed by the EGD department 16 of the casino, which is
responsible for the various EGDs 12, by the table games department
18, which is responsible for the various tables games 10, and by
the "Other Games" department 19, which is responsible for the
various other gambling games 14. The FRS 4 provides both revenue
("win") information 20 associated with casino revenue from the
gaming units 8, and expense information 22 associated with expense
for the gaming units 8. In accordance with the present invention,
an optimization procedure 24 is disclosed to optimize the counts of
the different gaming units 8 from decision functions in order to
optimize an objective function, such as revenue or profit, for the
casino. Although a particular casino is disclosed, it will be
appreciated that the invention is applicable to a wide range of
gambling enterprises, such as, for example, another gambling
enterprise or a casino having one or more departments.
[0050] As shown in FIG. 2, the steps of the optimization procedure
24 are employed to optimize revenue or profit for a gambling
enterprise. First, at 26, a plurality of different gaming units,
such as 8 of FIG. 1, are employed in the gambling enterprise. Then,
at 28, a plurality of counts are employed, with one of the counts
for each of the different gaming units. Next, at 30, a plurality of
decision functions are employed, with at least one of the decision
functions for each of the different gaming units. At 32, revenue or
profit optimization is employed as an objective function. Finally,
at 34, optimal values for the counts for each of the different
gaming units are determined from the decision functions in order to
optimize the objective function.
[0051] FIG. 3 shows another optimization procedure 40, which is
employed to optimize revenue for a gambling enterprise. First, at
42, a plurality of different classes of gaming units, such as 8 of
FIG. 1, are employed in the gambling enterprise. Next, at 44, a
plurality of counts is employed, with one of the counts for each of
the different classes. Then, at 46, at least one decision function,
such as one or more constraints, is employed for the different
classes. At 48, revenue optimization is employed as an objective
function. Next, at 50, time series revenue data is determined for
the different classes and a plurality of demand functions is
determined, with one of the demand functions for each of the
different classes. Finally, at 52, optimal values are determined
for the counts for each of the different classes from the at least
one decision function and the demand functions, in order to
optimize the objective function and optimize revenue from the
different classes of gaming units.
[0052] FIG. 4 shows another optimization procedure 60, which is
employed to optimize profit for a gambling enterprise. First, at
62, a plurality of different classes of gaming units, such as 8 of
FIG. 1, are identified in the gambling enterprise. Next, at 64, a
count is employed for each of the different classes. Then, at 66,
at least one decision function, such as one or more constraints, is
employed for the different classes. At 68, profit optimization is
employed as an objective function. Next, at 70, time series revenue
data is determined for the different classes and a demand function
is determined for each of the different classes. Then, at 72, time
series cost data is determined for the different classes and a cost
function is determined for the different classes. Finally, at 74,
optimal values for the counts for each of the different classes are
determined from the at least one decision function, the demand
function for each of the different classes and the cost function
for the different classes, in order to optimize the objective
function.
[0053] FIGS. 5A-5B show another optimization procedure 80, which is
employed to optimize revenue or profit for a gambling enterprise.
First, at 82, the objective function is defined. This determines
the value that is to be optimized, such as revenue generated by
gaming units on the casino floor, or profit generated from gaming
units on the casino floor to which casino departmental costs, both
fixed and variable, are applied to determine profitability. Next,
at 84, the gaming unit properties (classes) are identified.
Example 1
[0054] For example, as was discussed above in connection with FIG.
1, the different classes of the gaming units 8 on the casino floor
6 include a plurality of different classes of the table games 10
and a plurality of different classes of the EGDs 12.
Example 2
[0055] As another example, gaming units utilized in a casino
operation to generate revenue are grouped into classes based on
relevant characteristics that distinguish them from other units.
These classes could be, for example, game type for table games
(e.g., blackjack; craps; roulette) and denomination of wager for
EGDs (e.g., nickel; quarter; dollar).
Example 3
[0056] Within a table games operation, there are many types of
games (e.g., blackjack; craps; roulette; big six; pai gow; pai gow
poker). Within an EGD operation, there are many different types of
EGDs on the casino floor. These EGDs can be classified, for
example, in terms of denomination of wager (e.g., nickel; quarter;
dollar), type (e.g., slot; video poker; progressive;
participation), and "personality" (e.g., Double Diamonds; Blazing
7s; Wheel of Fortune). A gambling enterprise determines which
classification or characteristic of the gaming units on the casino
floor will be analyzed, in order to define the decision
variables.
[0057] Next, at 86, a plurality of decision variables (DVs)
associated with casino revenue are defined.
Example 4
[0058] Casinos generate gaming revenue in many ways (e.g., the
operation of table games; electronic gaming devices (EGDs); keno;
bingo; pulltabs; race and sportsbooks). Primary drivers of revenue
and profit are, most typically, table games and EGD operations.
Hence, DVs are typically assigned to the different classes of
tables games and to the different classes of EGDs, although a wide
range of other classes may be employed.
