U.S. patent application number 10/460238 was filed with the patent office on 2004-12-16 for method, apparatus, and computer readable storage medium for improved tracking of casino players.
Invention is credited to Muskin, Jon, Shackleford, Michael.
Application Number | 20040254005 10/460238 |
Document ID | / |
Family ID | 33510963 |
Filed Date | 2004-12-16 |
United States Patent
Application |
20040254005 |
Kind Code |
A1 |
Shackleford, Michael ; et
al. |
December 16, 2004 |
Method, apparatus, and computer readable storage medium for
improved tracking of casino players
Abstract
A method, apparatus, and computer readable storage which
determines and tracks a player's error in a game of skill such as
video poker. The player error is stored in a player's slot club
account so that a beginning player may be entitled to additional
complimentaries from the casino. The method includes (a) reading
account information on a player's slot club card; (b) allowing the
player to complete the hand; (c) calculating expected value points
for the hand which incorporate a numerical computation of the
player's error; and (d) accumulating the expected value points in
the player's slot club account using information stored on the slot
club card.
Inventors: |
Shackleford, Michael; (Las
Vegas, NV) ; Muskin, Jon; (Chevy Chase, MD) |
Correspondence
Address: |
NATIONAL IP RIGHTS CENTER, LLC
SCOTT J. FIELDS, ESQ.
550 TOWNSHIP LINE ROAD
SUITE 400
BLUE BELL
PA
19422
US
|
Family ID: |
33510963 |
Appl. No.: |
10/460238 |
Filed: |
June 13, 2003 |
Current U.S.
Class: |
463/13 |
Current CPC
Class: |
G07F 17/3239 20130101;
G07F 17/32 20130101 |
Class at
Publication: |
463/013 |
International
Class: |
A63F 009/24 |
Claims
What is claimed is:
1. A method of tracking casino players playing a hand of a game
involving skill, the method comprising: reading account information
on a player's slot club card; allowing the player to complete the
hand; calculating expected value points for the hand which
incorporate a numerical computation of the player's error; and
accumulating the expected value points in the player's slot club
account using information stored on the slot club card.
2. A method as recited in claim 1, wherein the game comprises video
poker.
3. A method as recited in claim 2, further comprising: deciding
whether to offer a promotion to the player using the accumulated
expected value points in the slot club account.
4. A method as recited in claim 3, wherein the promotion comprises
converting accumulated expected value points to an incentive dollar
amount for discounts.
5. A method as recited in claim 4, wherein the promotion comprises
placing playable money for the incentive dollar amount in the
player's slot club account.
6. A method as recited in claim 4, wherein the promotion comprises
sending a check to the player for the incentive dollar amount.
7. A method as recited in claim 6, wherein the check is cashable
only at a particular casino or casino group.
8. A method as recited in claim 2, further comprising accumulating
standard comp points in the player's slot club account based on the
player's wager which do not incorporate error separate from the
expected value points.
9. A method as recited in claim 8, further comprising deciding
whether to offer a promotion to the player using information
incorporating both the accumulated expected value points in the
slot club account and standard comp points in the slot club
account.
10. A method as recited in claim 8, further comprising aggregating
the standard comp points and the expected value points into one
value.
11. A method as recited in claim 10, wherein the aggregating is
performed by a casino computer not a video poker machine
implementing the hand.
12. A method as recited in claim 10, further comprising deciding
whether to offer a promotion to the player using the aggregated
points.
13. A method as recited in claim 10, further comprising converting
the value to an incentive dollar amount for discounts.
14. A method as recited in claim 13, wherein a promotion comprises
placing playable money for the incentive dollar amount in the
player's slot club account.
15. A method as recited in claim 13, wherein the promotion
comprises sending a check to the player for the incentive dollar
amount.
16. A method as recited in claim 15, wherein the check is cashable
only at a particular casino or casino group.
17. A method as recited in claim 2, wherein the calculation of
expected value points also takes into consideration the player's
choice of machine.
18. A method as recited in claim 17, wherein the calculated
expected value points incorporates an optimal return for the
machine.
19. A method as recited in claim 2, wherein the expected value
points are not automatically disclosed to the player
electronically.
20. A method as recited in claim 2, wherein the expected value
points comprise an equivalent of (optimal value of the dealt
hand-expected value of played hand)*bet.
21. A method as recited in claim 21, wherein the expected value
points take into consideration a return of the player's machine
choice.
22. A method as recited in claim 2, wherein the expected value
points comprise an equivalent of (optimal strategy house edge for
machine+optimal value of the dealt hand-expected value of played
hand)*bet.
23. A method as recited in claim 2, wherein the expected value
points take into consideration cash back given to the player.
24. A method as recited in claim 23, wherein the expected value
points comprise an equivalent of (optimal strategy house edge for
machine-cash back percentage+optimal value of the dealt
hand-expected value of played hand)*bet.
25. A method as recited in claim 3, wherein the deciding takes into
consideration cash back already given or allotted to the
player.
26. A method as recited in claim 2, wherein the expected value
points take into consideration cash back given to the player and a
return of the player's machine choice.
27. A method as recited in claim 2, further comprising computing a
player's skill level as (total expected value points/total amount
wagered).
28. A method as recited in claim 2, further comprising computing a
player's skill level as (optimal strategy return-(expected value
points/total amount bet)).
29. A method as recited in claim 2, further comprising computing a
player's skill level as (optimal strategy return+cash
back-(expected value points/total amount bet)).
30. A method as recited in claim 2, further comprising computing a
future expected loss of the player using the expected value
points.
31. A method as recited in claim 2, further comprising computing a
future expected daily loss of the player as (average house
edge*average hands per day*average wager).
32. A method as recited in claim 2, further comprising computing an
average expected value of hands played by the player.
33. A method as recited in claim 2, further comprising: inputting,
by a casino employee, the player's identification information on a
computer; outputting the player's standard information; and
outputting expected value information based on the accumulated
expected value points.
34. A method as recited in claim 33, wherein the expected value
information comprises a measure of the player's skill.
35. A method as recited in claim 33, wherein the expected value
information is equivalent to the average expected value of the
player's hands.
36. A method as recited in claim 2, further comprising: inputting,
by a casino player, the player's slot club card into a card reader;
outputting on a display standard points accumulated by the player
stored in the player's slot club account identified on the slot
club card; and keeping the expected value points shielded from the
player on the display.
37. A method as recited in claim 2, further comprising: identifying
the player as an advantage player based on the player's expected
return.
38. A method as recited in claim 2, further comprising: identifying
the player as an advantage player if the player's (expected total
return)>a predetermined expert return.
39. A method as recited in claim 38, further comprising identifying
the player as an advantage player if a total number of hands
player>a predetermined sample of hands.
40. A method as recited in claim 2, further comprising: identifying
the player as an advantage player if the player's (expected total
expected value points/amount wagered)<a predetermined
amount.
41. A method as recited in claim 40, further comprising identifying
the player as an advantage player if a total number of hands
player>a predetermined sample of hands
42. A method as recited in claim 2, further comprising: offering a
comp amount based on the expected value points and reduced by an
amount of standard comps already given.
43. A method as recited in claim 2, wherein the calculated expected
value points is a floating point number which is transmitted to a
casino computer where the expected value points are accumulated in
the player's slot club account.
44. A method as recited in claim 2, wherein the calculated expected
value points is a floating point number which is transmitted to a
casino computer using an integer representation, the casino
computer accumulating the expected value points in the player's
slot club account.
45. A method as recited in claim 2, wherein a unit that performs
the calculating is installed as a plug-in on a video poker machine
implementing the game of video poker.
46. A method of tracking casino players playing a hand of a video
poker game, the method comprising: reading account information on a
player's slot club card; allowing the player to complete the hand
of video poker; calculating expected value points for the hand
which incorporate the player's error; accumulating the expected
value points in the player's slot club account using information
stored on the slot club card; deciding whether to offer a promotion
to the player using the accumulated expected value points in the
slot club account; computing a player's skill level as (optimal
strategy return+cash back-(expected value points/total amount
bet)); computing a future expected daily loss of the player as
(average house edge* average hands per day*average wager);
identifying the player as an advantage player if the player's
(expected total return /amount wagered)>a predetermined amount;
offering a comp amount based on the expected value points and
reduced by an amount of standard comps already given; computing an
average expected value of hands played by the player; inputting, by
a casino employee, the player's identification information on a
computer; outputting the player's standard information; and
outputting expected value information based on the accumulated
expected value points, inputting, by a casino player, the player's
slot club card into a card reader; outputting on a display standard
points accumulated by the player stored in the player's slot club
account identified on the slot club card; and keeping the expected
value points shielded from the player on the display, wherein the
expected value points comprise an equivalent of (optimal strategy
house edge for machine+optimal value of the dealt hand-expected
value of played hand)*bet, wherein the promotion comprises
converting accumulated expected value points to an incentive dollar
amount for discounts, wherein the promotion comprises placing
playable money for the incentive dollar amount in the player's slot
club account, wherein the promotion comprises sending a check to
the player for the incentive dollar amount, wherein the check is
cashable only at a particular casino or casino group, wherein the
calculated expected value points is a floating point number which
is transmitted to a casino computer where the expected value points
are accumulated in the player's slot club account, wherein the
expected value information is equivalent to the average expected
value of the player's hands, wherein a unit that performs the
calculating is installed as a plug-in on a video poker machine
implementing the game of video poker.
47. A method of tracking casino players playing a hand of a game
involving skill, the method comprising: reading account information
on a player's slot club card; allowing the player to complete the
hand; calculating expected value points for the hand which
incorporate a numerical computation of the player's error;
combining the expected value points with standard comp points; and
accumulating the combined points in the player's slot club account
using information stored on the slot club card.
48. A method as recited in claim 47, further comprising maintaining
a ratio of the expected value points to the standard comp points in
the player's slot club account.
49. A method as recited in claim 47, wherein the game comprises
video poker.
50. A method as recited in claim 49, further comprising: deciding
whether to offer a promotion to the player using the accumulated
combined points in the slot club account.
51. A method as recited in claim 50, wherein the promotion
comprises converting the combined points into an incentive dollar
amount for discounts.
52. A method as recited in claim 51, wherein the promotion
comprises placing playable money for the incentive dollar amount in
the player's slot club account.
53. A method as recited in claim 52, wherein the promotion
comprises sending a check to the player for the incentive dollar
amount.
54. A method as recited in claim 53, wherein the check is cashable
only at a particular casino or casino group.
55. A method as recited in claim 47, wherein the accumulating
accumulates the standard comp points and accumulates an extra
standard comp point or points when the expected value points reach
a certain level.
56. A method of tracking casino players playing a hand of a video
poker, the method comprising: reading account information on a
player's slot club card; allowing the player to complete the hand;
calculating expected value points for the hand based on the
player's machine choice; and accumulating the expected value points
in the player's slot club account using information stored on the
slot club card.
57. A method of marketing to casino players, the method comprising:
computing and accumulating expected value points based on a
player's error and the player's wager; computing the player's skill
level based on the player's error; considering the player's
expected value points and the player's skill level to decide
whether to offer the player a promotion or incentive.
58. A method of storing player records, the method comprising:
storing standard player information in a player record; storing
expected value information based on a player's error and wager
alongside the standard player information in the player record; and
retrieving the standard player information and the expected value
information when requested by a client.
59. A method as recited in claim 58, wherein the expected value
information comprises points stored as a floating point number.
60. A method of tracking casino players playing a hand of a game
blackjack, the method comprising: receiving account information on
a player's slot club card; allowing the player to complete the hand
of blackjack; calculating expected value points for the hand which
incorporate the player's error; and accumulating the expected value
points in the player's loyalty account using information stored on
the slot club card.
