Note: Descriptions are shown in the official language in which they were submitted.
CA 02278949 1999-07-23
2
SLOT MACHINE WITH
COLLECTION-BASED AWARD FEATURE
FIELD OF THE INVENTION
The present invention relates generally to gaming machines and, more
particularly, to a bonus game for a gaming machine.
BACKGROUND OF THE INVENTION
Gaming machines, such as slot machines, video poker machines and the like,
have been a cornerstone of the gaming industry for several years. Generally,
the
popularity of such machines with players is dependent on the likelihood (or
perceived
likelihood) of winning money at the machine and the intrinsic entertainment
value of the
machine relative to other available gaming options. Where the available gaming
options
include a number of competing machines and the expectation of winning each
machine is
roughly the same (or believed to be the same), players are most likely to be
attracted to
the most entertaining and exciting of the machines. Shrewd operators
consequently
strive to employ the most entertaining and exciting machines available,
because such
machines attract frequent play and hence increase profitability to the
operator.
Accordingly, in the competitive gaming machine industry, there is a continuing
need for
15 gaming machine manufacturers to produce new types of games, or enhancements
to
existing games, which will attract frequent play by enhancing the
entertainment value
and excitement associated with the game.
One concept which has been successfully employed to enhance the entertainment
value of a game is the concept of a "secondary" or "bonus" game which may be
played in
20 conjunction with a "basic" game. The bonus game may comprise any type of
game,
either similar to or completely different from the basic game, which is
entered upon the
occurrence of a selected event or outcome of the basic game. The bonus game
concept is
the subject of U.S. patent application serial no. 08/835,840 [hereinafter "the
'840
application"], filed April 23, 1997, assigned to the assignee of the present
invention and
25 incorporated herein by reference. The '840 application discloses an
embodiment wherein
the basic game is a reel-type slot machine and the bonus game is a simulated
reel-type
slot machine implemented on a dot-matrix display. The bonus game is entered
upon the
appearance of a special symbol combination on the reels of the slot machine in
the basic
CA 02278949 1999-07-23
3
game. Generally, bonus games produce a significantly higher level of player
excitement
than the basic game because they provide a greater expectation of winning than
the basic
game and are accompanied with more attractive or unusual video displays and/or
audio.
Because the bonus game concept offers tremendous advantages in player appeal
and excitement relative to other known games, and because such games are
attractive to
both players and operators, there is a continuing need to develop new types of
bonus
games to satisfy the demands of players and operators. Preferably, such new
bonus
games will maintain, or even further enhance, the level of player excitement
offered by
bonus games heretofore known in the art. The present invention is directed to
satisfying
these needs.
SUMMARY OF THE INVENTION
In accordance with one aspect of the present invention, there is provided a
slot
machine for playing a game of chance having a collection-based award system.
The slot
machine is operable in a bonus round consisting of a fixed number of spins.
The outcome
of each spin is randomly selected under processor control. A display means is
provided for
displaying a number of symbol groups representing the outcome of the spins.
The symbol
groups include various collection symbols and standard symbols. A symbol group
evaluation means associated with the processor both identifies the numbers) of
collection
symbols displayed in the bonus round and determines whether any combinations
of
2o standard symbols defining a standard winning combinations occurs in the
bonus round. A
valuation means associated with the processor determines collection payoff
values of the
collection symbols displayed in the bonus round and determines standard payoff
values of
any standard winning combinations occurring in the bonus round. A summation
means
associated with the processor adds the collection payoff values and standard
payoff values
to define a bonus round payoff value, and a payoff means associated with the
processor
awards the bonus round payoff value to a player.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and other advantages of the invention will become apparent upon
reading the following detailed description and upon reference to the drawings
in which:
CA 02278949 1999-07-23
4
FIG. la is a simplified illustration of a spinning reel slot machine with dot
matrix
display on which the present invention may be implemented;
FIG. lb is a block diagram of a control system for the slot machine of FIG.
la;
FIG. 2 is an illustration of three reel strips which may be placed on the
reels of
the slot machine of FIG. 1 to implement the present invention;
FIG. 3a through 3c is a table identifying various symbol combinations which
may
occur in a basic game or bonus game using the reel strips of FIG. 2 according
to one
embodiment of the present invention;
FIG. 4 is a table summarizing payoffs, probabilities and expected values
associated with the occurrence of the combinations identified in FIG. 3 in a
basic game
according to one embodiment of the present invention;
FIG. 5 is a flow diagram identifying various steps in implementation of a
bonus
game with a collection-based award feature according to one embodiment of the
present
invention;
FIG. 6 is a table summarizing payoffs, probabilities and expected values
associated with the occurrence of the standard winning combinations identified
in FIG. 3
in a bonus game according to one embodiment of the present invention;
FIG. 7 is a table identifying various bonus game collection symbols which may
appear in a bonus game according to one embodiment of the present invention;
and
FIG. 8 is a table summarizing payoffs, probabilities and expected values
associated with the occurrence of the bonus game collection symbols identified
in FIG. 7
in a bonus game according to one embodiment of the present invention.
While the invention is susceptible to various modifications and alternative
forms,
specific embodiments have been shown by way of example in the drawings and
will be
described in detail herein. However, it should be understood that the
invention is not
intended to be limited to the particular forms disclosed. Rather, the
invention is to cover
all modifications, equivalents, and alternatives falling within the spirit and
scope of the
invention as defined by the appended claims.
DESCRIPTION OF SPECIFIC EMBODIMENTS
Turning now to the drawings and refernng initially to FTG. 1 a, there is
depicted a
slot machine 10 on which the present invention may be implemented. The slot
machine
CA 02278949 1999-07-23
10 is operable in a basic mode to play a "basic" slot machine game and in a
bonus mode
to play a "bonus" or secondary game. The slot machine 10 includes a display
window 12
through which a player may observe three spinning reels, 14, 16 and 18. The
slot
machine further includes a video display 24 for displaying various graphics
associated
5 with the basic game and/or bonus game. The video display 24 may comprise a
dot
matrix, CRT, LED, electro-luminescent display or generally any type of video
display
known in the art. In one embodiment, the basic game is implemented on the
reels 14, 16,
18, whereas the bonus game is implemented both on the reels 14, 16, 18 and the
video
display 24. It will be appreciated, however, that the basic game and/or the
bonus game
may be implemented entirely in video.
FIG. lb is a block diagram of a control system suitable for operating the slot
machine 10 of FIG. la. Coin/credit detector 38 signals a processor 40 when a
player has
inserted a number of coins or played a number of credits. Then, after the
player has
activated a switch 42 (e.g., by pulling lever 20 or pushing a button), the
processor 40
initiates basic game play by setting reels 14, 16, 18 in motion, randomly
selecting a stop
position of the reels 14, 16, 18 and, using technology well known in the art,
causing a
reel motor and step controller 44 to stop the reels 14, 16, 18 at the selected
stop position.