[0059] At 88, the analysis time period is determined.
Example 5
[0060] Preferably, about 36 months of data, if available, is
gathered for the time series revenue data, the demand functions and
the time series cost data. Although an example analysis period is
disclosed, it will be appreciated that a wide range of relatively
shorter and relatively longer analysis periods may be employed.
[0061] Even steps 90-96 determine a separate historical/current
demand function for each of the different classes of gaming units
(e.g., nickel EGD; quarter EGD; dollar EGD; blackjack; craps;
roulette). Depending on the nature of the data series, the
resultant best-fit equation (e.g., least squares; maximum r.sup.2
value) may be, for example, linear (e.g., y=mx+b, wherein m is the
slope and b is the y-intercept), polynomial (e.g.,
y=b+c.sub.1x+c.sub.2x.sup.2+c.sub.3x.sup.3+ . . . +c.sub.nx.sup.n,
wherein b and c.sub.1, c.sub.2, c.sub.3 . . . c.sub.n are
constants), logarithmic (e.g., y=c ln x+b, wherein c and b are
constants and ln is the natural logarithm function), exponential
(e.g., y=ce.sup.bx, wherein c and b are constants and e is the base
of the natural logarithm), or power (e.g., y=cx.sup.b, wherein c
and b are constants). For example, a linear trend line is generally
a best-fit when data values increase or decrease at a steady rate;
a polynomial trend line is generally a best-fit curve when data
values fluctuate and there are gains or losses over a large data
set; a logarithmic trend line is generally a best-fit curve when
the rate of change in the data values increases or decreases
quickly and then levels out; an exponential trend line is generally
a best-fit curve for data values that rise or fall at increasingly
higher rates; and a power trend line is generally a best-fit curve
when data values increase at a specific rate.
[0062] First, at 90, times series data for the decision variables
are retrieved. Typically, this includes employing a predetermined
analysis period, as was selected at 88, and a predetermined count
of samples of time series revenue data, including a revenue value
and a count of the different classes of gaming units for each of
the samples. For example, using the CMS 2, the FRS 4 of FIG. 1
and/or other relevant data sources, the time series data is
retrieved that reveals both total revenue generated ("win") from a
specific class of the gaming units 8, and the total number of units
of that class on the casino floor 6 during those same periods of
time. As determined at 96, the time series data of this type is
retrieved, at 90, for all of the different decision variables as
were determined at 86.
[0063] Due to the timeliness of data generally available from the
FRS 4 of FIG. 1 and other systems routinely used in casino
operations, a demand function (or cost function, as is discussed
below in connection with steps 108 and 110) may incorporate both
historical (e.g., one year ago; three years ago) and current (e.g.,
today; yesterday) demand characteristics in one equation or
mathematical expression. If desired, separate long-term (e.g.,
greater than one year) and short-term (e.g., less than one year)
demand curves may be determined and employed. However, it is
believed that relevancy issues suggest that demand curves
preferably aggregating the prior about three years of data (as
selected at step 88) will reveal the trends that are needed to
properly solve for the optimal state of the decision variables.
[0064] Next, at step 92, using suitable regression analysis
techniques, a demand function for each of the decision variables is
defined. With the regression analysis, each set of time series
revenue data is analyzed to determine its proper mathematical
expression. These expressions effectively represent the demand
function for each of the classes of gaming units utilized in the
casino. For example, a statistical regression analysis technique
models the relationship between variables. Scatter plots may
represent sample data points for different combinations of two
variables (e.g., X and Y). A regression line may be fit to the
scatter plot to reveal a linear or a non-linear relationship
between the two variables. Also, a coefficient of determination,
r.sup.2, may be employed as a measure of the strength of the
regression relationship, in order to measure how well the
regression line fits the data. For example, an r.sup.2 value of
about 0.9 may fit the data relatively well, while an r.sup.2 value
of about 0.75 would explain relatively less of the data and,
therefore, would not be as relatively good of a fit for the
data.
[0065] For example, the first pass through step 92 for a first
decision variable may employ regression analysis to convert the
time series revenue data for a corresponding one of the classes of
gaming units to a first type of mathematical expression (e.g., a
linear equation with an r.sup.2 value of about 0.9) for this demand
function. Then, the first pass through step 94 would determine that
there was no best fit, since only one type of mathematical
expression had been considered, and step 92 would be repeated.
[0066] Then, the second pass through step 92 for the first decision
variable may employ regression analysis to convert the time series
revenue data for the corresponding one of the classes of gaming
units to a second type of mathematical expression (e.g., a
polynomial equation with an r.sup.2 value of about 0.75) for this
demand function. Then, the second pass through step 94 would
determine that the linear equation, in this example, was the better
fit of those two types of mathematical expressions.