61. A method as recited in claim 60, further comprising: deciding
whether to offer a promotion to the player based on the accumulated
expected value points in the loyalty account.
62. A method as recited in claim 60, wherein the expected value
points comprise an equivalent of (optimal value of the dealt
hand-expected value of played hand)*bet.
63. A method as recited in claim 60, wherein the expected value
points comprise an equivalent of (optimal value of the dealt
hand-expected value of played hand)*bet.
64. A method as recited in claim 60, further comprising computing a
player's skill level as (total expected value points/total amount
wagered).
65. A method as recited in claim 60, further comprising computing a
future expected loss of the player using the expected value
points.
66. A method as recited in claim 60, further comprising computing a
future expected daily loss of the player as (average house
edge*average hands per day*average wager).
67. A method as recited in claim 60, further comprising computing
an average expected value of hands played by the player.
68. A method as recited in claim 60, further comprising sending the
player a check with an amount based on the expected value
points.
69. A method as recited in claim 60, wherein the expected value
points reflect the optimal return on the variation of blackjack
game played.
70. A method as recited in claim 60, further comprising
accumulating standard comp points in the player's loyalty account
based on the player's wager which do not incorporate error separate
from the expected value points.
71. A method as recited in claim 70, further comprising deciding
whether to offer a promotion to the player using information
incorporating both the accumulated expected value points in the
loyalty account and standard comp points in the loyalty
account.
72. A method as recited in claim 70, further comprising aggregating
the standard comp points and the expected value points into one
value.
73. A method as recited in claim 72, further comprising determining
an award based on the aggregated value.
74. A method as recited in claim 60, further comprising computing a
player's skill level as (total expected value points/total amount
wagered).
75. A method as recited in claim 60, further comprising computing a
player's skill level as (optimal strategy return-(expected value
points/total amount bet)).
76. A method as recited in claim 60, further comprising computing a
player's skill level as (optimal strategy return+cash
back-(expected value points/total amount bet)).
77. A method, comprising: displaying a game of skill hand during a
playing session resulting in a player entering a choice on the
player's computer; the choice either comprising perfect play or
comprising erroneous play; displaying to the player an offered
promotion based on erroneous play by the player, wherein the
promotion is displayed at a subsequent session later than the
playing session.
78. A method as recited in claim 77, wherein the offered promotion
is displayed after a sum of the player's error reaches a value.
79. A method as recited in claim 77, wherein the offered promotion
is displayed after a sum of the player's ((optimal value of
respective dealt hands-expected value of respective played
hands)*respective bet) reaches a value.
80. A method as recited in claim 77, wherein the offered promotion
is displayed after a sum of the player's ((optimal strategy house
edge for game chosen+optimal value of the respective dealt
hands-expected value of respective played hands)*respective bet)
reaches a value.
81. A method as recited in claim 77, wherein the offered promotion
is displayed after a sum of the player's ((optimal strategy house
edge for game chosen-cash back percentage+optimal value of the
respective dealt hands-expected value of respective played
hands)*respective bet) reaches a value.
82. A method as recited in claim 77, wherein the game of skill hand
is received from a remote server.
83. A method as recited in claim 77, wherein the promotion includes
bonus money placed in a player's gaming account.
84. A computer readable storage medium storing a method of tracking
casino players playing a hand of a game involving skill, the
storage medium controlling a computer by: reading account
information on a player's slot club card; allowing the player to
complete the hand; calculating expected value points for the hand
which incorporate the player's error; and accumulating the expected
value points in the player's slot club account using information
stored on the slot club card.
85. A computer readable storage medium as recited in claim 84,
wherein the game comprises video poker.
86. An apparatus tracking casino players playing a hand of a game
involving skill, the apparatus comprising: an input unit reading
account information on a player's slot club card; a game apparatus
allowing the player to complete the hand; a calculating unit
calculating expected value points for the hand which incorporate
the player's error; and an accumulating unit accumulating the
expected value points in the player's slot club account using
information stored on the slot club card.
87. An apparatus as recited in claim 86, wherein the game apparatus
comprises a video poker machine.
88. An apparatus for tracking casino players playing a hand of a
game involving skill, the apparatus comprising: means for reading
account information on a player's slot club card; means for
allowing the player to complete the hand; means for calculating
expected value points for the hand which incorporate a numerical
measure of the player's error; and means for accumulating the
expected value points in the player's slot club account using
information stored on the slot club card.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention is directed to a method, device, and
computer readable storage medium for tracking and marketing to
select casino players. More particularly, the present invention
relates to an improved system for tracking and marketing to select
players.
[0003] 2. Description of the Related Art
[0004] Casinos commonly use player tracking systems to track and
market to players. Player tracking systems issue to players a
"players card" or "slot club card" to a player, who then uses this
card when he plays casino games such as blackjack, craps, slot
machines, video poker, etc. Computers are used to keep track of a
player's bets. Based on the player's wagers (or "action"), the
player may be given incentives (or "complimentaries" or "comps") by
the casino, such as discounts on rooms or food, etc. The more
casino action a player gives a casino, generally the greater his or
her comps will be. If a player has wagered a small amount, he or
she will typically not be given any or much comps, as the casino
does not value this player's patronage. In this way, a casino
encourages players that they value to return to their casino and
gamble some more.
[0005] Certain casino games incorporate an element of player skill.
For example, in blackjack and video poker, a player is presented
with decisions to make. There exists a mathematical strategy for
these games so that the player can reduce the house edge as much as
possible by making the mathematically correct decisions. In fact,
in certain variations of video poker (such as a game known as "full
pay deuces wild") a player playing the optimal strategy will have a
slight advantage over the casino. These optimal strategies are
available on the Internet and on strategy cards.
[0006] A drawback of the current comp system is that casinos do not
calculate a player's skill when the player plays electronic games
such as video poker and video blackjack. Consider a first player
who is a beginner at video poker and does not follow the proper
strategy perfectly, and a second player who bets the same total
amount but plays the hands perfectly. The current system would
value these two players equally. However, of course the first
player is more valuable to the casino, and this player is also more
deserving of incentives in order to compensate for losses due to
being a beginner.
[0007] Therefore, what is needed is an improved comp system that
takes into consideration a player's skill in determining the
player's value and marketing efforts.
SUMMARY OF THE INVENTION
[0008] It is an aspect of the present invention to provide
improvements and innovations in casino player tracking,
complimentary, and marketing systems.
[0009] The above aspects can be obtained by a system that includes
(a) reading account information on a player's slot club card; (b)
allowing the player to complete the hand; (c) calculating expected
value points for the hand which incorporate a numerical computation
of the player's error; and (d) accumulating the expected value
points in the player's slot club account using information stored
on the slot club card.
[0010] These together with other aspects and advantages which will
be subsequently apparent, reside in the details of construction and
operation as more fully hereinafter described and claimed,
reference being had to the accompanying drawings forming a part
hereof, wherein like numerals refer to like parts throughout.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Further features and advantages of the present invention, as
well as the structure and operation of various embodiments of the
present invention, will become apparent and more readily
appreciated from the following description of the preferred
embodiments, taken in conjunction with the accompanying drawings of
which:
[0012] FIG. 1 is a flowchart illustrating a method of calculating
the optimal value of a dealt hand, according to an embodiment of
the present invention;
[0013] FIG. 2 is a flowchart illustrating a method of calculating
the expected value of a played hand, according to an embodiment of
the present invention;
[0014] FIG. 3 is flowchart illustrating an alternative method of
calculating the optimal value of a dealt hand, according to an
embodiment of the present invention;
[0015] FIG. 4 is a flowchart illustrating a method of calculating
the error points, according to an embodiment of the present
invention;
[0016] FIG. 5 is a block diagram illustrating the components used
to implement an improved player tracking system, according to one
embodiment of the present invention;
[0017] FIG. 6 is a diagram of a database record, according to one
embodiment of the present invention;
[0018] FIG. 7 is a flowchart illustrating a method of selective
marketing, according to one embodiment of the present
invention;
[0019] FIG. 8 is an illustration of an example of a display,
according to one embodiment of the present invention; and
[0020] FIG. 9 illustrates a flowchart of one method of identifying
an advantage player, according to an embodiment of the present
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0021] Reference will now be made in detail to the presently
preferred embodiments of the invention, examples of which are
illustrated in the accompanying drawings, wherein like reference
numerals refer to like elements throughout.
[0022] The present invention relates to improving player tracking,
evaluation, and marketing systems. The invention relates to
determining and using an individual player's skill level in order
to present a more complete picture of a player's ability and the
player's value to a casino.
[0023] Tracking a player's play can be accomplished either on table
games or on machine games. A table game typically requires a casino
employee to manually enter a player's plays. On a machine game, the
machine can automatically track a player's plays.
[0024] Video poker is a highly popular game in casinos, both in
land based and Internet casinos. Five cards are dealt to the
player, and the player chooses which of the five cards to keep and
which to replace. The goal is for the player to create certain
hands which pay according to an active paytable. A video poker
machine typically displays a description of the paying hands and
how much each hand pays as a multiple of the original bet.
[0025] Video poker comes in many variations, which include (but not
limited to): Jacks or Better, Deuces Wild, Joker Poker, etc. Each
variation has its own pay table and special rules. For example, in
Joker Poker, a wild joker is added to a standard deck. In Deuces
wild, all deuces (twos) are wild. Of course, the paytable is
adjusted to reflect each game's particular rules.
[0026] Table I below presents a payout chart for "full pay Jacks or
Better."
1 TABLE I Coins Bet Hand 1 2 3 4 5 Royal flush 250 500 750 1000
4000 Straight flush 50 100 150 200 250 Four of a kind 25 50 75 100
125 Full house 9 18 27 36 45 Flush 6 12 18 24 30 Straight 4 8 12 16
20 Three of a 3 6 9 12 15 kind Two pair 2 4 6 8 10 Jacks or better
1 2 3 4 5
[0027] Video poker should not be played according to "hunches" or
what some players may consider common sense. There is a known
mathematical strategy for playing the game to reduce (or even
eliminate) the house edge as much as possible. Table II presents a
sample "simple strategy" for "9/6" Jacks or Better video poker,
characterized by paying 9 for a full house and 6 for a flush, per
coin bet. The optimal return in 9/6 Jacks or Better is 99.54.
2TABLE II 1 Full house or better 2 4 to a royal flush 3 Straight,
three of a kind, or flush 4 4 to a straight flush 5 Two pair 6 High
pair 7 3 to a royal flush 8 4 to a flush 9 Low pair 10 4 to an
outside straight 11 2 suited high cards 12 3 to a straight flush 13
2 unsuited high cards (if more than 2 pick then pick lowest 2) 14
Suited 10/J, 10/Q, or 10/K 15 One high card 16 Discard
everything
[0028] The way this strategy works is as follows. When a player is
dealt a particular hand, the player will keep the set of cards that
have the highest rank in Table II. For example, if a player is
dealt the following hand: A 8 5 2 2, the highest ranked hand that
the player can make in Table II is #9 low pair (the pair of 2's).