A rotational position detector 46 provides feedback to the processor 40 to
ensure that the
reels 14, 16, 18 are stopped at the correct stop position. The symbols
displayed on the
reels at the preselected stop position define the basic game outcome.
A system memory 48 stores control software, operational instructions and data
associated with the slot machine 10. In one embodiment, the memory 48
comprises a
separate read-only memory (ROM) and battery-backed random-access memory (RAM).
However, it will be appreciated that the memory 48 may be implemented on any
of
several alternative types of memory structures or may be implemented on a
single
memory structure. A payoff mechanism 50 is operable in response to
instructions from
the processor 40 to award a payoff of coins or credits to the player in
response to certain
winning combinations stored in memory 48. As will be described in detail
hereinafter,
the payoff amounts corresponding to certain combinations is predetermined
according to
a pay table stored in system memory 48.
In the illustrated embodiment, the symbols displayed on the reels 14, 16, 18
define a symbol group consisting of nine symbols, with each symbol being
displayed in
CA 02278949 1999-07-23
either an upper, center, or lower display position on one of the reels 14, 16,
18. It will be
appreciated, however, that any of several alternative symbol group
configurations may be
employed, for example, where the slot machine 10 has fewer or greater numbers
of reels,
and/or where fewer or greater numbers of symbols are visible in the display
window 12.
In one embodiment, the combination of symbols which determine the basic game
outcome consist of only those symbols which are aligned with center payline
22. It will
be appreciated, however, that a basic game implemented on the slot machine 10
may use
a variety of other payline configurations to define the basic game outcome.
For example,
the slot machine 10 might include an upper payline (where the combination of
symbols
1o consisting of the upper symbol on each reel comprises the game outcome),
lower payline
(where the combination of symbols consisting of the lower symbol on each reel
comprises the game outcome), angled paylines (where the combination of symbols
consisting of the lower, center and upper symbols, respectively, or upper,
center and
lower symbols, respectively, on the three reels comprises the game outcome) or
diamond-
shaped paylines (where the combination of symbols consisting of the center
symbol on
the first and third reels and either the upper or lower symbol on the second
reel comprises
the game outcome).
Alternatively or additionally, another payline configuration known as a
scatter
pay configuration may be employed to define the basic game outcomes. In the
scatter
2o pay configuration, symbol combinations defining the game outcomes are not
required to
be aligned with fixed payline(s). Rather, the symbol group is determined to
include a
basic winning combination if any combination of three symbols consisting of
one symbol
from each of the three reels 14, 16, 18 corresponds to one of the symbol
combinations
identified in the pay table. Thus, for example, suppose the symbol combination
SYIVIBOLI, SYNIBOL2, SYNIBOL3 is a basic winning combination of a game played
on
the slot machine 10. In scatter-pay format, the winning combination occurs if
reel 14
displays SYMBOL1 in either of the upper, center or lower display positions,
reel 16
displays SYNIBOL2 in either of the upper, center or lower display positions
(which need
not correspond to the display position of SYMBOL1 on reel 14) and reel 18
similarly
3o displays SYMBOL3 in either of the upper, center or lower display positions
(which need
not correspond to the display positions of SYMBOL1 or SYMBOL2 on reel 14 or
16).
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7
In one embodiment, the symbol group displayed on reels 14, 16, 18 may indicate
any of three possible basic game outcomes, including ( 1 ) a traditional
winning outcome
causing the processor 40 to award the player a predetermined amount of coins)
or
credit(s); (2) a start-bonus outcome causing the processor 40 to trigger play
of a bonus
game; and/or (3) a losing outcome causing the processor 40 to continue
operation in the
basic mode without awarding any coins) or credit(s). Hereinafter, outcomes ( 1
) and (2)
will be identified by the term "standard" winning outcomes, to distinguish
them from
various collection-based outcomes which may appear in the bonus game and which
will
be described in detail later.
1 o Generally, each of standard winning outcomes ( 1 ) and (2) identified
above are
characterized by the display of one or more predefined combinations of
symbols. The
symbols defining the standard winning combinations are stored in a game
memory. In
one embodiment, the symbols defining both the traditional winning combinations
and
start-bonus combinations are shown in a pay table affixed to the slot machine
10 so that
players may view the standard winning combinations and, in the case of
traditional
winning combinations, their predefined payoff amounts. The payoff amounts
associated
with the start-bonus combinations are generally not predefined and,
accordingly, do not
typically appear on the pay table, although an average payoff amount
associated with the
start-bonus combinations might be displayed on the pay table.
2o FIG. 2 shows a set of reel strips for use with a slot machine of the type
shown in
FIG. 1 to implement a JACKPOT STAMPEDETM slot machine game, assigned to the
assignee of the present invention. The reel strips correspond to the reels 14,
16, 18 in FIG.
1 and will be identified by corresponding reference numerals 14, 16, 18. Each
of the reel
strips 14, 16, 18 include twenty-four symbols (including blanks) corresponding
to twenty-
four available reel stopping positions. The symbols include WILD, DOUBLE WILD,
3-
BAR, 2-BAR, 1-BAR, ROUND UP! and "Blank" defining "standard" symbols which, if
displayed in certain predefined combinations relative to payline 22, define
the standard
winning combinations. Also shown on the reel strips 14,16,18 are small COW
symbols,
including one CASH COW symbol, which are displayed on top of (and thereby
share the
same reel stopping position as) some of the standard symbols. In one
embodiment, the
COW and CASH COW symbols have no value in the basic game and do not form the
basis
CA 02278949 1999-07-23
8
of standard winning combinations in either the basic or bonus game but
nevertheless have
collection value in a bonus game, as will be described in detail later.
Specifically, the symbols which appear on reel strip 14 include, in sequence 1-
BAR,
Blank, ROUND UP!, Blank, 2-BAR/COW, Blank, 1-BAR, Blank, WILD, Blank, ROUND
UP!, Blank, 2-BAR/COW, Blank, 3-BAR/COW, Blank, 1-BAR, Blank, ROUND UP!,
Blank, 1-BAR/COW, Blank, ROUND UP! and Blank. The symbols which appear on reel
strip 16 include, in sequence, 2-BAR, Blank, WILD, Blank, 2-BAR/COW, Blank,
ROUND
UP!/COW, Blank, DOUBLE WILD, Blank, 1-BAR/CASH COW, Blank, ROUND UP!,
Blank, 3-BAR/COW, Blank, 2-BAR/COW, Blank, ROUND UP!, Blank, WILD, Blank,
ROUND UP! and Blank. Finally, the symbols which appear on reel strip 18
include, in
sequence, 1-BAR/COW, Blank, ROUND UP!, Blank, 2-BAR/COW, Blank, 3-BAR,
Blank, WILD, Blank, ROUND UP!, Blank, 2-BAR/COW, Blank, 1-BAR/COW, Blank,
ROUND UP!, Blank, 1-BAR, Blank, 3-BAR/COW, Blank, ROUND UP! and Blank.