[0067] Next, steps 92 and 94 may be repeated, as desired, for other
types of mathematical expressions (e.g., logarithmic; exponential;
power). Hence, depending on the nature of the time series revenue
data, the resultant best-fit (e.g., maximum r.sup.2 value) equation
may be, for example, linear, polynomial, logarithmic, exponential
or power. Then, the final pass through step 94 for the first
decision variable would select the mathematical expression which
provides a best fit (e.g., the maximum r.sup.2 value) for the time
series revenue data.
[0068] Then, at 96, it is determined if all of the demand functions
have been determined for the various decision variables. In this
example, since there are a plurality (e.g., six) of decision
variables, even steps 90-96 are repeated five times to determine
the mathematical expressions that provide the best fit for the
demand functions for all decision variables. After 96, the next
step is 98.
[0069] Step 98 determines whether the objective function from step
82 is profit optimization. If so, then the procedure resumes at
100. On the other hand, if the selected objective function from
step 82 is revenue optimization, then the procedure resumes at
116.
[0070] If profit is determined to be the objective function to be
optimized, at 82 and 98, then even steps 100-114 determine
historical/current cost functions for each of the decision
variables. At 100, the relevant gaming departments (e.g., table
games; EGD) associated with the different classes of gaming units
are determined. Next, at 102, additional time series data for the
selected analysis period of step 88 is acquired from the FRS 4 of
FIG. 1. For example, time series data on costs within the relevant
gaming departments are retrieved by line item in order to be able
to classify each line item as a fixed cost or a variable cost. In
addition, the total number of gaming units served by this gaming
department during these same time periods is also retrieved.
[0071] Next, at 104, fixed costs and variable costs are segregated.
Then, at 106, the variable costs and the fixed costs within the
various gaming departments are separately aggregated for each of
those departments.
[0072] At 108, an historical fixed cost function (i.e., a constant)
is determined for each department. As an example, there would be a
fixed cost constant for the table games department and a fixed cost
constant for the electronic gaming devices department.
[0073] Similar to step 92, a variable cost function for each of the
gaming departments is defined using suitable regression analysis
techniques at 110. For example, there would be a first variable
cost function for the table games department as a function of the
count of table game units, and a second variable cost function for
the electronic gaming devices department as a function of the count
of electronic gaming devices. For example, a statistical regression
analysis technique models the relationship between variables.
Scatter plots may represent sample data points for different
combinations of two variables (e.g., X and Y). A regression line
may be fit to the scatter plot to reveal a linear or a non-linear
relationship between the two variables. Also, a coefficient of
determination, r.sup.2, may be employed as a measure of the
strength of the regression relationship, in order to measure how
well the regression line fits the data. For example, an r.sup.2
value of about 0.9 may fit the data relatively well, while an
r.sup.2 value of about 0.75 would explain relatively less of the
data and, therefore, would not be as relatively good of a fit for
the data.
[0074] For example, the first pass through step 110 for the table
games department may employ regression analysis to convert the
aggregated historical variable costs to a first type of
mathematical expression (e.g., a linear equation with an r.sup.2
value of about 0.9) for this historical variable cost function.
Then, the first pass through step 112 would determine that there
was no best fit, since only one type of mathematical expression had
been considered, and step 110 would be repeated.
[0075] Then, the second pass through step 110 for the table games
department may employ regression analysis to convert the aggregated
historical variable costs to a second type of mathematical
expression (e.g., a polynomial equation with an r.sup.2 value of
about 0.75) for this historical variable cost function. Then, the
second pass through step 112 would determine that the linear
equation, in this example, was the better fit of those two types of
mathematical expressions.
[0076] Next, steps 110 and 112 may be repeated, as desired, for
other types of mathematical expressions (e.g., logarithmic;
exponential; power). Hence, depending on the nature of the variable
cost data series, the resultant best-fit (e.g., maximum r.sup.2
value) equation may be, for example, linear, polynomial,
logarithmic, exponential or power. Then, the final pass through
step 112 for the table games department would select the
mathematical expression which provides a best fit (e.g., the
maximum r.sup.2 value) for the historical variable costs.
[0077] Then, at 114, it is determined if all of the variable cost
functions have been determined for the various gaming departments.
In this example, since there is also the EGD department, even steps
110-114 are repeated to determine the mathematical expression that
provides the best fit for the historical variable costs for that
department. After 114, the next step is 116.
[0078] At 116, one or more constraints associated with the
different classes of gaming units are determined. Examples of
constraints are discussed below in connection with Examples 6 and
11-14. For example, there exists limiting conditions that affect
the operation of table games, EGDs, and other gaming units of a
casino. For example, there is the finite size of the available
space on the casino floor. In addition, management may decide, for
marketing or other reasons, that a minimal or maximum number of a
specific gaming unit type is needed. Next, at 118, one or more
mathematical expressions are developed to represent the relevant
constraints on the overall operation of the casino floor.
[0079] Next, the optimization method is determined. Based on a
review of all of the demand, cost, and constraints functions, at
120, either a linear programming application or a non-linear
programming application is employed to solve the objective function
and, thus, to determine the optimal values for the counts of gaming
units of each class (e.g., decision variable) that would optimize
the objective function (i.e., revenue; profit).