Thus, the player should keep the pair of 2's and discard the other
cards. The strategy in Table II, if played perfectly on a 9/6 Jacks
or Better game, will return to a player 99.46%. Longer and more
advanced strategies can improve on this return marginally, as far
as the optimal strategy return of 99.54%. Note there are more
optimal strategies for this game and this is merely presented as an
example
[0029] A beginning player that does not make the optimal play (the
above example strategy in Table II is close, but not optimal) is
basically giving money to the casino. For example, consider the
player that gets dealt: A 8 5 2 2, as in the example above. The
correct play is to keep the pair of 2's. If the player is playing a
one dollar machine and puts in $5, the expected value of keeping
the pair of 2's would be $4.12. However, if a beginning player
keeps the pair of 2's but also the A (as a "kicker"), then his
expected value would be only $3.38. Thus, the player just gave 74
cents to the casino, on average. Of course, making the wrong play
may result in a bigger win than playing correctly, however what is
more important than the instant result is the long term average for
a player's skill level.
[0030] An improved player tracking system would keep long term
track of the players unnecessary cost for each hand dealt. A
beginning player that makes more mistakes should be entitled and
considered for special promotions and marketing efforts by the
casinos. More on ways of computing this cost and ways to track it
will be described below.
[0031] As an example of ways to play a hand, consider a player that
is dealt: 2 hearts; 4 spades; 8 hearts; 9 clubs, and queen spades.
The player can keep or discard each of the 5 cards, for 32 possible
ways to play the hand. A table can be created for each way to play
the hand, and a breakdown of the number of paying (and losing)
hands possible. Table III and Table IV, based on 9/6 Jacks or
Better, represent such a table for the example hand given. For
example, given that the play keeps all of his cards, row 1
indicates that this results in only 1 way to make a non-paying hand
("nothing"). This has an expected value of 0. If the 2, 4, 8 and
queen are kept, row 3 indicates that there are 44 ways to make a
non-paying hand, and 3 ways to make a high pair (i.e. 3 other
queens to match the kept queen). The expected value here is 0.06,
that is for every $1 bet, the player can expect on average to
return 6% or 6 cents. From Tables III and IV it is clear that the
best play is to keep only the queen, as it is the play with the
highest expected value.
3TABLE III High Two 3 of a Kept cards Nothing pair pair kind
Straight 2h, 4s, 8h, 9c, Qs 1 0 0 0 0 2h, 4s, 8h, 9c 47 0 0 0 0 2h,
4s, 8h, Qs 44 3 0 0 0 2h, 4s, 8h 1024 21 27 9 0 2h, 4s, 9c, Qs 44 3
0 0 0 2h, 4s, 9c 1024 21 27 9 0 2h, 4s, Qs 913 132 27 9 0 2h, 4s
14295 780 711 281 128 2h, 8h, 9c, Qs 44 3 0 0 0 2h, 8h, 9c 1024 21
27 9 0 2h, 8h, Qs 913 132 27 9 0 2h, 8h 14258 780 711 281 0 2h, 9c,
Qs 913 132 27 9 0 2h, 9c 14423 780 711 281 0 2h, Qs 12248 2955 711
281 0 2h 148980 15357 8874 4102 382 4s, 8h, 9c, Qs 44 3 0 0 0 4s,
8h, 9c 1024 21 27 9 0 4s, 8h, Qs 913 132 27 9 0 4s, 8h 14359 780
711 281 64 4s, 9c, Qs 913 132 27 9 0 4s, 9c 14423 780 711 281 0 4s,
Qs 12083 2955 711 281 0 4s 148534 15357 8874 4102 828 8h, 9c, Qs
897 132 27 9 16 8h, 9c 14183 780 711 281 240 8h, Qs 12200 2955 711
281 48 8h 148455 15357 8874 4102 907 9c, Qs 12136 2955 711 281 112
9c 148290 15357 8874 4102 907 Qs 118674 45456 8874 4102 589 None
1205537 213648 71802 31502 5979
[0032]
4TABLE IV Full 4 of a Str Royal Kept cards Flush house kind flush
flush Exp Value 2h, 4s, 8h, 9c, Qs 0 0 0 0 0 0.00000 2h, 4s, 8h, 9c
0 0 0 0 0 0.00000 2h, 4s, 8h, Qs 0 0 0 0 0 0.06383 2h, 4s, 8h 0 0 0
0 0 0.09436 2h, 4s, 9c, Qs 0 0 0 0 0 0.06383 2h, 4s, 9c 0 0 0 0 0
0.09436 2h, 4s, Qs 0 0 0 0 0 0.19704 2h, 4s 0 18 2 0 0 0.23244 2h,
8h, 9c, Qs 0 0 0 0 0 0.06383 2h, 8h, 9c 0 0 0 0 0 0.09436 2h, 8h,
Qs 0 0 0 0 0 0.19704 2h, 8h 165 18 2 0 0 0.26192 2h, 9c, Qs 0 0 0 0
0 0.19704 2h, 9c 0 18 2 0 0 0.20086 2h, Qs 0 18 2 0 0 0.33500 2h
328 288 52 2 0 0.29658 4s, 8h, 9c, Qs 0 0 0 0 0 0.06383 4s, 8h, 9c
0 0 0 0 0 0.09436 4s, 8h, Qs 0 0 0 0 0 0.19704 4s, 8h 0 18 2 0 0
0.21665 4s, 9c, Qs 0 0 0 0 0 0.19704 4s, 9c 0 18 2 0 0 0.20086 4s,
Qs 165 18 2 0 0 0.39605 4s 326 288 52 4 0 0.30707 8h, 9c, Qs 0 0 0
0 0 0.25624 8h, 9c 0 18 2 0 0 0.26007 8h, Qs 0 18 2 0 0 0.34684 8h
325 288 52 5 0 0.30909 9c, Qs 0 18 2 0 0 0.36263 9c 490 288 52 5 0
0.31464 Qs 327 288 52 2 1 0.47442 None 2982 2124 344 18 3
0.34198
[0033] FIG. 1 is a flowchart illustrating a method of calculating
the optimal value of a dealt hand, according to an embodiment of
the present invention. Calculating the optimal value of a dealt
hand is important so that the system knows how much the hand is
worth if no error has been made. Figure illustrates the "cycling"
method calculating the optimal value by cycling through all 32 ways
to compute values.
[0034] The method starts with operation 100, which initializes a
loop through the 32 different combinations of cards that can be
kept/discarded. There are five cards dealt, and each card can be
kept or discarded, for 2{circumflex over ( )}5=32 different
possibilities. Thus, the method does a computation for all 32
possibilities.
[0035] From operation 100, the method then proceeds to operation
102, which determines which cards to discard. This can be done by
giving a binary equivalent of the loop value (from 1 to 32) can be
computed and assigned to the cards 1-5, and cards with a `1` value
are kept while cards with a `0` value are discarded. In another
embodiment, five separate loops from 1 to 2 can be used (instead of
one loop from 1 to 32) which represent the status of each card.
[0036] Once the discarded cards are determined, the method then
proceeds to operation 104, which computes the average return for
each of the 32 ways to play the hand. This can be done by cycling
through nested loops for each of the discarded cards so that every
possible card combination is cycled through. For example, if only
one card is discarded, then that card is cycled through the 47
cards which were not dealt on the initial deal. If two cards are
discarded, then the first discarded card is cycled through the 47
cards which were not dealt on the initial deal, and the second
discarded card is cycled through 46 cards (5 cards were already
dealt on the initial deal, and 1 card was dealt to the first
discarded card). Alternatively, to save computing time, redundant
combinations do not have to be cycled through. For example, instead
of running through 47*46=2162 combinations, this can be reduced in
half since the order of the cards does not matter. One way of
accomplishing this is to number the cards left in the deck from 0
to 46. For the first card, cards numbered 0 through 45 are cycled
through. For the second card, (1+first card index) to 47 are cycled
through. This only requires (47*46)/2=1081 combinations.
[0037] In this way, every possible card combination is produced.
The return (according to a selected paytable) is stored for each of
the combinations and averaged for each of the 32 possible ways to
hold/discard cards.
[0038] From operation 104, the method then proceeds to operation
106, which takes the highest return of the 32 combinations. This
represents the value for the optimal play given the 5 cards
initially dealt.
[0039] The method illustrated in FIG. 2 illustrates how to
calculate the optimal value of a dealt hand. However, a beginning
player may not always choose to play his hand in the optimal
way.
[0040] FIG. 2 is a flowchart illustrating a method of calculating
the expected value of a played hand, according to an embodiment of
the present invention. The expected value of the played hand is
calculated so that it can be subtracted from the optimal value of
the hand to determine the player error.
[0041] The method starts with operation 200, in which the player
selects the cards the player wishes to keep/discard. This can be
using any standard input device, such as a touch screen, buttons,
keyboard, mouse, etc.
[0042] From operation 200, the method proceeds to operation 202
which cycles through all the possible ways the discarded cards can
be dealt. This is similar to operation 104 from FIG. 1. The returns
for each of the hands are computed and tabulated using a selected
paytable for the game.
[0043] From operation 202, the method proceeds to operation 204,
which calculates the average of the tabulated hands is computed,
which represents the return for the way the hand was played.
[0044] FIG. 3 is a flowchart illustrating an alternative method of
calculating the optimal value of a dealt hand, according to an
embodiment of the present invention. This alternative method uses a
"formula based" approach and is faster than the method illustrated
in FIG. 1.
[0045] The method starts with operation 300, which cycles through
all 32 ways to play a video poker hand. See the description above
for more details.
[0046] From operation 300, the method proceeds to operation 302,
wherein if all five cards are kept, the hand is simply scored. Then
the method proceeds back to operation 300, which cycles through the
next combination (unless all 32 ways have been cycled through).
[0047] From operation 302 (assuming all five cards were not kept),
the method proceeds to operation 304, wherein if 4 cards are kept,
then the 47 possible replacement cards are cycled through which are
scored and averaged. Then the method proceeds back to operation
300, which cycles through the next combination (unless all 32 ways
have been cycled through).
[0048] From operation 304 (assuming four cards were not kept), the
method proceeds to operation 306, wherein if 3 cards are kept, then
the 1081 ((47*46)/2) possible sets of two replacement cards are
cycled through which are scored and averaged. Then the method
proceeds back to operation 300, which cycles through the next
combination (unless all 32 ways have been cycled through).
[0049] From operation 306 (assuming three cards were not kept), the
method proceeds to operation 308, wherein a formula based approach
is used to calculate the return. At this point, the number of cards
to cycle through becomes costly in terms of computing time, so the
following formula based approach results in a faster computation
time.
[0050] Operation 308 implements a formula based approach to
calculate the expected return when the number of cards to deal gets
prohibitively high (typically 4 or 5 cards). This approach
calculates the number of each type of winning hand possible based
on the current cards the player holds, and then calculates the
overall expected value.
[0051] The formula based approach comprises operation 310, which
cycles through all the winning hands on the respective
paytable.
[0052] From operation 310, the method then proceeds to operation
312, wherein for each winning hand cycled through in operation 310,
computes the number of different ways that winning hand can be
made. The program contains a routine for each category of cards
that can be kept (i.e. a pair, two consecutive cards, etc.) Each
routine then tabulates every possible way the winning hand can be
made given the kept cards. Given one or two cards, it is easy to
write down all of the different ways a winning hand can be made.
This is essentially what the routine does.
[0053] From operation 310 (after all winning hands have been cycled
through), the method then proceeds to operation 314, which computes
the particular expected value. This is computed by computing the
product of the number of different ways each winning hand can be
made by what that winning hand pays according to the respective
paytable. This product is then divided by the number of winning
hands to get the expected value. The particular expected value will
be computed for each of the 32 ways to play each hand, and
stored.
[0054] From operation 300 (after all 32 ways to play the hand have
been cycled through), the method then proceeds to operation 316,
which determines the best particular expected value. This is
determined by taking the highest expected value of the 32 values
stored from operation 310. A matrix of 32 decimal numbers should be
kept, one for each way to play the hand. All expected values should
be in terms of one betting unit, based on the number of coins bet.