Each of the possible combinations associated with one embodiment of the
JACKPOT STAMPEDETM game are identified in the "Reel 1," "Reel 2" and "Reel 3"
columns of FIGS. 3a, 3b and 3c. The combinations identified in lines 52, 54
and 76-162
represent traditional winning combinations which, if displayed in alignment
with payline
22, will cause the processor 40 to credit the player a predefined amount of
coins or credits
corresponding to the particular combination and to the number of coins played.
The
2o combinations identified in lines 56 through 74 represent "start-bonus"
combinations
which, if displayed in alignment with payline 22, will cause the processor 40
to enter a
bonus mode in which credits are awarded to the player in a bonus game. The
amount of
credits awarded to the player in the bonus game is not predetermined but
rather depends
on the outcome of the bonus game. The bonus game will be described in detail
in
relation to FIG. 5.
The "#/Reel 1," "#/Reel 2" and "#/Reel 3 columns identify, respectively, the
numbers) of reel positions on reels 14, 16, 18 that will support the various
standard
winning combinations. The "Hits" column identifies, for each combination of
symbols,
the product of the three "#/Reel" columns and represents the numbers) of times
the
winning combinations can occur relative to a single active payline.
A number of the combinations identified in FIGs. 3a through 3c will
hereinafter
be discussed in detail. First, consider the WILD, DOUBLE WILD, WILD symbol
CA 02278949 1999-07-23
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combination (line 52). Because there is only one WILD symbol on reel 14, one
DOUBLE WILD symbol on reel 16 and one WILD symbol on reel 18, the "#/Reel"
values for the WILD, DOUBLE WILD, WILD symbol combination are 1, 1 and 1,
respectively. Thus, the"Hits" value for the WILD, DOUBLE WILD, WILD symbol
combination is 1 (i.e., 1 x 1 x 1). Next, consider the WILD, WTLD, WILD
combination
(line 54). The number of WILD symbols appearing on reels 14, 16 and 18 are 1,
2 and 1,
respectively. Thus, the"Hits" value for the WILD, WILD, WILD symbol
combination is
2(i.e.,lxlxl).
The start-bonus combinations which may occur in the JACKPOT STAMPEDE
game are identified on lines 56 through 74 of FIG. 3a. Specifically, the start-
bonus
combinations include two ROUND UP! symbols and a DOUBLE WILD symbol (line 56),
one ROUND UP! symbol, a DOUBLE WILD symbol and a WILD symbol (lines 58, 60),
three ROUND UP! symbols (line 62), two ROUND UP! symbols and a W1LD symbol
(lines 64, 66, 68), and one ROUND UP! symbol and two WILD symbols (lines 70,
72, 74).
~ 5 The occurrence of any of the start-bonus combinations in alignment with
payline 22 will
cause the processor 40 to trigger play of a ROUND UP! bonus game, which will
be
described in detail in relation to FIG. 5.
Consider the three ROUND UP!/DOUBLE WILD combinations (lines 56, 58,
60). The first of the kOUND UP!1DOUBLE WILD combinations (line 56) consists of
a
ROUND UP! symbol on reel 1 (i.e., reel 14), a DOUBLE WILD symbol on reel 2
(i.e., reel
16), and a ROUND UP! symbol on reel 3 (i.e., reel 18). Because there are four
ROUND
UP! symbols on reel 14, one DOUBLE WILD symbol on reel 16 and four ROUND UP!
symbols on reel 18, the "#/Reel" values for the ROUND UP!/DOUBLE WILD
combination on line 56 are 4, 1 and 4, respectively. The "Hits" value for the
combination on line 56 is therefore 16 (i.e., 4 x 1 x 4). Similarly, for the
second of the
ROUND UP!/DOUBLE WILD combinations (line 58), consisting of a WILD symbol on
reel 1 (i.e., reel 14), a DOUBLE WILD symbol on reel 2 (i.e., reel 16), and a
ROUND UP!
symbol on reel 3 (i.e., reel 18), the "#/Reel" values are 1, l and 4,
respectively, because
there is one WILD symbol on reel 14, one DOUBLE WILD symbol on reel 16 and
four
ROUND UP! symbols on reel 18. The "Hits" value for the combination on line 58
is
therefore 4 (i.e., 1 x 1 x 4). Next, for the third of the ROUND UP!/DOUBLE
WILD
combinations (line 60), consisting of a ROUND UP! symbol on reel 1 (i.e., reel
14), a
CA 02278949 1999-07-23
10
DOUBLE WILD symbol on reel 2 (i.e., reel 16), and a WILD symbol on reel 3
(i.e., reel
18), the "#/Reel" values are 4, 1 and l, respectively, thus defining a "Hits"
value of 4 (i.e.,
4 x 1 x 1 ). The sum of the three "Hits" values, 24, defines the total number
of "Hits" of the
ROUND UP!/DOUBLE WILD combinations 56, 58, 60.
The combinations identified on lines 76 through 162 comprise, in order of
descending value, various traditional winning combinations and combination 164
(i.e.,
Anything, Anything, Anything) comprises a losing symbol combination which may
occur
in the JACKPOT STAMPEDE''"' game. The "# PER REEL" and "Hits" values for each
of these combinations are computed in similar fashion to those heretofore
described.
FIG. 4 is a table summarizing payoffs, probabilities and expected values
associated with the occurrence of the standard winning combinations identified
in FIG. 3
in the basic mode of the JACKPOT STAMPEDE"r' game. The standard winning
combinations are designated in FIG. 4 with the following notations: "W DW W"
(corresponding to the combination identified in line 52 of FIG. 3a); "W W W"
(line 54);
"RU DW" (lines 56, 58, 60); "Round Up" (lines 62 through 74); "3-BAR DW"
(lines 76,
78, 80); "3-BAR" (lines 82 through 94); "2-BAR DW" (lines 96, 98, 100); "2-
BAR" (lines
102 through 114); "1-BAR DW"(lines I 16, 118, 120); "1-BAR" (lines 122 through
134);
"2 Wild DW" (lines 136, 138); "2 Wild" (lines 140, I42, 144); "any bar DW"
(line 146);
"any bar" (lines 148, 150, 152, 154); "1 Double Wild" (line 156); and "I Wild"
(lines 158,
160, 162).