[0080] Next, at 122, it is determined which optimizing algorithm is
appropriate based on the resultant constraints and demand functions
for revenue optimization (or constraints, demand and cost functions
for profit optimization). If all decision functions and expressions
are linear, then linear programming is applied at 124. Otherwise,
if any one or more of the decision functions or expressions is
non-linear, then non-linear programming is applied at 134.
[0081] Linear programs, as applied at 124, are models that seek a
solution to an objective function subject to certain limiting
conditions or constraints. In linear programs, all equations must
be linear in nature (i.e., a power of 1). Linear programming, thus,
employs linear functions in which each variable appears in a
separate term, there are no powers greater than 1, and there are no
logarithmic, exponential, or trigonometric terms. For example, the
expression y=mx+b is an example of a linear function.
[0082] In contrast, non-linear programs, as applied at 134, are
models that seek a solution to an objective function subject to
certain limiting conditions or constraints, although all equations
are not required to be non-linear in nature. Non-linear
programming, thus, employs one or more functions that are not
linear. For example, the expression y=500x.sup.2+35x+6 is
non-linear, since x has a power of 2, which is greater than 1.
[0083] In the optimization analysis, at 124 or 134, mathematical
expressions that represent all of the constraint and demand (or
constraint, demand and cost) functions are input (e.g., into a
spreadsheet 152 as shown in FIG. 6). Then, a linear programming
application, at 124, or a non-linear programming application at 134
(e.g., applications 154,156 of FIG. 6), is applied to this data to
determine the solution to the objective function (i.e., the optimum
count of each of the gaming units 8 of FIG. 1 needed to optimize
revenue or profit).
[0084] These values are reviewed, at 126 and 136, for
reasonableness (e.g., as discussed in greater detail, below, in
connection with step 126 of Example 6) and, if necessary, the
constraints are responsively adjusted (e.g., as discussed in
greater detail, below, in connection with step 128 of Example 7),
at 128 and 138, respectively, until optimal and reasonable values
of decision variables are obtained. Steps 136 and 138 are
essentially the same as steps 126 and 128, respectively. After step
128 or 138, step 120 is repeated in order to re-determine the
optimal values for the counts (at even steps 120-128 or even steps
120, 122 and 134-138).
[0085] FIG. 6 shows a suitable processor, such as a personal
computer (PC) 150, employed with the optimization procedure 80 of
FIGS. 5A-5B. The various data are imported to the spreadsheet 152
(e.g., Excel marketed by Microsoft Corporation of Redmond, Wash.),
the demand functions (even steps 90-96) or demand and cost
functions (even steps 100-114) are determined, constraints (steps
116 and 118) presented as mathematical expressions are
incorporated, and the linear or non-linear programming applications
154,156 (e.g., Large-Scale LP Solver Engine or Large-Scale GRG
Solver Engine marketed by Frontline Systems Inc. Incline Village,
Nev.) are employed, although the invention is applicable to a wide
range of methods for optimizing profit or revenue of a gambling
enterprise, and a wide range of other suitable processors,
operating systems, databases, interfaces, programming languages,
spreadsheet applications, report applications, and linear and/or
non-linear programming applications may be employed. The resultant
optimal values of the gaming unit counts are then displayed on
display 158. Preferably, these optimal values are employed, as
shown with the optimization procedure 24 of FIG. 1, to adjust the
counts of the gaming units 8 on the casino floor 6 to correspond to
the optimal values.
[0086] Linear programming and non-linear programming provide a
variety of deterministic approaches used to solve complex
computational problems when maximization or minimization of
multiple values or decision variables (DVs) contained within a
complex problem is desired. These generate results associated with
multiple variables in an attempt to optimize a particular value for
a specific problem. The various linear and/or non-linear functions,
which will reproduce the optimal value, are collectively often
referred to as the objective function.
[0087] Although linear and non-linear programming are disclosed,
other suitable algorithms may be employed to optimize decision
variables associated with revenue or profit generated on the casino
floor. For example, software algorithms may be employed including
mathematical algorithms using, for example, quadratic techniques,
matrix algebra and/or simultaneous equation techniques.
Example 6
[0088] This example is directed to solving a selection problem of
gaming units on a casino floor. It will be appreciated that
acquiring the best and most productive gaming units for a casino is
important to the corresponding casino operator, since any
incremental increase in patron volume, generated by providing the
most popular mix of gaming units to patrons, can have a significant
impact on revenue and, thus, profitability. In addition, since
casinos incur significant costs in acquiring table games and EGDs,
it is important to spend capital dollars on the highest performing
equipment, in order to generate a reasonable return.
[0089] This example selection problem is disclosed with respect to
FIGS. 5A-5B. First, at 82, the objective function is defined as
optimization of profitability generated from gaming units on the
casino floor. Although one definition of the objective function is
disclosed in this example, this objective function can be defined
in other ways, such as, for example, if generating the highest
revenue, without regard for the costs involved in operating various
gaming departments, is of concern, then the objective function
would be defined as the optimization of revenue generated from the
gaming units.