The maximum expected value will be the greatest of these 32
numbers.
[0055] It is noted that any combination of the cycling or formula
based approaches can be used. For example, all possible replacement
cards can be cycled through; or the formula based approach can be
used to all situations; or a mixture of the two approaches can be
used (i.e. for 1-2 discards, the cards can be cycled through. For
more 3-5 discards, the formula based approach is used). The
preferred method is to use the cycling approach for 1-2 cards and
the formula based approach for all others.
[0056] Appendix A illustrates an example of C++ code used which
illustrates the formulaic approach to determine the amount of
winning combinations of hands with 4 discards, which can then be
used to calculate the expected value of the dealt hand. Other
numbers of discards can be accomplished similarly.
[0057] An example of the above formula based method follows:
[0058] A player is playing Jacks or Better at the 25 cent coinage
level and plays 5 coins. The player is dealt the following cards: 2
of hearts, 4 of spades, 8 of hearts, 9 of clubs, queen of spades.
The method will determine the expected value of keeping just the
queen of spades. Following is the logic the computer would follow
to determine the number of combinations of each possible hand on
the draw. The computer would loop through all combinations of
ranks.
[0059] Royal flush: The 10, jack, king, and aces of spades are all
still in the deck, therefore there is 1 royal flush
combination.
[0060] Straight flush: The possible spans for a straight flush are
8 to queen and 9 to king. All necessary cards are still in the
deck, therefore number of combinations is 2.
[0061] Four of a kind: For the ranks 3, 5, 6, 7, 10, jack, king,
and ace all four cards are still in the deck, therefore there is
one combination each for a total of 8. All three other queens are
also still in the deck and the player can still get any of the 44
kickers with the three queens. So the number of four of a kinds is
8+44=52.
[0062] Full house: The queen can be either part of the three of a
kind or pair. If the queen is part of the three of a kind then
there are 3 ways to pick 2 queens from the remaining 3. There are
12 ranks left for the pair. 8 of them have all four cards left and
4 have just three left. Of the ranks with all four cards left there
are 6 ways to choose 2 cards out of 4. Of the 4 ranks with 3 left
there are 3 ways to choose 2 cards out of 3. So the total number of
full houses, queens up, is 3*(8*6+4*3)=180. For the number of full
houses where the queen is part of the pair there are 3 ways to
choose one more queen out of the three left. Of the other 12 ranks
there are 4 ways to choose 3 out of 4 cards for the 8 ranks with
all four cards remaining. Of the other 4 ranks with 3 cards left
there is only 1 way to pick 3 out of 3 cards. So the number of full
houses where the queen is the pair is 3*(8*4+4*1)=108. So the total
number of full houses is 180+108=288.
[0063] Flush: Spades are the only possible suit for the flush. The
player discarded the 8 of spades so there are 11 spades left in the
deck. There are 330 ways to pick 4 spades out of 11 to complete the
flush. However 3 of those will result in a straight flush or royal
flush. So the number of flush combinations is 330-3=327.
[0064] Straight: There are three possible spans for a straight: 8
to queen, 9 to king, and 10 to ace. The player already discarded an
8 and 9, which will cut down the number of straight combinations.
Let n8=number of 8's left in deck, and so on for each rank. The
number of possible straights can be expressed as:
n8*n9*n10*nJ+n9*n10*nJ*nK+n10+nJ+nK+nA=3*3-
*4*4+3*4*4*4+4*4*4*4=592. However 3 of these combinations result in
a straight flush or royal flush. So the final number of straight
combinations is 592-3=589.
[0065] Three of a kind: There are two types of three of a kind in
this situation: (1) queen is in the three of a kind, (2) queen is a
singleton. To determine the number of type (1) three of a kind
there are 3 ways to pick 2 out of the three queens left in the
deck. There are also 44 non-queens left in the deck. The number of
ways to pick 2 cards out of 44 is 44*43/2=946. However we know from
the full house section that 8*6+4*3 that 60 of these combinations
result in a pair. So there are 3*(946-60)=2658 ways to form a type
(1) three of a kind. For the type (2) full houses there are 12
ranks left for the three of a kind, and 11 for the other singleton.
The program would circulate through all 132 combinations of three
of a kind and singleton ranks. 4*3=12 will result in both ranks
having only three cards left, in which case there will be 1*3=3
ways to complete the three of a kind. 8*4=32 ways will result in
the 3 of a kind coming from a rank with all 4 cards left and the
singleton from a rank with 3. Then there were will be 4*3=12 ways
to complete the three of a kind. 4*8=32 ways will result in the
three of a kind coming from a rank with 3 cards left and the
singleton from a rank with 4 cards left. There are 1*4=4 ways to
complete the three of a kind. 8*7=56 ways will result in both the
three of a kind and the singleton coming from ranks with all four
cards left. There will be 4*4=16 ways to complete each three of a
kind. So the total number of type (2) three of a kinds is
(12*3+32*12+32*4+56*16)=1444. The total number of three of a kinds
is 2658+1444=4102.
[0066] Two pair: There are two types of two pairs: (1) queen is
part of a pair, (2) queen is the singleton. Of the type (1) two
pairs there are 3 possible ranks for the other queen. There are
8*7=56 ways the other pair and singleton can both come from ranks
with 4 cards left, for a total of 6*4=24 combinations each. There
are 8*4=32 ways the three of a kind can come from a rank of 4 and
the singleton from a rank of 3, for a total of 6*3=18 each. There
are 4*8=32 ways the three of a kind can come from a rank of 3 and
the singleton from a rank of 4, for a total of 3*4=12 combinations
each. There are 4*3=12 ways both the other pair and the singleton
can come from ranks with 3 left each, for a total of 3*3=9
combinations each. So the total number of type (1) two pairs is
3*(56*24+32*18+32*12+12*9)=7236. Of the type (2) two pairs there
are 8*7/2=28 ways both pairs can come from ranks 4, and there are
6*6 ways to pick the suits from each set. There are 8*4=32 ways to
pick one pair from a rank of 4 and one from a rank of 3, and there
are 6*3=18 ways to pick the suits from each set. There are 4*3/2=6
ways to pick both pairs from ranks of 3, and there are 3*3=9 ways
to pick the suits from each set. So the total number of type (2)
two pairs is (28*36+32*18+6*9)=1638. The total number of two pairs
is therefore 7236+1638=8874.
[0067] Pair: There are two types of pairs: (1) pair of queens, (2)
pair of another high card. For the type (1) pairs the program picks
one of 3 suits for the other queen and then will cycle through all
12*11*10/6=220 ways to pick 3 ranks out of 12 for the singletons.
8*7*6/6=56 of those ways will result in all 3 singletons coming
from ranks of 4, for 4{circumflex over ( )}3=64 ways to pick the
suits each. (8*7/2)*4=112 of those ways will result in 2 singletons
coming from ranks of 4 and one from a rank of 3, for 4{circumflex
over ( )}2*3=48 ways to pick the suits each. 8*(4*3/2)=48 of those
ways will result in 1 singleton coming from a rank of 4 and two
from a rank of 3, for 4*3{circumflex over ( )}2=36 ways to pick the
suits. 4*3*2/6=4 ways result from all three singletons coming from
ranks of 3, or 3{circumflex over ( )}3=27 ways to pick the suits.
So the number of type (1) pairs is
3*(56*64+112*48+48*36+4*27)=32388 combinations of type (1) pairs.
For the type (2) pairs there are 3 ranks to choose from for the
other pair. All three ranks have all four cards left so each has
4*3/2=6 ways to arrange the suits. There are 11*10/2=55 ways to
pick the ranks of the other two singletons. 7*6/2=21 ways result in
both singletons from ranks of 4, for 4{circumflex over ( )}2=16
ways to pick the suits. 7*4=28 ways result in one singleton from a
rank of 4 and one from a rank of 3, for 4*3=12 ways to pick the
suits. 4*3/2=6 ways result in both singletons from ranks of 3, for
3{circumflex over ( )}2=9 ways to pick the suits. So the number of
type (2) pairs is 3*6*(21*16+28*12+6*9)=13068. The total number of
pairs is 32388+13068=45456.
[0068] Non-paying hand: There are 47*46*45*44/24=178365 ways to
pick 4 replacement cards out of 47 left in the deck. The total
number of paying combinations is 59691, adding up the totals for
each type of hand. 178365-59691=118674 ways to have a non-paying
hand.
[0069] Table V below summarizes the number of combinations of each
hand and the product of each combination and what it pays under the
9/6 Jacks or Better pay table with maximum coins played, for the
above example.
5TABLE V Hand Pays Probability Combinations Return Combinations
Royal flush 800 1 800 Straight flush 50 2 100 Four of a kind 25 52
1300 Full house 9 288 2592 Flush 6 327 1962 Straight 4 589 2356
Three of a kind 3 4102 12306 Two pair 2 8874 17748 Pair 1 45456
45456 Nothing 0 118674 0 Total 178365 84620
[0070] The expected value of this hand is the return combinations
divided by the probability combinations, or 84620/178365=0.4744. In
other words for each $1 bet the player can expect to get back 47.44
cents. In the case of the player betting 5 quarters this hand is
now worth $1.25*0.4744=59.3 cents.
[0071] The above describes how to calculate the optimal value of a
dealt hand, and an expected value of the way a player plays the
hand. Calculating the player error involves these two values and
can provide the player error, which can then be used for marketing
purposes.
[0072] One way the player error can be calculated is by:
(optimal value of the dealt hand-expected value of played hand)
[0073] The players expected value loss can be calculated by:
(optimal value of the dealt hand-expected value of played
hand)*bet
[0074] In other words, the latter formula is the expected amount
(not necessarily the actual amount) that the casino gains from the
error made by the player. This expected value loss (or even just
the player error) can be stored as "expected value points" for
purposes of tracking and storing. The casino can keep track of the
expected value points, either cumulatively (maintains only a total)
or individually (maintains each entry separately), in a player's
loyalty account (or slot club account), to be explained below in
more detail. Generally, "loyalty account" and "slot club account"
represent the same concept and can typically be used
interchangeably. In this way, the casinos can specially market
incentives, promotions, and other offers to the beginning players
which can compensate them for their mistakes. The more expected
value points a player may accrue, the casino may offer more
incentives, or there may be a greater likelihood of offering an
incentive. Expected value points are basically a measure of a
player's expected loss, and can be calculated in numerous ways.
Expected value points incorporate a computation of the player's
error, but also may incorporate other variables such as the amount
wagered, etc.
[0075] Note that the preferred way of calculating expected value
points are non-fixed numbers which are a measure of the magnitude
of the player's error, a system can alternatively assign fixed (or
discrete) numerical values to a player's error. For example, if a
player plays a hand perfectly it will be scored as a `0`; if a
minor error is made (which falls within a predetermined range of
error or a predetermined categorization of errors) it can be scored
as a `1`; if a major error is made it can be scored as a `2`, or
any such system using any range of discrete values, which then can
be optionally multiplied by a conversion factor. Of course, since
this method has reduced accuracy, it is not the preferred
method.
[0076] Note that if a player chooses not to play the full amount of
coins, on some paytables he will suffer a loss of expected return.
For example, in the paytable in Table I, by playing 5 coins, the
return on a royal flush is disproportionate to the return by
playing 1-4 coins. Therefore, it is of course to the player's
advantage in this case to play all 5 coins. The expected value
point calculation considers the aspect of a player playing less
than 5 coins as well, by calculating the EV for all possible hands.