The "1 coin," "2 coin" and "3 coin" columns identify, respectively, the payoff
amounts associated with the various combinations in FIGs. 3 and 4. In the case
of the
traditional winning combinations, the payoff amounts are predetermined amounts
stored
in system memory. Specifically, in the embodiment shown in FIG. 4, the "W DW
W"
combination (line 52, FIG. 3a) will award 400 coins or credits in a 1-coin
game, 800 coins
or credits in a 2-coin game and 1600 coins or credits in a 3-coin game; the "W
W W
combination (line 54) will award 125 coins or credits in a 1-coin game, 250
coins or credits
in a 2-coin game and 400 coins or credits in a 3-coin game; the "3-BAR DW"
combination
(lines 76, 78, 80) will award 60 coins or credits in a 1-coin game, 120 coins
or credits in a
30 2-coin game and 180 coins or credits in a 3-coin game; the "3-BAR"
combination (lines 82
through 94) will award 30 coins or credits in a 1-coin game, 60 coins or
credits in a 2-coin
game and 90 coins or credits in a 3-coin game; the "2-BAR DW" combination
(lines 96,
CA 02278949 1999-07-23
11
98, 100) will award 40 coins or credits in a 1-coin game, 80 coins or credits
in a 2-coin
game and 120 coins or credits in a 3-coin game; the "2-BAR" combination (lines
102
through 114) will award 20 coins or credits in a 1-coin game, 40 coins or
credits in a 2-coin
game and 60 coins or credits in a 3-coin game; the "1-BAR DW" combination
(lines 116,
118, 120) will award 20 coins or credits in a 1-coin game, 40 coins or credits
in a 2-coin
game and 60 coins or credits in a 3-coin game; the "1-BAR" combination (lines
122
through 134) will award 10 coins or credits in a 1-coin game, 20 coins or
credits in a 2-coin
game and 30 coins or credits in a 3-coin game; the "2 Wild DW" combination
(lines 136,
138) will award 10 coins or credits in a 1-coin game, 20 coins or credits in a
2-coin game
and 30 coins or credits in a 3-coin game; the "2 Wild" combination (lines 140,
142, 144)
will award 5 coins or credits in a 1-coin game, 10 coins or credits in a 2-
coin game and 15
coins or credits in a 3-coin game; the "any bar DW" combination (line 146)
will award 10
coins or credits in a 1-coin game, 20 coins or credits in a 2-coin game and 30
coins or
credits in a 3-coin game; the "any bar" combination (lines 148, 150, 152, 154)
will award 5
coins or credits in a 1-coin game, 10 coins or credits in a 2-coin game and 15
coins or
credits in a 3-coin game; the "1 Double Wild" combination (line 156) will
award 2 coins or
credits in a 1-coin game, 4 coins or credits in a 2-coin game and 6 coins or
credits in a 3-
coin game; and the "1 Wild" combination (lines 158, 160, 162) will award 1
coin or credit
in a 1-coin game, 2 coins or credits in a 2-coin game and 3 coins or credits
in a 3-coin
game.
In the case of the "start-bonus" combinations, the payoff amounts represent
average payoff amounts which may be expected in the bonus game. Specifically,
bonus
games started with "RU DW" combinations (lines 56, 58, 60) will pay, on
average, 38.92
coins or credits in a 1-coin game, 77.85 coins or credits in a 2-coin game and
116.77 coins
or credits in a 3-coin game. Bonus games started with "Round Up" combinations
(lines 62
through 74) will pay half those amounts, specifically 19.46 coins or credits
in a 1-coin
game, 38.92 coins or credits in a 2-coin game and 58.38 coins or credits in a
3-coin game.
The "Pulls/Hit" column of FIG. 4 identifies, on average, the number of pulls
that
would be required to "hit" each respective symbol combination. Where the reels
each
3o have twenty-four reel stop positions, as in the JACKPOT STAMPEDE'~'M game,
there are
13,824 (24 x 24 x 24) possible symbol combinations. The "Pulls/Hit" value for
any
particular combination is determined by dividing the number of possible
combinations
CA 02278949 1999-07-23
12
(i.e., 13,824) by the "Hits" value associated with that combination. As
heretofore
described, the "Hits" value for any particular combination is a function of
the number of
reel positions of the symbols supporting that combination. For example,
because there is
only one reel position on each of reels 14, 16, 18 that will support the
"WILD, DOUBLE
WILD, WILD" symbol combination, the "Hits" value for that combination is 1 and
the
"Pulls/Hit" value is 13,824 (i.e. 13,824 = 1). Thus, it would take 13,824
pulls, on
average, to "hit" the "WILD, DOUBLE WILD, WILD" symbol combination.
Next consider the "RU DW" outcome of FIG. 4. The "RU DW" outcome occurs
upon the display of either of the three combinations identified in lines 56,
58 and 60 of
FIG. 3 in alignment with center payline 22 of the slot machine 10. The "Hits"
value for
each combination is 16, 4 and 4, respectively. The total number of "Hits"
supporting the
three "RU DW" combinations is therefore 24 and the "Pulls/Hit" value is 576
(i.e. 13,824
24). Thus, it would take 576 pulls, on average, to "hit" any one of the "RU
DW"
combinations.
The "Pulls/Hit" values for the remaining outcomes of FIG. 4 are computed in
like
fashion. The "Pulls/Hit" value at the bottom of the column (i.e., 4.57)
represents the
number of pulls, on average, that would be required to hit any of the winning
combinations. This is computed by dividing the number of possible symbol
combinations (i.e., 13,824) by the total number of "Hits" supporting winning
2o combinations in FIG. 3 (i.e., 3,025).
The "Probability" column identifies the probabilities of hitting the winning
outcomes in FIG. 4 in a single spin. This is computed for each outcome by
taking the
inverse of the "Pulls/Hit" value associated with that outcome. Thus, for
example, the
probability of hitting a "3BAR" combination is 1 divided by 864, or 0.001157
The
number at the bottom of the Probability column (i.e., 0.219) represents the
probability of
hitting any of the combinations of FIG. 4 in a single spin.
The "1 coin EV," "2 coin EV" and "3 coin EV" columns identify the normalized
expected values of the winning outcomes in FIG. 4 for a 1-coin game, 2-coin
game and
3-coin game, respectively. These values are computed for each outcome by
taking the
product of the respective "1 coin," "2 coin" or "3 coin" pay value associated
with that
outcome and the "Probability" value associated with that outcome, then
dividing by the
number of coins) played. Thus, for example, the 2BAR outcome has a 1-coin
expected
CA 02278949 1999-07-23
13
value of 0.062211 (20 x 0.003111 = 1 ), a 2-coin expected value of 0.062211
(40 x
0.003111 = 2) and a 3-coin expected value of 0.062211 (60 x 0.003111 = 3). The
payout
rate of the basic game is computed independently for a 1-coin, 2-coin and 3-
coin game by
summing the normalized expected values in the respective "1 coin EV," "2-coin
EV" and
"3 coin EV" columns. Thus, the payout rates for a 1-coin and ~-coin game are
0.911
(91.1 %) and the payout rate for a 3-coin game is 0.922 (92.2%o).