[0090] Next, at 84, the gaming units are classified in terms of the
type of game they represent within the table games department
(e.g., blackjack; craps; roulette). For EGDs, the gaming units on
the casino floor are identified by their denomination (or the
minimum allowable wager). These identifying properties are defined
as the decision variables, at 86, and are shown, for this example,
in Table 1:
TABLE-US-00001 TABLE 1 Notation Represents Decision Variable: Table
Games (DV.sub.TG1) Blackjack Decision Variable: Table Games
(DV.sub.TG2) Craps Decision Variable: Table Games (DV.sub.TG3)
Roulette Decision Variable: EGDs (DV.sub.EGD1) Nickel EGD Decision
Variable: EGDs (DV.sub.EGD2) Quarter EGD Decision Variable: EGDs
(DV.sub.EGD3) Dollar EGD
[0091] Based on the availability of data, the analysis period in
this example, as selected at 88, is 36 months. Then, time series
revenue data including total revenue generated and total units on
the floor per period for 36 months is retrieved, at 90, from the
FRS 4 of FIG. 1 for DV.sub.TG1 (i.e., all blackjack tables). Next,
at 92, this data is analyzed to determine, using regression
analysis techniques for a linear equation, the corresponding
mathematical expression that represents the data most accurately.
That expression, in this case, is determined to be Equation 1:
y=$12,180*DV.sub.TG1 (Eq. 1)
wherein: y is monthly revenue generated from blackjack tables on
the casino floor (DV.sub.TG1).
[0092] Next, at 94, as was discussed in greater detail, above, in
connection with FIGS. 5A-5B, by reviewing statistical properties
(e.g., r.sup.2 statistic) associated with this example linear
equation and any other equation types (not shown), it is determined
that Equation 1 represents a "best fit" equation and, thus,
represents the proper demand function for DV.sub.TG1.
[0093] Then, at 96, it is determined if all demand functions have
been determined. Since there are six decision variables, in this
example, the process is repeated, at 90, 92 and 94, until the
demand function for each of the six decision variables is
determined. In this example, the six demand functions, as
determined, are shown in Table 2:
TABLE-US-00002 TABLE 2 Equation Decision Variable Demand Function 1
DV.sub.TG1 y = $12,180 * DV.sub.TG1 2 DV.sub.TG2 y = $19,980 *
DV.sub.TG2 3 DV.sub.TG3 y = $14,340 * DV.sub.TG3 4 DV.sub.EGD1 y =
$2,460 * DV.sub.EGD1 5 DV.sub.EGD2 y = $2,490 * DV.sub.EGD2 6
DV.sub.EGD3 y = $930 * DV.sub.EGD3
[0094] Although six linear equations are shown in Table 2, it will
be appreciated that a wide range of counts and of different types
of equations may be employed, such as, without limitation,
polynomial, logarithmic, exponential, or power. Although monthly
revenue is disclosed, smaller or larger time periods may be
employed.
[0095] Next, at 98, it is determined whether the objective function
is to optimize profit. For this example, the answer is yes. Hence,
at 100, information is generated on the cost functions that exist
within the casino operation that are impacted by the decision
variables. Otherwise, if the answer were no, then, the procedure
would resume at 116 of FIGS. 5A-5B. This path is discussed below in
connection with Example 8.
[0096] The relevant gaming departments to be analyzed are
determined at 100. For this example, those include the table games
department 18 and the EGD department 16 of FIG. 1, although casino
management could also choose to incorporate the cost functions
associated with other departments (not shown) that are related to
other gaming units, such as 14, and other gaming activities (e.g.,
casino cage; soft count). Then, at 102, time series data including
total expenses incurred by the table games department 18 and the
EGD department 16 along with corresponding number of total gaming
units on the casino floor 6, respectively, for each of the example
36 months is retrieved from the FRS 4. At 104, a distinction is
made between fixed and variable costs for the table games
department 18 and the EGD department 16, and like data is
aggregated, at 106, in order to produce four separate time series
that represent fixed table games costs, variable table game costs,
fixed EGD costs and variable EGD costs. As fixed costs are, by
definition, not a function of total units on the casino floor, the
fixed cost functions for the EGD and table games departments 16,18
consist simply of constants, at 108. These constants, for this
example, are determined as shown in Equations 7 and 8:
FC.sub.TG=$16,280 (Eq. 7)
wherein: FC.sub.TG represents the monthly fixed costs in the table
games department.
FC.sub.EGD=$21,150 (Eq. 8)
wherein: FC.sub.EGD represents the monthly fixed costs in the EGD
department. The remaining time series data represents variable
costs for the table games department 10 and the EGD department 12.
These time series are analyzed, at 110, to determine the
mathematical expression that represents the data most accurately.