It is noted that the optimal strategy could be different depending
on the number of coins played, because if less than full coins are
played because the player will not seek royal flushes as
aggressively. The system should preferably know the optimal return
for each of number coins played. Generally, though, the majority of
players play the full number of coins.
[0077] Further, casinos may wish to track or compute just the
(optimal value of the dealt hand-expected value of played hand) or
(1-this value) as a measure of the player's skill level (typically
skill level is independent of amount bet). This can also be
computed by tracking the amount of expected value points and
dividing by the total amount bet. More on skill levels will be
discussed below.
[0078] The choice a player makes regarding the variation of video
poker as well as the paytable offered also affects the player's
return and should ideally also be considered by the casino. For
example, for the variation of video poker known as Deuces Wild, a
paytable known as "full pay" optimally returns 100.77%. Table VI
below illustrates a paytable for full pay deuces wild. This means
that someone who knows the optimal strategy for this paytable of
Deuces Wild can make 0.77% on every bet, on average. On the other
hand, Table VII illustrates an alternative payable of "Deuces
Wild," which returns 98.91% if the player uses optimal
strategy.
6TABLE VI Full Pay Table Coins Bet Hand 1 2 3 4 5 Natural royal
flush 250 500 750 1000 4000 Four deuces 200 400 600 800 1000 Wild
royal flush 25 50 75 100 125 Five of a kind 15 30 45 60 75 Straight
flush 9 18 27 36 45 Four of a kind 5 10 15 20 25 Full house 3 6 9
12 15 Flush 2 4 6 8 10 Straight 2 4 6 8 10 Three of a kind 1 2 3 4
5
[0079]
7 TABLE VII Coins Bet Hand 1 2 3 4 5 Natural royal flush 250 500
750 1000 4000 Four deuces 200 400 600 800 1000 Wild royal flush 25
50 75 100 125 Five of a kind 15 30 45 60 75 Straight flush 9 18 27
36 45 Four of a kind 4 8 12 16 20 Full house 4 8 12 16 20 Flush 3 6
9 12 15 Straight 2 4 6 8 10 Three of a kind 1 2 3 4 5
[0080] A casino would prefer that a player play the version in
Table VII over that in Table VI. This concept also applies across
to other variations of video poker as well (such as "Joker Poker")
which also have their own sets of pay tables and returns. The
casino would prefer that a player play a version of Joker Poker
that pays 94.1% over either of the Deuces wild versions illustrated
in Tables VI and VII. Of course, these return percentages reflect
play at the optimal strategy level. The player's choice of machine
can also be considered a part of the player's "error," as it is in
his interest to choose the machine with the highest return
percentage.
[0081] The expected value point formula given above can be
optionally modified to take into consideration the machine choice.
This formula is as follows:
(optimal strategy house edge+optimal value of the dealt
hand-expected value of played hand)*bet
[0082] Wherein the optimal strategy house edge is the house edge
when the player knows and plays the optimal strategy. This number
is equivalent to (1-optimal player return). Thus, the house edge on
a game that returns 98.91% is 1.09%. Thus, the above formula adds
on the house edge to the player error. The expected value of a
player's play is due to both mistakes by the player and the house
edge, and the above formula accounts for both.
[0083] Alternatively, it is also possible to incorporate the
machine choice without regard for the player's error. This can be
done by computing and storing only the (optimal strategy house
edge*bet). This gives the casino a picture of a player's machine
choice, but not his play. This alternative may be easier to
implement by casinos, because casinos currently maintain a list of
machines with identification numbers, and there is no need to track
actual player decisions. Of course, this system is less powerful
than the above formulas.
[0084] Some casinos typically give a "cash back" allowance on every
video poker bet (i.e. 0.5%). For example, if a player wagers $5 on
a hand of video poker, the player will get 2.5 cents added to his
player loyalty account. A player that plays full pay deuces wild
perfectly (player advantage of 100.77%) with a 0.5% cash back
allowance gets back 1.27% on each bet. Of course, this isn't a very
attractive proposition for the casino. This cash back can also be
worked into the formula for expected value points as follows:
(optimal strategy house edge-cash back percentage+optimal value of
the dealt hand-expected value of played hand)*bet
[0085] Using the above formula to calculate the expected value
points, it is easy for the casino to see if they are, on average,
making or losing money on each game played and how much. All of the
above formulas may be rehashed in different ways but still produce
an identical or comparable result. It should not matter how the
calculation is actually done. Further, the above formula
considering the cash back is the preferred formula to use.
[0086] Each casino typically maintains an electronic list (or
database) of video poker machines (variation and paytable) they
currently carry and an identification number. Such a list should
also include the (optimal) player return for each one. The player
return for each game should already be well known from the game
literature; if not, it can be pre-computed by dealing every
possible combination of cards, playing them optimally, as described
above, and taking the average return. The player return can also be
electronically stored on each machine as well.
[0087] A skill level, as discussed above, can optionally be
computed for each player as well. This number can provide a casino
employee with an idea of a player's skill level or expected return.
One way to compute this is:
1-(sum of expected value points/total amount bet)
[0088] While this calculation is optional, presenting a casino
employee with this data may assist in the casino's evaluation of a
player's abilities. The higher the above calculation is, the
greater a player's skill. For the purposes of the above formula,
any method can be used to calculate the expected value points.
Further, a less preferred method would be to divide the expected
value points by the product of the average bet and total number of
hands instead of the total amount bet, or dividing the total player
error (not considering the wager) by the total number of hands
(these methods can be applied to the alternative formulas below
also). Alternatively, another less preferred method is to just
divide the expected value points by the total number of hands, but
preferably maintaining each coinage separately. Of course,
depending on what information the system stores, other formulas can
be devised which produces equivalent results.
[0089] A player's skill level can be helpful in certain situations.
For example, consider a first player who plays $50,000 in action
and a second player who plays $1,000,000 in action. However, both
players have accumulated the same number expected value points
(i.e. 1000). However, a casino may not value these two players
equally. From the numbers, the second player plays better than the
first (i.e. the second player has a higher expected return).
Therefore, the first player (with the lower expected return) may
receive preferential treatment because he will likely lose more in
the same period of time than the second player. Therefore, a more
informative evaluation of a player's play history could optionally
and preferably take into consideration both his expected value
points and his skill level. Of course, an evaluation can also
merely take into consideration either one of these values as well.
On the other hand, a casino may prefer the second player because
the second player shows more loyalty to the casino. It is entirely
up to the casino to weigh any of the variables discussed herein (or
others) in any way, individually or in combination with other
variables, to determine the players they value.
[0090] A more advanced way of computing a player's skill level
which also takes into consideration the player's machine choice is
as follows:
optimal strategy return-(expected value points/total amount
bet)
[0091] wherein the optimal strategy return is what a machine
returns if a player uses optimal strategy, and is equivalent to
(1-the optimal strategy house edge). Thus, for example, if a player
loses 1% due to errors on a Jacks or Better 9/6 machine which has a
99.54% optimal strategy return, his skill level using the previous
formula would be 98.54%.
[0092] Another way of calculating a player's skill rating which
considers both the player's machine choice and cash back is as
follows:
optimal strategy return+cash back-(expected value points/total
amount bet).
[0093] Thus, if the above described player were to get 0.5% cash
back from the casino on every bet, his skill level would be 99.04%.
The above formula is preferred as it considers the most possible
factors.
[0094] If a player plays different games with different optimal
strategy returns, then a weighted average may be used (for example
one way is to weight each strategy return by the amount bet on that
variation). Further, the preferred and simpler way of computing
skill is the above formula: optimal strategy return-(expected value
points/total amount bet). However, in some cases this may not
practical, for example if the expected value point formula used
takes into consideration a factor not relevant to a skill
determination.
[0095] A player's expected win/loss can also be estimated for a
future session. For example, assuming a casino is reviewing a
player's record and wishes to decide whether to offer him comps or
special incentives to return. The player's future losses per day
may be calculated as follows:
(1-expected return for player)*(average hands per day)*(average
wager)
[0096] The expected return in the above formula can be computed
using the formula given above. Further, the above formula can
optionally be multiplied by the number of days of an expected
visit.
[0097] It is also noted that the above formulas for calculating
expected value points are merely examples, but a number of
alternative formulas can also be used. The general principle is to
generate a number which reflects a player's skill level and/or
correlates to a monetary amount that a beginning player would be
penalized over the long run. It is noted that the player error is
different from the player's win/loss. It is possible that a
beginning player could have a large win yet have a high number of
expected value points. It is also noted that typically the method
does not take into account the player's final hand on the draw.
[0098] A casino may wish to disburse a dollar amount in comps based
on the expected value points. Expected value comps are a dollar
amount and can be computed as follows:
constant*expected value points
[0099] wherein the constant is used to convert expected value
points to an actual dollar amount. The casino may set this constant
at a level of their choosing. Of course, if the conversion to be an
equal one, the constant can be set to 1. A non-linear formula can
also be used. Also, separate "levels" or discrete award amounts can
be used. For example, a casino may issue an award (cash back,
check, etc.) in the amount of $25, $50, $100, etc., wherein the
expected value points (or expected value points*constant) should
fall within respective ranges to earn a respective award
amount.
[0100] Further, the present invention can optionally take into
consideration comps already given based on the standard comp
system. As discussed above, the standard comp system returns an
amount to each player based on their wagers, but not their skill
level. The comp system described herein can work alongside the
current standard comp system. If a player is comped a certain
amount using the standard comp system, a casino may not want to
double comp the player according to expected value points
(depending on formulas used to calculate them). Instead, the comps
the player has already received can be subtracted from his
"expected value comps" (comps based on expected value points).
[0101] One way that a dollar amount of expected value comps to be
disbursed can be computed is as follows:
(constant*expected value points)-standard comps already given
[0102] Wherein, the standard comps already given is a dollar amount
already given based on the current comp system. Thus, the formula
above rewards a player extra above and beyond what he would
normally get for his beginner status. Thus, for example, if a
casino gives a player comp points based on 0.5% cash back, and he
plays $200, the player receives $1 in standard comps. If the player
has also earned $5 in expected value comps due to his error, a
casino may wish to subtract to award the player $5-$1=$4 in extra
comps based on expected value points. A casino may especially wish
to limit comps in this manner if the constant used to convert
expected value points to dollars is high or equal to 1. The
standard comps already given in the above formula can also
optionally be multiplied by a conversion constant. It is further
noted that adjusting the comps between the two types as described
is entirely optional and a casino may or may not wish to do so
depending on their preferences and the way their system is
configured. In some cases, awarding both sets of comps
independently makes sense, in other cases, the award may be too
high without adjusting.
[0103] Further, in another embodiment of the present invention,
standard comp points (based purely on a player's action) can be
aggregated with points based on player error. For example, standard
comp points can be accumulated in the conventional manner. However,
expected value points can also be tracked and accumulated by the
apparatus implementing the game. When the accumulated values (1 or
more) of expected value points exceeds a predetermined number, a
standard comp point or points is added (or "kicked in") to the
player's slot club account, and then the total expected value
points accumulated therein should preferentially be subtracted from
the predetermined number. For example, for every x expected value
points earned (calculated using any formula), y standard comp
points are kicked in to the player. A simpler way of performing
this is to add in 1 standard comp point for every x expected value
points. Carryovers of expected value points can be maintained from
hand to hand.
[0104] Thus, using this method, it is not necessary for the system
to separately store both standard comp points and expected value
points in a player's slot club account. Thus, this method should be
easier to implement than storing both values in a slot club account
database. However, this embodiment is less preferred because it is
not as powerful as having both components stored and available for
viewing and calculations. An optional ratio can also be stored in
the player's slot club account indicated the proportion of comp
points were obtained from expected value points (player error).