The "Max Contribution" column indicates, for a 3-coin game, the percentage
contribution of the respective "3 coin EV" values to the total payout rate for
a 3-coin
game. Thus, for example, for the "Round Up" outcome, the contribution is 23%
(0.208355 = 0.922). The remaining "Max Contribution" values are computed in
similar
a
fashion.
FIG. 5 is a flow diagram identifying various steps in implementation of a
bonus
game with a collection-based award feature according to one embodiment of the
present
invention. Each of the steps will be described with reference to the JACKPOT
STAMPEDES game. It will be appreciated, however, that the present invention is
not
limited to the JACKPOT STAMPEDES game or any other particular game. Start of
the
bonus game (or bonus "round") (step 200) is triggered by the display of a
designated start-
bonus combination (e.g., a "Round Up" or "RU DW ' combination) on the center
payline
22 of the slot machine 10 in basic mode. Generally, the bonus round consists
of spinning
the reels 14, 16, 18 under processor control a fixed number of times, each
consecutive spin
defining a "bonus spin." The bonus spins may be performed automatically under
processor
control or in response to player input (e.g., pulling a lever or depressing a
start button), but
generally do not require the play of any additional coins or credits other
than the amount
played in the basic game.
In step 202, a game controller (e.g., processor) determines the number of
bonus
spins to be afforded in the bonus round. This may be accomplished by the
processor
executing a game program defining the number of bonus spins. For example, in
one
embodiment, the bonus round is defined by the game program to include five
bonus spins
for any start-bonus combination. It will be appreciated, however, that the
bonus round
3o may be defined by the game program to include any number of bonus spins,
and/or the
numbers) of bonus spins may be varied in response to the particular start-
bonus
combination which triggered the bonus game. For example, in an alternative
CA 02278949 1999-07-23
14
embodiment, a bonus game started in response to "Round Up" combination might
consist
of five bonus spins, whereas a bonus game started in response to a "Round Up
Double
Wild" combination might consist of ten bonus spins.
Once the numbers) of bonus spins are designated, a counting means associated
with the processor monitors the spins and provides feedback to the processor
to ensure
that the proper number of bonus spins are accomplished in the bonus round. In
step 204,
the counting means sets a "Spin" variable to 1, indicating that the next spin
will be the
first bonus spin. Then, in step 206, the processor spins the reels 14, 16, 18,
randomly
selects a stop position of the reels 14, 16, 18 and causes the reels to stop
at the selected
1 o stop position in generally the same manner as in the basic game. In each
bonus spin, the
symbols displayed on the reels 14, 16, 18 at the selected stop position (step
208) define a
symbol group consisting of various symbols displayed at nine display positions
(e.g., an
upper, center, and lower display position on each of the reels 14, 16, 18).
In one embodiment, the reels 14, 16, 18 spun in the bonus round are the same
t 5 reels 14, 16, 18 spun in the basic game and include the same symbols. It
will be
appreciated, however, that the bonus game may employ separate reels or
simulated
mechanical reels illustrated on the video display 24, and/or may include
different
symbols. In an embodiment of the JACKPOT STAMPEDES game including the same
symbols, the symbols eligible for display in the bonus game include the
"standard"
2o symbols WILD, DOUBLE WILD, 3-BAR, 2-BAR, 1-BAR, ROUND UP! and Blank and
"bonus collection" symbols COW and CASH COW. As described in relation to FIG.
2, the
COW and CASH COW symbols are displayed on top of (and thereby share the same
reel
stopping position as) some of the standard symbols.
The symbols displayed on the reels in each bonus spin define a bonus game
25 outcome. The amount of coins or credits awarded to the player in the bonus
game is
determined by the cumulative value of any standard winning combinations)
occurring in
the bonus spins, plus the cumulative value of any bonus collection symbols
(e.g., COW
and CASH COW symbols) appearing on reels 14, 16, 18 in the bonus spins.
In step 210, a symbol evaluation means (e.g., the game controller) evaluates
the
30 symbol group appearing on the reels 14, 16, 18 of the slot machine in the
present spin
(e.g., the first bonus spin) and determines whether the symbol group includes
a standard
winning combination. In one embodiment of the JACKPOT STAMPEDES game, the
CA 02278949 1999-07-23
symbol group is determined to include a standard winning combination if the
three-
symbol combination aligned with the center payline 22 corresponds to one of
the winning
combinations identified in FIG. 6. In one embodiment, the standard winning
combinations identified in FIG. 6 are the same as the standard winning
combinations
5 which may occur in the basic game (FIG. 4) and have the same probability of
occurrence
in either the basic game or bonus game.
If the symbol group is determined to include a winning combination, the game
controller (e.g., processor) determines the amount of payoff associated with
the
combination at step 212. In one embodiment, if the bonus mode has been entered
at step
1 o 200 in response to a "Round Up" combination, the processor will determine
the pay
values) for standard winning combinations) according to the values shown in
FIG. 6.
If, however, the bonus mode has been entered at step 200 in response to a "RU
DW"
combination, the processor will determine the pay values) for standard winning
combinations) to be twice that of the values shown in FIG. 6.
15 Generally, with the exception of the "Round Up" and "RU DW" combinations,
the combinations identified in FIG. 6 have the same pay values upon their
occurrence in
the bonus round as they would have in the basic mode (FIG. 4), whereas the
"Round Up"
and "DW ' combinations have different pay values in the basic mode (FIG. 4)
and the
bonus mode (FIG. 6). For example, the 1-coin pay value of the "RU DW '
combination
in the basic mode (FIG. 4) is 38.92 coins or credits, whereas the 1-coin pay
value for the
same combination in the bonus mode (FIG. 6) is 20 coins or credits. Different
pay
amounts may also be found by comparing the 2-coin and 3-coin pay values of the
"RU
DW" combination in FIG. 4 and FIG. 6, or by comparing any of the 1-coin, 2-
coin or 3-
coin pay values for the "Round Up" combination in FIG. 4 and FIG. 6.
Generally, these differences may be attributed to a change in status of the
respective combinations upon the transition from the basic mode to the bonus
mode.
More particularly, in one embodiment of the present invention, there can be no
bonus
round within a bonus round. Consequently, whereas the "Round Up" and "RU DW"
combinations occurnng in the basic mode (FIG. 4) define start-bonus
combinations and
3o trigger play of the bonus round, the same combinations occurring in the
bonus mode
(FIG. 6) do not trigger play of another bonus round but rather result in fixed
payoffs) of
coins or credits. Thus, the psy values shown in FIG. 4 for the occurrence of
the "Round
CA 02278949 1999-07-23
16
Up" and "RU DW" combinations in the basic mode are average pay values which
may be
expected in the bonus round, whereas the pay values shown in FIG. 6 for those
same
combinations are fixed to a predetermined value.