The expression for variable cost table games data, in this example,
is determined to be Equation 9:
VC.sub.TG=$9,459*.SIGMA.DV.sub.TG. (Eq. 9)
wherein: VC.sub.TG represents the monthly variable costs generated
from the table games department as a function of the total number
of table game units on the casino floor (.SIGMA.DV.sub.TG).
[0097] As was discussed in greater detail, above, in connection
with FIGS. 5A-5B, by reviewing statistical properties (e.g.,
r.sup.2 statistic) associated with the example linear Equation 9,
it is determined, at 112, that Equation 9 represents a "best fit"
equation and thus represents the proper variable cost function for
the table games department (VC.sub.TG).
[0098] Next, at 114, it is determined if all variable cost
functions have been determined and the process is repeated, at 110
and 112, in order that the variable cost function for the EGD
department is determined. In this example, the fixed cost constants
and variable cost functions are summarized by Table 3:
TABLE-US-00003 TABLE 3 Equation Cost Function 7 FC.sub.TG FC.sub.TG
= $16,280 8 FC.sub.EGD FC.sub.EGD = $21,150 9 VC.sub.TG VC.sub.TG =
$9,459 * .SIGMA. DV.sub.TG 10 VC.sub.EGD VC.sub.EGD = $420 *
.SIGMA. DV.sub.EGD
[0099] Although four linear equations are shown in Table 3, it will
be appreciated that a wide range of counts and of different types
of equations may be employed, such as, without limitation,
polynomial, logarithmic, exponential, or power. Although monthly
revenue is disclosed, smaller or larger time periods may be
employed.
[0100] Next, at 116, constraints are determined that realistically
represent the state of the casino operation. In this example, the
constraints are determined and translated into mathematical
expressions, at 118. For example, the casino floor may be limited
to 24,000 square feet. Subsequently, all decision variables are
assigned a square footage amount (i.e., the area that they require
to be operational). For example, these assignments may be:
DV.sub.TG1: 40 sq. ft.; DV.sub.TG2: 100 sq. ft.; DV.sub.TG3: 80 sq.
ft.; DV.sub.EGD1: 20 sq. ft.; DV.sub.EGD2: 20 sq. ft.; and
DV.sub.EGD3: 20 sq. ft.
[0101] In this example, the decision variable values are
represented by integers (e.g., there cannot be half of a table
game; there cannot be a third of an EGD) and are non-negative.
[0102] Finally, given casino management's understanding of their
target gaming patrons, minimums and maximums may be imposed on the
selection problem in order to assure that the solution is
reasonable and, thus, serves the needs of the casino patrons. These
minimum and maximum counts are defined for this example as shown in
Table 4:
TABLE-US-00004 TABLE 4 Minimum Decision Variable Maximum 10
DV.sub.TG1 20 1 DV.sub.TG2 10 1 DV.sub.TG3 5 25 DV.sub.EGD1 100 25
DV.sub.EGD2 1000 25 DV.sub.EGD3 500
[0103] All demand, cost and constraint expressions for this
selection problem are reviewed, at 120, to determine if all
expressions are linear. This is to determine which optimization
process is employed--linear programming or non-linear programming.
In this example, all expressions are linear, at 122, and, thus, the
procedure resumes at 124. At 124, suitable linear programming
techniques are applied to solve for the values of the decision
variables that will maximize the objective function and optimize
profitability given the set constraints. This provides the solution
shown in Table 5:
TABLE-US-00005 TABLE 5 Decision Variable Value DV.sub.TG1 20
DV.sub.TG2 10 DV.sub.TG3 5 DV.sub.EGD1 100 DV.sub.EGD2 500
DV.sub.EGD3 490
[0104] Then, at 126, this solution is reviewed for reasonableness.
Since this is a workable mix of blackjack, craps, and roulette
tables, and nickel, quarter and dollar slot machines that will fit
within the 24,000 square foot casino, it is accepted and the
example is done at 140.
Example 7
[0105] This example shows an unreasonable solution and the
constraints being adjusted or added at 128 of FIG. 5B. This example
is similar to Example 6 except that Table 6 replaces Table 4 and
Table 7 replaces Table 5.
[0106] As shown in Table 6, given the initial constraints provided
in Table 7, the solution at 124 of FIG. 5B suggests that the casino
should employ 594 blackjack tables and only one of each of the
values of the other decision variables (e.g., craps, roulette,
Nickel EGD, Quarter EGD, Dollar EGD). This solution is considered
unreasonable at 126, and the constraints are adjusted at 128 to be
those shown in Table 4 of Example 6, which would produce a
reasonable solution at 124 and 126.