[0105] In this manner, a beginning player can be compensated for
his mistakes by using standard comp points. He may or may not know
that he has received extra points due to his errors.
[0106] Combining points based on player error with points based on
gaming action can be done with the following formula:
aggregated comp points=a*standard component+b*error component
[0107] wherein the standard component is any standard formula or
counter used to allocate comps (i.e. constant, wager,
wager*constant, f(wager), etc.), and the error component can be any
of the respective formulas described herein, such as: (optimal
value of the dealt hand-expected value of played hand)*bet. The
coefficients a and b are conversion factors chosen by the casino
based on their own preferences of how much they wish to weight both
variables. One possible choice of coefficients would be a=1 (so the
player always gets his standard comp points) and b=0.1 (where the
player gets 10% of his error converted to comp points), but of
course any choice of coefficients can be used.
[0108] An example of how the above formula can work is as follows.
Suppose a casino routinely gives a player 1 comp point for every $2
bet. Each comp point may for example be equivalent to a penny, but
of course casinos are free to choose values and/or significance of
their comp points. If a=1 and b=0.1, then the player always gets
his standard comp points. In addition, the player also gets
0.1*error (calculated using a formula as per the casinos choosing).
Thus, the player's aggregated total incorporates both points
resulting from his wager (action) as well as points resulting from
his error.
[0109] If a casino aggregates both the standard comp points and the
expected value comp points immediately after play, the casino may
wish to also include a number which represents which portion (or
percentage) of the total points are due to standard comp points (or
expected value comp points). For example, if one aggregate number
is maintained, and a percentage of 30 is also maintained, this
could represent that 30% of the aggregated points are due to
standard comp points (or of course expected value comp points
depending on the nomenclature the casino uses). This ratio (or
percentage, etc) gives the casino more information and allows the
casino to calculate the player's skill as well by separating a
players total into the two components and then using any of the
formulas presented herein to calculate skill.
[0110] The previously described method for aggregating standard
comps and comps based on player error can be computed and
aggregated at the machine level itself immediately after each hand.
However, the two types of points (the standard comp points and the
expected value corn points) can also be stored separately in the
player's slot club account and aggregated at a later time. In this
manner, aggregated comp points can be computed by:
a*standard accumulated comp points+b*expected value comp points
[0111] Wherein, a and b are conversion factor coefficients chosen
by the casino. One possible choice of coefficients is a=1 (so the
player gets full value from his standard comp points) and b=0.1
(the player gets 10% of his expected value comp points converted
into the aggregated amount), but of course the casino is free to
choose coefficients which suit their particular needs.
[0112] Having an aggregated amount of comp points instead of two
separate ones allows a casino employee to deal with one number
representing comp points instead of two separate numbers. This is a
simpler system, although maintaining and making available the two
separate numbers is more powerful because the casino employees have
more information at their disposal. Before aggregating, the casino
may wish to subtract one type of comp from the other (or any
percentage of one from any percentage of the other, etc.)
[0113] It is also noted that casinos may wish to keep the expected
value points shielded from the players, and in this case the
casinos of course can choose to do so as they please. Depending on
a casino's preferences, they can simply aggregate the standard comp
points and expected value comp points (either instantly or later
on), or maintain them separately, and choose to disclose or not
disclose what they wish. Casinos are of course free to use all of
the data described herein in any manner they wish.
[0114] FIG. 4 is a flowchart illustrating a method of calculating
the expected value points according to an embodiment of the present
invention.
[0115] The method starts with operation 400, which calculates the
player error as (optimal value of the dealt hand)-(expected value
of played hand), using the methods described above to calculate
these values.
[0116] The method then proceeds to optional operation 402, which
adds the optimal strategy house edge for the particular machine to
the result in operation 400, as described above.
[0117] From operation 400, the method can proceed to optional
operation 404, which adds the (optimal strategy house edge-cash
back percentage) to the result in operation 400.
[0118] From operations 400, 402, or 404, the method then proceeds
to operation 406, which multiples the previous result times the
current wager. This result comprises the expected value points.
[0119] Or alternatively, the method can begin at (or continue from
any of the other operations) operation 408, which implements an
alternative method (than illustrated in FIG. 4) of computing the
expected value points. The alternative method can incorporate any
method, equation, or concept discussed herein, or any combination
of methods, equations, or concepts discussed herein.
[0120] FIG. 5 is a block diagram illustrating the components used
to implement an improved player tracking system, according to one
embodiment of the present invention.
[0121] A video poker machine 500 is attached to a slot club card
interface unit 502. An error calculating unit 504 receives
particular card and play information from the video poker machine
500 and calculates any of the variables discussed above such as the
expected value loss or expected value points. The error calculating
unit 504 may preferably comprise a software routine running on the
video poker machine 500, alongside or embedded in the video poker
software routine itself. The error calculating unit 504 may exist
as a plug-in on the video poker machine. In other words, the
software which implements the error calculating unit 504 can be
loaded, installed (electronically or physically) or updated to
compliment the main video poker software. Such a modular
architecture allows the present system to be incorporated into
video poker machines easily. The error calculating unit 504 may
also be an external unit (not pictured) attached to the video poker
machine 500, or the error calculating unit 504 may be a part (not
pictured) of the slot club interface unit 502.
[0122] The slot club interface unit 502 comprises a card reader 506
which receives a player's slot club card and is able to
electronically read the player's account identification from the
card. The slot club interface unit 502 also comprises a connection
unit 508 communicating between the slot club interface unit 502 and
the video poker machine 502. The slot club interface unit 502 also
comprises a casino communication unit 510 which communicates player
information, including but not limited to the player error, to the
casino database 516. The slot club interface unit 502 also
comprises a processing unit (not pictured) which communicates with
and controls the operations of the components therein. The
processing unit receives data from the video poker machine 500 and
calculations output from the error calculating unit 504, receives
account data from the card reader 506, and sends this data to the
casino communication unit 510 so that the data can be stored in the
player's slot club account.
[0123] The casino communication unit 510 can also comprise an
optional but preferable floating point (FP) unit 512. The FP unit
512 is capable of performing and storing floating point
calculations and transmitting a floating point number to the casino
database 516 using any standard floating point number transmission
protocol. The FP unit can exist as a separate unit and also/or be
distributed throughout the system where floating point calculations
are needed. Communication between the casino communication unit 510
and the casino database 516 is done via a computer communications
network, such as a LAN. Currently, any standard comp point amount
sent through such a casino communications network is an integer
value, or just a bit indicated a single point has been earned. In
the present invention, by using the floating point unit 512, the
slot club interface unit 502 is able to transmit floating point
numbers to the casino database 516 using the casino communication
unit 510. The casino database 516 may also have a floating point
unit 512 which can receive/decode floating point numbers from the
LAN (or other communications network) and then update a player's
respective account using the floating point number. Using such a
floating point unit(s) results in greater accuracy when
transmitting expected value points (and related information) to the
casino database 516.
[0124] If no such floating point unit (or capability) exists,
floating point numbers may still be rounded or transmitted by using
an integer representation of the floating point number. This can
comprise multiplying the number by 100 and transmitting the number
as an integer. Further, an integer method could be used wherein
each 1% of a penny (or other denomination) counts as a "subpoint."
Subpoints are accumulated, and when the subpoint total reaches 100,
a regular penny is added to the expected value points and 100 is
subtracted from the subpoints. On a high denomination machine, the
subpoints may exceed 100 by a factor of several times; in this
case, then int(subpoints/100) is added to the expected value
points, and the subpoints are adjusted to equal mod (subpoints,
100).
[0125] The casino database 514 (can comprise a single or networked
databases) typically stores a record for each casino player that
has a slot club player account (or "player loyalty account.") This
record includes all kinds of information about the player,
including his name, address, playing history, etc. The record also
stores information regarding the calculated player error. A casino
marketing computer 516 can access the casino database 516 in order
to make intelligent marketing decisions for particular players
considering their player error.
[0126] The components in FIG. 5 typically operate as follows: A
player puts his slot club card into the slot club card reader 506.
The slot club card reader 106 reads the card and identifies the
player's account in the database 516. The player completes a hand
of video poker on the video poker machine 500. The error
calculating unit 504 calculates the player error (or any other
measure as discussed above), and transmits this information (and
any other standard prior art information) using the connection unit
508 to the slot club interface unit 502. The slot club interface
unit 502 transmits the information to the casino database 516 using
the casino communication unit 510.
[0127] Therefore, as a result of the above system, the casino
management, having access to the casino database using the casino
marketing computer 516, now has a record which represents
information regarding the skill of players and/or a representation
of the player's losses due to his errors, and any other value
disclosed herein. This skill information can be used numerous ways
in marketing efforts, promotions, and incentives, etc., which will
be discussed in more detail below.
[0128] Further, when different types of comp points (expected value
points and standard comp points) are maintained (as discussed
above) and transmitted separately, the casino communication unit
510 can transmit these types of comps separately to the casino
database 514. A header can be used (a just a bit or byte)
identifying the type of comp (i.e. expected value, standard, etc.),
and it can then be transmitted. Thus, if two types of comps are
maintained, two transmissions can be executed for each update.
Alternatively, data can be transmitted once which combines both
types of comps into one data group (or record), for example a first
byte is a standard comp amount and a second byte is an expected
value comp amount. Expected value comp points are typically
calculated in the error calculating unit 504, although other units
may calculate this as well. Standard comp points can be computed by
a standard comp computing unit (not pictured) within the video
poker machine 500, or else computed by other units as well, such as
a unit within the slot club interface unit 502. Typically, an
expected value comp point amount is a floating point number while a
standard comp point amount is an integer, although any combination
of floating point/integer can be used for each type of comps.
[0129] The above described methods and apparatus store a players
expected value points and possibly additional information (which
can include any of the variables or computations discussed herein),
in addition to the standard information, in the player's loyalty
account.
[0130] FIG. 6 is a diagram of a database record, according to one
embodiment of the present invention.
[0131] A database 600 stores a player record 602 for each player in
the casino database 516. The player record 602 comprises standard
information 604 which is currently stored in a player's loyalty
account. Such information may comprise player name, address,
birthdates, standard comp points accumulated, etc.
[0132] The player record 602 also comprises an expected value
information 606 which can comprise any combination of expected
value points (as computed using any of the above formulas),
individual bets made, total bets made, machine choice (either type
of machine or expected return of optimal play on machine) and any
other value discussed herein. Expected value information is
information that relates to a player's play and includes
information that can be used to determine a player's skill as well
as his expected win/loss if this player were to return. Any entries
in the player record can comprise floating point data for greater
accuracy. The expected value points (and other related information)
may be stored as an integer but preferably as a floating point
number.
[0133] The expected value information 606 is typically not shared
with the players (although it can be at the casino's choice). The
expected value information 606 is for the casino staff/management
to review (either automatically or manually) to decide upon
promotions or incentives to the players (discussed more below).
[0134] If the casino chooses to aggregate to the types of points at
the onset without separating them, then one aggregate value (not
pictured) need be stored in the record instead of both.
[0135] The information stored regarding the expected value (and any
other information discussed herein) can be used in numerous ways to
market to beginning or desirable players. Beginning players can
receive and appreciate special offers which the experienced player
may not receive. Such targeted marketing should ideally also
increase house profits as well.
[0136] Such offers, marketing, or incentives can comprise offering
free or discounted rooms or food, offering cash back upon return to
the casino, sending targeted, advertisements for the casino,
offering discounts on gift shop items or shows, gift certificates
that can be used for any of the above, or any other standard way a
casino may attempt to attract players. A casino may also send a
check back to a player based on his expected value points.