After the standard payoff associated with the present bonus spin (e.g., the
first
bonus spin) has been determined at step 212, or after the present bonus spin
has been
determined not to include a standard winning combination at step 210, the
process
proceeds to step 214. At step 214, the symbol evaluation means (e.g.,
processor)
evaluates the symbol group associated with the present bonus spin for the
presence of
bonus collection symbols, which in the JACKPOT STAMPEDES game comprise COW
and CASH COW symbols. In one embodiment, the symbol group is determined at
step
214 to include bonus collection symbols) if bonus collection symbols (e.g.,
COW. and/or
CASH COW symbol(s)) are displayed in any of the nine display positions of the
symbol
group. Specifically, in the JACKPOT STAMPEDES game, the symbol group is
determined to include bonus collection symbols if COW or CASH COW symbols) are
displayed in any combination of the upper, center or lower display positions
of reel 14,
16 and 18.
At step 216, if the symbol group is determined to include any bonus collection
symbols, the game controller (e.g., processor) causes the video display 24 to
display an
appropriate animation representing the bonus collection symbols) appearing in
the symbol
group. Thus, for example, if the symbol group in the first bonus spin includes
two COW
symbols and one CASH COW symbol, the processor at step 216 causes the video
display
24 to display two animated COW symbols and one animated CASH COW symbol. This
step is repeated for each consecutive bonus spin to display the cumulative
numbers) of
collection symbols) appearing (or "collected") in the bonus round.
In step 218, the game controller (e.g., processor) determines the amount of
payoff
associated with the collection symbols appearing in the bonus round. As will
be
appreciated, this step may be accomplished independently for each bonus spin
or deferred
until completion of all bonus spins (at step 224). In the JACKPOT STAMPEDES
game,
COW symbols collected in the bonus round have a fixed value corresponding to
the
number of coins or credits played upon entering the bonus round and also
corresponding
to the symbol combination (e.g., "Round Up" or "Round Up Double Wild") which
triggered the bonus round. In one embodiment, if one coin or credit is played
in the basic
CA 02278949 1999-07-23
17
game and a "Round Up" combination triggers a JACKPOT STAMPEDETM bonus game,
every COW symbol displayed (or "collected") in the bonus round has a value of
1 coin or
credit. Similarly, if two or three coins or credits are played in the basic
game and a
"Round Up" combination triggers play of a JACKPOT STAMPEDETM bonus game,
every COW symbol displayed in the bonus round has a value of 2 or 3 coins or
credits,
respectively. For any number of coins) or credits) played, if the bonus round
has been
entered in response to a "Round Up Double Wild" combination, the values of the
COW
symbols are doubled. Thus, COW symbols collected in a bonus round started with
a
"Round Up Double Wild" combination have respective values of 2 coins or
credits in a
10 1-coin game, 4 coins or credits in a 2-coin game and 6 coins or credits in
a 3-coin game.
In one embodiment of the JACKPOT STAMPEDES game, CASH COW
symbols collected in the bonus round have a value which is randomly determined
by the
game controller at step 218 and determined independently for each CASH COW
symbol.
The determination of CASH COW values) may be accomplished after each bonus
spin or
15 may be deferred until completion of all bonus spins (at step 224).
Specifically, for each
CASH COW symbol appearing in the bonus round, the processor randomly selects a
base
value from a table of CASH COW base values stored in system memory, then
computes
the product of the base value and one or more multipliers to determine the
value of that
CASH COW.
20 In one embodiment, the table of base values from which the base value is
selected
comprises 30 individual base values stored in game memory, each of which has a
one-in-
thirty chance to be selected. The individual base values are: 5 ( 15
occurrences), 10 (5
occurrences), 15 (6 occurrences), 20 ( 1 occurrence), 30 ( 1 occurrence), 40 (
1 occurrence)
and 50 ( 1 occurrence). The average base value is 11.833. It will be
appreciated that the
25 number of base values and/or their amounts may be varied to effect
different payouts by
altering the game program.
In one embodiment, the selected base value corresponding to each CASH COW
is multiplied by one or more multipliers to determine the value of that CASH
COW. The
multipliers are determined by the number of coins played and/or by the symbol
30 combination (e.g., "Round Up" or "Round Up Double Wild") which triggered
the bonus
round. Specifically, if the bonus round has been entered in a 1-coin game and
in
response to a "Round Up" combination, the value of each CASH COW is determined
by
CA 02278949 1999-07-23
18
the processor to be the product of the randomly selected base value and a "1X"
multiplier. Similarly, if the bonus round has been entered in response to a
"Round Up"
combination in a 2-coin or 3-coin game, the value of each CASH COW is
determined by
the processor to be the product of the randomly selected base value and a "2X"
or "3X"
multiplier, respectively. If the bonus round has been entered in response to a
"RU DW"
combination, the values of the CASH COW symbols are doubled. Thus, CASH COW
symbols collected in a bonus game started with a "Round Up Double Wild"
combination
have a value of "2X" times the randomly selected base value in a 1-coin game,
"4X"
times the randomly selected base value in a 2-coin game and "6X" times the
randomly
selected base value in a 3-coin game.
After the amount of payoff associated with the collection symbols in the
present
bonus spin (e.g., the first bonus spin) has been determined (step 218) or
after the present
bonus spin has been determined not to include any bonus collection symbols
(step 214),
the counting means evaluates at step 220 whether the present spin is the last
bonus spin.
If the present spin is not the last bonus spin, the counting means increments
at step 222
the "Spin" variable by 1 and the process is repeated beginning with step 206.
Thus, for
example, where the bonus round is defined to include five spins and where the
present
spin is the first spin, the counting means at step 222 will add one to the
"Spin" variable
to indicate that the next spin is the second spin. After the designated number
of bonus
2o spins (e.g., five spins) are completed, thereby causing the counting means
to determine at
step 220 that the present spin is the last spin, the process proceeds to step
224 to compute
the bonus game payoff. As will be appreciated, the counting of bonus spins may
be
accomplished in any of several ways. For example, in one embodiment, the
counting
means might start with a "Spin" variable equal to the maximum number of bonus
spins and
decrement by one after each spin.
In step 224, the bonus game payoff is determined by the game controller by
summing any standard payoffs) computed at step 212 and any collection payoffs)
computed at step 218. Alternatively, the standard payoffs) and/or collection
payoffs) and
their sum may be computed independently at step 224 without reliance on steps
212 or 218
(e.g., with elimination of steps 212 and/or 218). In such alternative
embodiment, the
computation of standard payoffs) and/or collection payoffs) at step 224 is
accomplished in
generally the same manner as described in relation to steps 212 and 218. After
computation
CA 02278949 1999-07-23
19
of the bonus game payoff, the player is awarded a number of coins or credits
corresponding
to the bonus game payoff at step 226 and the bonus game is ended at step 228,
causing the
processor to return to the basic mode.