TABLE-US-00006 TABLE 6 Minimum Decision Variable Maximum 1
DV.sub.TG1 2000 1 DV.sub.TG2 2000 1 DV.sub.TG3 2000 1 DV.sub.EGD1
2000 1 DV.sub.EGD2 2000 1 DV.sub.EGD3 2000
TABLE-US-00007 TABLE 7 Decision Variable Value DV.sub.TG1 594
DV.sub.TG2 1 DV.sub.TG3 1 DV.sub.EGD1 1 DV.sub.EGD2 1 DV.sub.EGD3
1
Example 8
[0107] This example is similar to Example 6, except that revenue is
optimized rather than profit, Table 2 is replaced by Table 8, Table
3 is not employed, Table 4 is replaced by Table 9, and Table 5 is
replaced by Table 10:
TABLE-US-00008 TABLE 8 Equation Decision Variable Demand Function
1' DV.sub.TG1 y = $24,000 * DV.sub.TG1 2' DV.sub.TG2 y = $19,980 *
DV.sub.TG2 3' DV.sub.TG3 y = $14,340 * DV.sub.TG3 4' DV.sub.EGD1 y
= $2,460 * DV.sub.EGD1 5' DV.sub.EGD2 y = $2,490 * DV.sub.EGD2 6'
DV.sub.EGD3 y = $930 * DV.sub.EGD3
TABLE-US-00009 TABLE 9 Minimum Decision Variable Maximum 10
DV.sub.TG1 100 2 DV.sub.TG2 100 2 DV.sub.TG3 100 25 DV.sub.EGD1 100
25 DV.sub.EGD2 500 25 DV.sub.EGD3 500
TABLE-US-00010 TABLE 10 Decision Variable Value DV.sub.TG1 100
DV.sub.TG2 100 DV.sub.TG3 100 DV.sub.EGD1 25 DV.sub.EGD2 50
DV.sub.EGD3 25
Example 9
[0108] This example is similar to Example 6, except that revenue is
optimized rather than profit, Table 2 is replaced by Table 11,
Table 3 is not employed, Table 4 is replaced by Table 12, and Table
5 is replaced by Table 13:
TABLE-US-00011 TABLE 11 Equation Decision Variable Demand Function
1'' DV.sub.TG1 y = $24,000 * DV.sub.TG1 2'' DV.sub.TG2 y = $19,980
* DV.sub.TG2 3'' DV.sub.TG3 y = $14,340 * DV.sub.TG3 4''
DV.sub.EGD1 y = $2,460 * DV.sub.EGD1 5'' DV.sub.EGD2 y =
$DV.sub.EGD2.sup.2 + $400 * DV.sub.EGD2 + $50 6'' DV.sub.EGD3 y =
$930 * DV.sub.EGD3
TABLE-US-00012 TABLE 12 Minimum Decision Variable Maximum 10
DV.sub.TG1 100 2 DV.sub.TG2 100 2 DV.sub.TG3 100 25 DV.sub.EGD1 100
25 DV.sub.EGD2 500 25 DV.sub.EGD3 500
TABLE-US-00013 TABLE 13 Decision Variable Value DV.sub.TG1 100
DV.sub.TG2 88 DV.sub.TG3 2 DV.sub.EGD1 27 DV.sub.EGD2 500
DV.sub.EGD3 25
In this example, the demand function (Equation 5'') for EGD.sub.2
is clearly non-linear (i.e., contains a term with a power greater
than 1). Therefore, suitable non-linear programming techniques are
employed, at 134, to solve for the values of the decision variables
that will maximize the objective function (optimize revenue) given
the set constraints. In this example, the values are accepted and
the example is done at 142.
Example 10
[0109] This example shows detailed single decision variable
variations in historical and current demand. Demand functions are
generated from data readily available from the CMS 2 and FRS 4 of
FIG. 1. Generally, such data is available on a daily basis and can
often be obtained on an hourly or by-shift basis. Table 14 shows a
typical partial (for economy of disclosure, only some of the data
at some of the dates are shown) data series used to determine the
demand function for Blackjack tables:
TABLE-US-00014 TABLE 14 Date No. Units (Var. X) Blackjack Revenue
(Var. Y) Jan. 5, 2004 20 $9,320 Jan. 4, 2004 20 $9,010 Jan. 3, 2004
20 $8,885 Jan. 2, 2004 20 $8,600 Jan. 1, 2004 20 $9,576 Dec. 31,
2003 20 $8,045 Dec. 30, 2003 22 $11,000 . . . . . . . . . Mar. 16,
2000 28 $12,010 Mar. 15, 2000 28 $11,980
[0110] Running a regression analysis on the data from Table 14 will
reveal the demand function. As this data series includes both
generally current revenue data (e.g., yesterday; one week ago; last
month) as well as historical data (e.g., last year; two years ago),
the resultant curve will show the effects of changes in revenue
(variable Y) on changes in number of units (variable X) over both
the short and long term. In this way, the demand function
incorporates both short-term demand information as well as
historical demand information.
[0111] Examples 11-14 consider other alternative example
constraints that can be imposed in the disclosed method, at
116.