[0137] Another way of providing an incentive would be to issue a
check cashable only at the casino or specified group of casinos (so
the player must visit) or credit a player's slot club account
electronically with "playable money." U.S. Pat. No. 6,244,958
teaches how a player's slot club account can actually store
playable money to be used for wagering (note that this is different
than comp points). A casino that wishes to market to a desirable
play based on criteria discussed herein can credit a player's
account with an amount of money (may be based on expected value
information, such as a fraction of expected value points
earned).
[0138] FIG. 7 is a flowchart illustrating a method of selective
marketing, according to one embodiment of the present
invention.
[0139] The method starts with operation 700, which cycles through
all active player accounts.
[0140] The method then proceeds to operation 702, which selects
certain player accounts according to standard criteria. Casinos
typically do not market to everyone, but select certain criteria,
such as amount of action, date since last visit, etc. A casino's
standard criterion and any other prior art procedures can be
implemented here.
[0141] From operation 702, the method proceeds to operation 704,
which selects player accounts based on marketing criteria. The
selection is done against pre-selected marketing criteria. For
example, the casino management may choose as a marketing criterion
that players should show a skill level (expected player return)
below 98%. Alternatively, a casino may prefer players who have
expected value points greater than a predetermined number. The
casino may also estimate an average daily loss for the player, and
if this loss exceeds a predetermined amount the player may be
offered a promotion. The marketing criteria can include expected
value points, standard points, an aggregated value, or any other
combination the casino chooses.
[0142] More than one criterion can be used as well. For example, a
casino can choose as marketing criteria all players with a skill
below a certain level and with standard comp points (or expected
value comps, or aggregated comps, etc.) above a certain level.
[0143] Ideally, the casino should determine based on their specific
data which set of marketing criteria will result in the most
profits. Any of the numbers, variables, and calculations described
herein can be compared to fall within or outside of predetermined
range(s) in order to qualify for additional marketing efforts.
[0144] From operation 704, the method proceeds to operation 706,
which markets to the selected players. The special marketing may
comprise any of the ways discussed herein, or any other known in
the art.
[0145] A casino may offer a credit to players for any of the above
based on the expected value points. For example, if a player's
expected value points in the player's loyalty account indicate that
a player lost $100 due to player error, the casino may offer the
player complimentaries based on this amount.
[0146] Casinos can issue an award amount based on either standard
comp points, expected value comp points (which can be computed as
either any formula for expected value points optionally multiplied
by a constant) or a combination of the two types of points (or
concepts). The awarded amount can be computed by converting the
respective comp amount (standard comps, expected value comps,
aggregated comps) to a dollar amount, for example by multiplying by
a constant (1 can be used for an even conversion from comp points
to dollars). A dollar amount award can further be optionally
reduced/increased by multiplying by or adding/subtracting a
constant. An award can also be adjusted to be a fixed selected
amount (i.e. $25, $50, $75, $100, or any number), by checking a
range for the fixed amounts and awarding the fixed amount that
corresponds to the respective range the award amount falls between.
This may be done so a player would not get an award (such as a
check) for an odd amount, such as $23.28, in which the player may
wonder how the amount was determined. For example, if a player's
expected value points=98, and the conversion factors used to
convert this to dollars is 1, the player can get an award of $98. A
casino may optionally wish to reduce this amount by multiplying by
0.75, resulting in $73.5. The casino may further wish to subtract
$5 from this award, resulting in $68.5. Lastly, the casino can
optionally convert this to an even amount of $75. Again, casinos
are free to choose parameters to suit their marketing
preferences.
[0147] For example, in an embodiment of the present invention, if a
player has earned what amounts to $20 in standard comp points and
$50 in expected value comp points, the casino may wish to award the
player $20+$50=$70 in general comps. Alternatively, the casino may
wish to typically restrict certain awards to certain type of comps.
For example, the casino may wish to issue checks to be cashed at
the casino only based on expected value points (or use the expected
value points for the sole purpose of issuing checks). Thus, in this
case, the casino would award this player $20 in general comps but
send a $50 check to the player. Similarly, a casino may wish to
issue discounts on hotel rooms based on expected value points, but
apply standard comp points to food and beverage. Casinos are free
to mix, match, configure, and use these systems in any manner they
wish to suit their preferences. Further, any measure of comp points
(i.e. standard comp points, expected value comps, and aggregated
points (either aggregated immediately or later on) can be used in
any manner described herein.
[0148] Once comp points are used they are typically subtracted from
the player's account. Any kind of comp points may also expire after
a predetermined amount of time, at the casinos option.
[0149] Sometimes a manual review of a player's player (or loyalty)
account is performed. This may occur when a player calls a casino
to ask for complimentaries. In this case, a special display can be
produced for a player which includes expected value information as
described above.
[0150] Casinos can also maintain a separate list of preferred
players based on their characteristics. For example, such a list
may contain players with expected value points over a predetermined
amount, or any other combination of criteria. The list may be
shared with other casinos.
[0151] FIG. 8 is an illustration of an example of a display,
according to one embodiment of the present invention.
[0152] Player information 800 is displayed which includes standard
information such as player name, address, birthdates, etc, standard
comp points (generally based on the number and average amount of
the player's wagers) and any other standard information that a
player tracking program may currently keep which may also include a
player's win/loss.
[0153] Alongside the player information is expected value
information 802. The expected value information can comprises the
player's expected value points, the total amount bet, average bet,
total hands played, and the player's expected return. The player's
expected return can be computed using any of the above formulas,
such as (1-(expected value points/total amount bet). The expected
value information is information which the casino personnel could
use in making their decision whether this player is deserving of
additional incentives, comps, and/or promotions etc. This
information can be used alone or in conjunction with the standard
comp points which are typically kept by casinos. The expected value
points may also be considered as the comps available. Alternatively
another "expected value points comps" entry can be displayed (not
pictured) which displays the comp amount available based on
expected value points, the comp amount available computed using any
method such as those discussed herein.
[0154] The player's comps given 804 can also be displayed. This can
be broken down into separate comps given based on the expected
value points and standard points (as pictured). Ideally, an amount,
date, and use for these comps is also displayed, as well as any
other information useful a casino employee. Alternatively, if the
casino uses an embodiment wherein comps are aggregated but not
separated into components (i.e. standard, expected value), then the
type of comp (i.e. standard, expected value) will not be needed in
the display.
[0155] In the embodiment of the present invention described herein
wherein comps are computed based on action and error, and these
comps are aggregated into a single comp amount, then this single
amount can be presented to the casino employee (not pictured), in
place of or in addition to the comps available amount display for
each of the components. For example, the display in FIG. 8 can also
display (not pictured), "aggregated comp points: 68.4" (assuming
the conversion is a simple addition of points but not
weighted).
[0156] The display in FIG. 8 can also optionally display all the
different types of comp points in terms of dollar amounts as well,
this would typically done if a conversion is needed from points to
dollars for any of the types of points.
[0157] If the points based on action and error are aggregated into
one value immediately upon play, if the ratio is maintained (as
discussed above), the data can then be split into its components to
display both sets.
[0158] Of course, a display according to the present invention may
include any combination of the above information or additional
information (whether described herein or elsewhere) as needed.
[0159] It is also noted that the expected value points and related
information would typically not be automatically presented to the
player, as this information is typically used for casino marketing
purposes. The player can check his/her total standard points by
inserting his/her card into most slot machines, which indicate
total standard points in a small display by the card reader. On the
other hand, a casino employee may mention the expected value points
at their discretion, for example if questioned by a casino patron
about why their comps were at the level they were at.
[0160] In an additional embodiment, expected value points may
expire after a certain time. For example, if a certain amount of
time goes by, comps based on the expected value points are no
longer able to be utilized by the player.
[0161] Also, the present invention can identify "advantage"
players, either automatically or by a casino employee upon
reviewing a player's record. An advantage player can be defined as
a player who plays at an expected return high enough that the
casino does not care for his business, and may take such action as
eliminating cash back points, prohibiting play games vulnerable to
a player advantage, or barring from casino property. As stated
above, some variations/paytables of video poker may have a high
expected return. If a casino offers a full pay deuces wild game,
and also offers a player 0.5% cash back on all bets, a player that
plays optimal strategy will have an expected return of 101.27
(including cash back). A player that bets large denominations and
plays very quickly can theoretically beat the house for a sizable
amount of money in the long run. The present invention can identify
advantage players by their skill level (as discussed above). Once
identified, a casino may choose to reduce or not issue comps at all
to such players, or even bar them. One way an expert player can be
identified as follows:
expected total return>a predetermined expert return,
and the total number of hands>a predetermined sample of
hands
[0162] Wherein the expected total return is the expected amount
that the player should have received from his wagers, which can
also take into consideration cash back by the casino. Note that
this is not the actual amount, as the method is not concerned with
the player's actual losses. A preferred formula for expected total
return for use in this case is:
expected total return=optimal strategy return+(total cash
back/total amount bet)-(expected value loss/total amount bet)
[0163] The above formula results in a value of 100% when the player
is playing even with the house, and over 100% when the player is
playing at an advantage. Note that if the player plays different
versions of a game with different optimal strategy house edges,
then a weighted average can be used for the optimal strategy house
edge.
[0164] A preferred predetermined expert return is 100%, although
other returns can be used as well, for example the casino may allow
a player to return 100.1% before labeling him an advantage
player.
[0165] The predetermined sample of hands is used so that a player
isn't labeled an advantage player if he plays a number of hands
which isn't a large enough sample of his play. A preferred
predetermined sample of hands is 1000, although of course the
casino can set this amount as to their preferences.
[0166] An alternative formula to that can be used to identify an
advantage player is:
(expected value points/total amount bet)<a predetermined expert
threshold
and the total number of hands>a predetermined sample of
hands
[0167] Wherein the predetermined expert threshold is set by the
casino but can preferably be zero (equivalent to 100 in the
previous methodology), and the expected value point formula can be
any logical formula including the ones described above, but
preferably uses the formula which incorporates the cash back.
[0168] FIG. 9 illustrates a flowchart of one method of identifying
an advantage player, according to an embodiment of the present
invention.
[0169] The method starts with operation 900, which checks to see if
(the expected total return/total amount bet)>greater than a
predetermined threshold. If not, the method proceeds to operation
906 wherein the player is not identified as an advantage player
(i.e. identified as a non-advantage player) and the method
terminates.
[0170] If the check in operation 900 results in a positive result,
the method proceeds to operation 902 which checks to see if the
number of hands played>predetermined number of hands. If not,
the method proceeds to operation 906 wherein the player is not
identified as an advantage player (i.e. identified as a
non-advantage player) and the method terminates.
[0171] If the check in operation 902 results in a positive result,
the method then proceeds to operation 904 which identifies the
player as an advantage player.
[0172] Further, the invention is not limited to video poker. The
same methods/embodiments described herein can also be used for
blackjack as well, either electronic or table based. Of course, if
the blackjack game is table based, an input mechanism must be used
to enter the cards dealt and the player's play. Cards may be
scanned electronically by a video camera and inputted into the
system electronically and automatically.
[0173] For blackjack, a table of the optimal value of a dealt hand
and an expected value of a dealt/played hand can be found on the
Internet or in blackjack literature such as Professional Blackjack,
Fourth Edition, by Stanford Wong, pages 302-333. These values can
simply be substituted in the formulas above to implement the
present invention. Hence the figures herein (except for FIGS. 2 and
3, which aren't needed for blackjack) can be applied to a blackjack
game as well. Also, "machine choice" in the above context of video
poker can be substituted by the version of blackjack the player
chooses to play (i.e. "Spanish 21," "Double Exposure," etc.) since
each of these variations have different optimal returns. The
variation of blackjack game played (like the variation of video
poker played) can also be stored in the player's slot club
account.