FIG. 7 identifies various possible configurations of bonus game collection
symbols
which may appear in the JACKPOT STAMPEDETM game and their probabilities of
occurring on each reel. More specifically, the entries on the left-hand column
of FIG. 7
identify various bonus game symbol outcomes and orientations which may occur
on each
respective reel in the JACKPOT STAMPEDES bonus game. Other than the "non-
winners" entry, each symbol outcome, if displayed on either of reels 14, 16,
18, includes
at least one bonus game collection symbol. The "non-winners" entry represents
various
symbol outcomes which do not contain any bonus game collection symbols. The
"Reel
1," "Reel 2" and "Reel 3" columns identify, respectively, the number of stop
positions of
reels 14, 16, 18 (see FIG. 2) that will support the various symbol outcomes
identified in
the left-hand column. The "Prob/Reel 1," "Prob/Reel 2" and "Prob/Reel 3"
columns
15 indicate, respectively, the probability of the various symbol outcomes
occurring on reels
14, 16, 18.
The symbol outcomes and probabilities identified in FIG. 7 will hereinafter be
described in detail. First consider the "Payline Cash Cow" outcome. This
refers to the
display of a CASH COW symbol on the center payline 22 of either of the reels
14, 16, or
18. As may be observed in FIG. 2, reel strips 14 and 18 do not include any
CASH COW
symbols. Thus, there are no stop positions on reel 14 (i.e., "Reel 1") or reel
18 (i.e. "Reel
3") which will support the "Payline Cash Cow" outcome. Consequently, the
probabilities of the "Payline Cash Cow" outcome occurring on reel 14 (i.e.,
"Prob/Reel
1") or reel 18 (i.e. "Prob/Reel 3") are zero. Reel strip 16, however, includes
one CASH
25 COW symbol. Thus, there is one stop positions on reel 16 (i.e., "Reel 2")
which will
support the "Payline Cash Cow" outcome. Consequently, the probability of the
"Payline
Cash Cow" outcome occurring on reel 16 is 0.041667 (i.e., 1 = 24).
Next consider the "Blank Cash Cow High" and "Blank Cash Cow Low"
outcomes. These refer to the display of a Blank symbol on the center display
position
and a CASH COW symbol on the upper display position or lower display position,
respectively, on either of the reels 14, 16, or 18. Because there are no CASH
COW
symbols on reel 14 or 16, there are no stop positions on reel 14 (i.e., "Reel
1") or reel 18
CA 02278949 1999-07-23
(i.e. "Reel 3") which~will support the "Blank Cash Cow High" or "Blank Cash
Cow
Low" outcomes. Consequently, the probabilities of either the "Blank Cash Cow
High" or
"Blank Cash Cow Low" outcomes occurring on reel 14 (i.e., "Prob/Reel 1") or
reel 18
(i.e. "Prob/Reel 3") are zero. Because reel strip 16 includes one CASH COW
symbol,
5 with Blank symbols both above and below, there is one stop positions on reel
16 (i.e.,
"Reel 2") that will support the "Blank Cash Cow High" outcome and one stop
position
on reel 16 that will support the "Blank Cash Cow Low" outcome. Consequently,
the
probabilities of either the "Blank Cash Cow High" or "Blank Cash Cow Low"
outcome
occurring on reel 16 (i.e., "Prob/Reel 2") is 0.041667 (i.e., 1 = 24).
10 The "Payline Cows" outcome refers to the display of a COW symbol (other
than a
CASH COW) on the center payline 22 of either of the reels 14, 16, or 18. As
may be
observed in FIG. 2, reel strip 14 includes four COW symbols, reel strip 16
includes four
COW symbols and reel strip 18 includes five COW symbols. Thus, there are four
stop
positions on reel 14 (i.e., "Reel 1"), four stop positions on reel 16 (i.e.,
"Reel 2") and five
15 stop positions on reel 18 (i.e., "Reel 3") which will support the "Payline
Cows" outcome.
The probability of the "Payline Cows" outcome occurring on reels 14 or 16
(i.e.,
"Prob/Reel 1" and "Prob/Reel 2") is 0.16667 (i.e., 4 = 24) and the probability
of the
"Payline Cows" outcome occurnng on reel 18 (i.e., "Prob/Reel 3") is 0.208333
(i.e., 5
24).
20 The "Blank High" and "Blank Low" outcomes refer to the display of a Blank
symbol on the center display position and a single COW symbol (other than a
CASH
COW) on the upper display position or lower display position, respectively, on
either of
the reels 14, 16, or 18, whereas the "Blank High/Low" outcome refers to the
display of a
Blank symbol on the center display position and COW symbols (other than CASH
COWS) on both the upper display position and lower display position of the
reels 14, 16,
or 18. First consider the "Blank High/Low" outcome. As may be observed in FIG.
2,
only one of the Blank symbols on reel strips 14 and 18 has a COW symbol on
both sides
(e.g., both "High"and "Low") and therefore there is only one stop position on
reels 14
and 18 which will support the "Blank High/Low" outcome. Reel strip 16,
however, has
two Blank symbols with COW symbols both "High" and "Low" and therefore there
are
two stop positions on reel 16 which will support the "Blank High/Low" outcome.
The
probability of the "Blank High/Low" outcome occurring on reels 14 or 18 (i.e.,
CA 02278949 1999-07-23
21
"Prob/Reel 1" and "Prob/Reel 3") is 0.041667 (i.e., 1 = 24) and the
probability of the
"Blank High/Low" outcome occurring on reel 16 (i.e., "Prob/Reel 2") is
0.008333 (i.e., 2
24).
The "non-winners" outcome refers to the display of various sets of three
consecutive symbols on reels 14, 16 or 18 which do not conta:r_ any COW
symbols or
CASH COW symbols. Stated differently, a "non-winners" outcome in the context
of
FIG. 7 defines an outcome on respective reels 14, 16 or 18 which does not
contribute to
the collection portion of the bonus game payoff. It is important to note,
however, that a
"non-winners" outcome may contribute to the standard portion of the bonus game
payoff,
where the symbol group displayed on reels 14, 16, 18 includes a standard
winning
combination which does not include a COW or CASH COW symbol on either of reels
14, 16, 18.