Example 11
[0112] If the decision variables are units defined by their
manufacturer (e.g., Bally Gaming System EGDs; International Gaming
Technology EGDs), then constraints may be developed to, for
example, force a solution requiring at least a certain minimum
number of units for one or more manufacturers in order to take
advantage of quantity purchasing discounts. Hence, there may be a
plurality of different electronic gaming devices, with one of the
decision functions being a minimum count of the different
electronic gaming devices from a particular manufacturer. The
constraint, thus, associates a discount from the particular
manufacturer with the minimum count, and ensures that the discount
is received by providing the minimum count with the optimal values,
as determined.
Example 12
[0113] If the decision variables are units defined by their
personality or "theme" (e.g., Double Diamond; Wheel of Fortune),
then constraints may be developed to, for example, force a solution
requiring a certain maximum number of units for each theme to
ensure that there are not too many of one type and thus provide a
variety of choices available to the gaming patron. Hence, for
example, by employing as one of the decision functions a maximum
count of the different EGDs of a particular one of the
personalities or themes (e.g., Double Diamond), then the constraint
is employed to require that maximum count when the optimal values
are determined.
Example 13
[0114] Constraints may be developed to force the solution set to
adhere to a certain market positioning (e.g., relatively more table
games and relatively less EGDs; relatively more EGDs and relatively
less table games). Hence, the constraint may require, for example,
a greater count of the EGDs with respect to the table games, when
the optimal values are determined.
Example 14
[0115] Constraints may be developed to consider the physical space
available for unit placement. Here, for example, the casino floor
may have a physical area, and there may be a physical area
associated with each of the different gaming units. The constraint
may require that the total combined physical area of the different
EGDs and the total combined physical area of the different table
games is less than or equal to the total physical area of the
casino floor when the optimal values are determined.
Example 15
[0116] Although Equations 7-10 of Table 3 show total fixed costs
and total variable costs for each of the EGD and table games
departments, it is possible to determine an historical fixed cost
function and an historical variable cost function for each of the
different classes of gaming units. For example, the FRS 4 of FIG. 1
may provide, directly or indirectly, fixed and variable cost
functions for each one of the gaming units 8, or for each of the
classes of the gaming units.
Example 16
[0117] Although the CMS 2 and FRS 4 of FIG. 1 are shown, data
collection with respect to relevant data associated with the gaming
units or unit characteristics or classifications may originate from
a wide range of sources (e.g., manufacturers; suppliers; taxing
authorities; regulatory authorities; industry organizations).
Example 17
[0118] Step 90 of FIG. 5A may obtain the current and historical
times series data for the decision variables from a user interface
of a financial reporting system, such as, for example, a graphical
user interface, a text user interface, a DOS user interface, or any
other electronic or automated user interface (e.g., of the CMS 2 or
FMS 4 of FIG. 1), wherein a user retrieves revenue ("win") and
total unit count time series data by classes (e.g., decision
variables).
Example 18
[0119] Similar to Example 17, step 102 of FIG. 5A may determine the
time series data on fixed and variable costs for relevant gaming
departments (e.g., table games department; EGD department) from a
user interface of a financial reporting system.
Example 19
[0120] As an alternative to or in addition to even steps 90-96 of
FIG. 5A, if participation gaming units are/were on the casino floor
at any time during the selected analysis period of step 88, then a
separate time series is retrieved that shows total revenue from
participation games, along with the number of games on the casino
floor for the same time period.
Example 20
[0121] As an alternative to or in addition to even steps 100-114 of
FIG. 5A, if participation gaming units are/were on the casino floor
at any time during the selected analysis period of step 88, then a
separate time series is retrieved that shows total participation
royalties (i.e., costs to the casino) and other costs, along with
the number of games on the casino floor for the same points in
time. These royalties and other costs are segregated between fixed
and variable costs at 104. A fixed cost function for participation
games is determined at 108. A variable cost function for
participation games is defined using the regression analysis
techniques at step 110. Depending on the nature of the variable
cost data series, the resultant best-fit equation (e.g., least
squares) from step 112 may be, for example, linear, polynomial,
logarithmic, exponential or power.
[0122] The disclosed linear and non-linear programming techniques
for a gambling enterprise as applied to particular gaming unit
types and classes is extremely advantageous to gambling operators.
These techniques, more specifically, permit the gambling industry
to predict and optimize revenue or profit for a particular gaming
unit type or class and to determine exactly what combination of
gaming unit types or classes should be deployed on the casino floor
for maximum revenue or profit.
[0123] While for clarity of disclosure reference has been made
herein to the exemplary user interface display 158 for displaying
optimal counts, it will be appreciated that such counts may be
stored, printed on hard copy, be computer modified, or be combined
with other data. All such processing shall be deemed to fall within
the terms "display" or "displaying" as employed herein.
[0124] While specific embodiments of the invention have been
described in detail, it will be appreciated by those skilled in the
art that various modifications and alternatives to those details
could be developed in light of the overall teachings of the
disclosure. Accordingly, the particular arrangements disclosed are
meant to be illustrative only and not limiting as to the scope of
the invention which is to be given the full breadth of the claims
appended and any and all equivalents thereof.
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