[0174] The methods/embodiments described herein can also be applied
to other games of skill as well, such as Pai Gow Poker, 3 Card
Poker, Carribean Stud Poker, and any game where there is a
mathematical way of playing each hand.
[0175] In another embodiment of the present invention, the
invention can also be applied to Internet casinos. Internet casinos
are casinos which use a server to generate random numbers and
transmit hand comprising values of cards (or dice, etc.) to a
client computer, wherein a player can play casino games on the
client computer for real money. The internet casino may wish to
email special offers to players based on their expected value
points or skill level. Such special offers can include bonus money
which can automatically or manually be placed in the player's
gaming account. A player's gaming account is an account which
stores an amount representing real money which a player owns and
uses to play with.
[0176] It is noted that generally, comp points may represent a "raw
form" while dollar amounts are actual monetary amounts. In some
cases, casinos may implement systems wherein one point=one dollar,
and thus these terms may be used interchangeably. In other cases, a
conversion between these two concepts (for some or all of types of
comp points) may be needed an implemented by multiplying/dividing
by a conversion factor or putting the subject for conversion into a
formula.
[0177] It is also noted that any and/or all of the above
embodiments, configurations, variations of the present invention
described above can mixed and matched and used in any combination
with one another. Any claim herein can be combined with any others
(unless the results are nonsensical). Further, any mathematical
formula given above also includes its mathematical equivalents, and
also variations thereof such as multiplying any of the individual
terms of a formula by a constant(s) or other variable.
[0178] Moreover, any description of a component or embodiment
herein also includes hardware, software, and configurations which
already exist in the prior art and may be necessary to the
operation of such component(s) or embodiment(s).
[0179] The many features and advantages of the invention are
apparent from the detailed specification and, thus, it is intended
by the appended claims to cover all such features and advantages of
the invention that fall within the true spirit and scope of the
invention. Further, since numerous modifications and changes will
readily occur to those skilled in the art, it is not desired to
limit the invention to the exact construction and operation
illustrated and described, and accordingly all suitable
modifications and equivalents may be resorted to, falling within
the scope of the invention.
8APPENDIX A // (c) Michael Shackleford, The Wizard of Odds // This
routine illustrates calculating the number of possible ranks for a
given hand using // the formulaic approach, for 1 card held. The
other scenarios can be done similarly. // There is already a matrix
call "indeck" that holds the distribution of the remaining // deck.
The r and s that get passed are the rank and suit of the one card.
Ranks are // numbered 0 to 12. The totals hold the number of
combinations of each hand. Total[9] // is for royal flushes, and so
on down. void fast1(int r, int s, int total[]) { int
i,j,k,l,numcom; if (r>=4) if (r!=12)
total[8]+=indeck[r-4][s]*indeck[r-3][s]*indeck[r-2][s]*-
indeck[r-1][s]; else total[9]=indeck[r-4][s]*indeck[r-3][s]*-
indeck[r-2][s]*indeck[r-1][s]; if ((r>=3)&&(r<=11))
if (r!=11)
total[8]+=indeck[r-3][s]*indeck[r-2][s]*indeck[r-1][s]*ind-
eck[r+1][s]; else total[9]=indeck[r-3][s]*indeck[r-2][s]*ind-
eck[r-1][s]*indeck[r+1][s]; if ((r>=2)&&(r<=10)) if
(r!=10) total[8]+=indeck[r-2][s]*indeck[r-1][s]*indeck[r+1][s]*ind-
eck[r+2][s]; else total[9]=indeck[r-2][s]*indeck[r-1][s]*ind-
eck[r+1][s]*indeck[r+2][s]; if ((r>=1)&&(r<=9)) if
(r!=9) total[8]+=indeck[r-1][s]*indeck[r+1][s]*indeck[r+2][s]*inde-
ck[r+3][s]; else total[9]=indeck[r-1][s]*indeck[r+1][s]*inde-
ck[r+2][s]*indeck[r+3][s]; if (r<=8) if (r!=8)
total[8]+=indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]*indeck[r+4][s];
else total[9]=indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]*ind-
eck[r+4][s]; if (r==12) total[8]+=indeck[0][s]*indeck[1][s]*-
indeck[2][s]*indeck[3][s]; else if (r==0)
total[8]+=indeck[12][s]*indeck[1][s]*indeck[2][s]*indeck[3][s];
else if (r==1) total[8]+=indeck[12][s]*indeck[0][s]*indeck[2][s]*i-
ndeck[3][s]; else if (r==2) total[8]+=indeck[12][s]*indeck[0-
][s]*indeck[1][s]*indeck[3][s]; else if (r==3)
total[8]+=indeck[12][s]*indeck[0][s]*indeck[1][s]*indeck[2][s]; if
(r>=4) total[4]+=indeck[r-4][4]*indeck[r-3][4]*indeck[r-2][4]*i-
ndeck[r-1][4]; if ((r>=3)&&(r<=11))
total[4]+=indeck[r-3][4]*indeck[r-2][4]*indeck[r-1][4]*indeck[r+1][4];
if ((r>=2)&&(r<=10))
total[4]+=indeck[r-2][4]*indeck[r-1-
][4]*indeck[r+1][4]*indeck[r+2][4]; if
((r>=1)&&(r<=9))
total[4]+=indeck[r-1][4]*indeck[r+1][4]*indeck[r+2][4]*indeck[r+3][4];
if (r<=9) total[4]+=indeck[r+1][4]*indeck[r+2][4]*indeck[r-
+3][4]*indeck[r+4][4]; if (r==12) total[4]+=indeck[0][4]*ind-
eck[1][4]*indeck[2][4]*indeck[3][4]; else if (r==0)
total[4]+=indeck[12][4]*indeck[1][4]*indeck[2][4]*indeck[3][4];
else if (r==1) total[4]+=indeck[12][4]*indeck[0][4]*indeck[2][4]*i-
ndeck[3][4]; else if (r==2) total[4]+=indeck[12][4]*indeck[0-
][4]*indeck[1][4]*indeck[3][4]; else if (r==3)
total[4]+=indeck[12][4]*indeck[0][4]*indeck[1][4]*indeck[2][4];
total[4]-=(total[8]+total[9]); if (indeck[13][s]==12) total[5]=495;
else if (indeck[13][s]==11) total[5]=330; else if
(indeck[13][s]==10) total[5]=210; else if (indeck[13][s]==9)
total[5]=126; else if (indeck[13][s]==8) total[5]=70;
total[5]-=(total[8]+total[9]); /* four of a kind */ for (i=0;
i<=12; i++) { if ((i!=r)&&(indeck[i][4]==4)) total[7]++;
if ((i!=r)&&(indeck[r][4]==3)) total[7]+=indeck[i][4]; } /*
full house */ for (i=0; i<=12; i++) { if (i!=r) { if
(indeck[r][4]==3) { if (indeck[i][4]==4) total[6]+=30; else if
(indeck[i][4]==3) total[6]+=12; else if (indeck[i][4]==2)
total[6]+=3; } else if (indeck[r][4]==2) { if (indeck[i][4]==4)
total[6]+=14; else if (indeck[i][4]==3) total[6]+=5; else if
(indeck[i][4]==2) total[6]++; } else if (indeck[r][4]==1) { if
(indeck[i][4]==4) total[6]+=4; else if (indeck[i][4]==3)
total[6]++; } } } /* three of a kind */ for (i=0; i<=11; i++) {
for (j=i+1; j<=12; j++) { if ((i!=r)&&(j!=r)) { if
(indeck[i][4]==4) total[3]+=4*indeck[j][4]; else if
(indeck[i][4]==3) total[3]+=indeck[j][4]; if (indeck[j][4]==4)
total[3]+=4*indeck[i][4]; else if (indeck[j][4]==3)
total[3]+=indeck[i][4]; if (indeck[r][4]==3)
total[3]+=(3*indeck[i][4]*indeck[j][4]); else if (indeck[r][4]==2)
total[3]+=(indeck[i][4]*indeck[j][4]); } } } /* two pair */ for
(i=0; i<=11; i++) { for (j=i+1; j<=12; j++) { if
((i!=r)&&(j!=r)) { if
((indeck[i][4]==2)&&(indeck[j][4]==2)) { total[2]++;
total[2]+=(indeck[r][4]*4); } else if
((indeck[i][4]==2)&&(indeck[j][4]==3)) { total[2]+=3;
total[2]+=(indeck[r][4]*9); } else if
((indeck[i][4]==3)&&(indeck[j][4]==2)) { total[2]+=3;
total[2]+=(indeck[r][4]*9); } else if
((indeck[i][4]==2)&&(indeck[j][4]==4)) { total[2]+=6;
total[2]+=(indeck[r][4]*16); } else if
((indeck[i][4]==4)&&(indeck[j][4]==2)) { total[2]+=6;
total[2]+=(indeck[r][4]*16); } else if
((indeck[i][4]==3)&&(indeck[j][4]==3)) { total[2]+=9;
total[2]+=(indeck[r][4]*18); } else if
((indeck[i][4]==3)&&(indeck[j][4]==4)) { total[2]+=18;
total[2]+=(indeck[r][4]*30); } else if
((indeck[i][4]==4)&&(indeck[j][4]==3)) { total[2]+=18;
total[2]+=(indeck[r][4]*30); } else if
((indeck[i][4]==4)&&(indeck[j][4]==4)) { total[2]+=36;
total[2]+=(indeck[r][4]*48); } else if
((indeck[i][4]==1)&&(indeck[j][4]==4))
total[2]+=(indeck[r][4]*6); else if
((indeck[i][4]==1)&&(indeck[j][4]==3))
total[2]+=(indeck[r][4]*3); else if
((indeck[i][4]==1)&&(indeck[j]- [4]==2))
total[2]+=(indeck[r][4]); else if
((indeck[i][4]==4)&&(indeck[j][4]==1))
total[2]+=(indeck[r][4]*6); else if
((indeck[i][4]==3)&&(indeck[j][4]==1))
total[2]+=(indeck[r][4]*3); else if
((indeck[i][4]==2)&&(indeck[j]- [4]==1))
total[2]+=(indeck[r][4]); } } } /* pair */ for (j=0; j<=10; j++)
for (k=j+1; k<=11; k++) for (l=k+1; l<=12; l++) if
((r!=j)&&(r!=k)&&(r!=l)) { if (r>=9)
total[1]+=(indeck[r][4]*indeck[j][4]*- indeck[k][4]*indeck[l][4]);
if (j>=9) { if (indeck[j][4]==4) numcom=6; else if
(indeck[j][4]==3) numcom=3; else if (indeck[j][4]==2) numcom=1;
else numcom=0; total[1]+=(numcom*indeck[k][4]*indeck[l][4]); } if
(k>=9) { if (indeck[k][4]==4) numcom=6; else if
(indeck[k][4]==3) numcom=3; else if (indeck[k][4]==2) numcom=1;
else numcom=0; total[1]+=(numcom*indeck[j][4]*indeck[l][4]); } if
(l>=9) { if (indeck[l][4]==4) numcom=6; else if
(indeck[l][4]==3) numcom=3; else if (indeck[l][4]==2) numcom=1;
else numcom=0; total[1]+=(numcom*indeck[j][4]*indeck[k][4]); }}
total[0]=178365; for (i=1; i<=9; i++)total[0]-=total[i]; }
* * * * *