The numbers of "non-winners" identified in FIG. 7 are computed for each reel
by
subtracting the number of reel stop positions for that reel which include
collection symbols
from the total number of reel stop positions. Specifically, for reel strip 14
(i.e., "Reel 1"),
there are 11 reel stop positions which include collection symbols-- 4 stop
positions
supporting the "Payline Cow" outcome, 3 stop positions supporting the "Blank
High"
outcome, 3 stop positions supporting the "Blank Low" outcome and 1 stop
position
supporting the "Blank High/Low" outcome. The number of "non-winners" on reel
strip 14
is therefore 13 (i.e., 24 - 11) and the probability of a "non-winner"
occurring on reel 14
(i.e., "Prob/Reel 1") is 0.541667 (i.e., 13 = 24). For reel strip 16 (i.e.,
"Reel 2"), there are
13 reel stop positions which include collection symbols-- 1 stop position
supporting the
"Payline Cash Cow" outcome, 1 stop position supporting the "Blank Cash Cow
High"
outcome, 1 stop position supporting the "Blank Cash Cow Low" outcome, 4 stop
positions
supporting the "Payline Cows" outcome, 2 stop positions supporting the "Blank
High"
outcome, 2 stop positions supporting the "Blank Low" outcome and 2 stop
positions
supporting the "Blank High/L.ow" outcome. The number of "non-winners" on reel
strip 16
is therefore 11 (i.e., 24 - 13) and the probability of a "non-winner"
occurring on reel 16
(i.e., "Prob/Reel 2") is 0.45833 (i.e., 11 = 24). Finally, for reel strip 18
(i.e., "Reel 3"),
there are 14 reel stop positions which include collection symbols-- 4 stop
positions
supporting the "Payline Cows" outcome, 4 stop positions supporting the "Blank
High"
outcome, 4 stop positions supporting the "Blank Low" outcome and 1 stop
position
CA 02278949 1999-07-23
22
supporting the "Blank High/L,ow" outcome. The number of "non-winners" on reel
strip 18
is therefore 10 (i.e., 24 - 14) and the probability of a "non-winner"
occurring on reel 18
(i.e., "Prob/Reel 3") is 0.41667 (i.e., 10 = 24).
It can be seen from FIG. 7 that there is a minimum of zero and a maximum of
two
COW symbols that may appear on any individual reel 14, 16, 18. Accordingly,
there is a
minimum of zero and a maximum of six COW symbols that may appear on the
combination of reels 14, 16, 18. One may derive the probability of every
possible number
of COW symbols (i.e., from zero to six) which may appear on the combination of
reels 14,
16, 18 in a single spin by first computing the probability per reel of either
0, 1 or 2 COW
symbols appearing on that reel, determining the various combinations of 0, 1
or 2 COW
symbols on each reel that will support a particular number of COW symbols in a
single
spin, then for each combination supporting that number of COW symbols,
multiplying the
appropriate probability per reel values to determine the probability of that
combination
occurring in a single spin. The probability of any particular number of COW
symbols
t 5 appearing in a single spin is the sum of the probabilities of the
combinations supporting that
number.
The probability per reel of either 0, 1 or 2 COW symbols appearing on each
individual reel is computed as follows. The probability of no COWs occurnng on
any
individual reel is simply the number of reel stop positions for that reel in
which no COW
symbols appear (e.g., the "non-winners" plus any CASH COW outcomes) divided by
the
total number of reel stop positions. Similarly, the probability of one COW
occurring on
any individual reel is the number of reel stop positions for that reel in
which one COW
symbol appears (e.g., the sum of "Payline Cows," "Blank High" and "Blank Low"
outcomes) divided by the total number of reel stop positions. The probability
of two
COWS occurring on any individual reel is the number of reel stop positions for
that reel in
which two COW symbols appear (e.g., the "Blank High/L.ow" outcome) divided by
the
total number of reel stop positions.
First consider the number of reel stop positions on respective reels 14, 16,
18 in
which no COW symbols appear. For reel 14 (i.e., "Reel 1"), there are 13 "non-
winners"
and no CASH COW outcomes, so the number of reel stop positions in which no COW
symbols appear is 13 and the probability of no COWS appearing on reel 14 is
therefore
0.541667 (i.e., 13 = 24). For reel 16 (i.e., "Reel 2"), there are 11 "non-
winners" and three
CA 02278949 1999-07-23
23
CASH COW outcomes, so the number of reel stop positions in which no COW
symbols
appear is 14 and the probability of no COWs appearing on reel 16 is therefore
0.58333 (i.e.,
14 = 24). For reel 18 (i.e., "Reel 3"), there are 10 "non-winners" and no CASH
COW
outcomes, so the number of reel stop positions in which no COW symbols appear
is 10 and
the probability of no COWs appearing on reel 18 is therefore 0.41667 (i.e., 10
= 24). _
Next consider the number of reel stop positions on respective reels 14, 16, 18
in
which one COW symbol appears. For reel 14, there are 4 "Payline Cows," 3
"Blank High"
outcomes and 3 "Blank Low" outcomes, so the number of reel stop positions in
which one
COW symbol appears is 10 and the probability of one COW appearing on reel 14
is
therefore 0.41667 (i.e., 10 = 24). For reel 16, there are 4 "Payline Cows," 2
"Blank High"
outcomes and 2 "Blank Low" outcomes, so the number of reel stop positions in
which one
COW symbol appears is 8 and the probability of one COW appearing on reel 16 is
therefore 0.3333 (i.e., 8 = 24). For reel 18, there are 5 "Payline Cows," 4
"Blank High"
outcomes and 4 "Blank Low" outcomes, so the number of reel stop positions in
which one
~ 5 COW symbol appears is 13 and the probability of one COW appearing on reel
18 is
therefore 0.541667 (i.e., 13 = 24).
The number of reel stop positions on respective reels 14, 16, 18 in which two
COW
symbols appears is simply the number of "Blank High/Low" outcomes on each
reel. For
reel 14 and reel 18, there is 1 "Blank High/L.ow" outcome and therefore the
probability of
two COW symbols appearing on reel 14 or reel 18 is 0.041667 (i.e., 1 = 24).
For reel 16,
there are 2 "Blank High/Low" outcomes and therefore the probability of two COW
symbols appearing on reel 16 is 0.08333 (i.e., 2 = 24).
The derivation of probability of certain numbers of COW symbols which may
appear in a single spin will hereinafter be described in detail. First
consider the probability
of zero COW symbols appearing on the combination of reels 14, 16, 18. There is
only one
combination of 0, 1 or 2 COW symbols on each respective reel (i.e., 0 COW
symbols on
reel 14, 0 COW symbols on reel 16 and 0 COW symbols on reel 18) that will
support zero
COW symbols for the combination. The probabilities per reel associated with 0,
0 and 0
COW symbols on respective reels 14, 16, 18 are 0.541667, 0.58333 and 0.41667.
The
probability of zero COWS appearing in the combination is therefore 0.1316551.
CA 02278949 1999-07-23
. . 24
The computation of probability of six COW symbols appearing on the combina!ion
of reels 14, 16, 18 is similar to that for zero COW symbols because there is
only one
combination of 0, 1 or 2 COW symbols on each respective reel (i.e., 2 COW
symbols on
reel 14, 2 COW symbols on reel 16 and 2 COW symbols on reel 18) that will
support a
total of six COW symbols. The probabilities per reel associated with 2, 2 and
2 COW
symbols on respective reels 14, 16, 18 are 0.041667, 0.08333 and 0.041667. The
probability of six COW symbols appearing in the combination is therefore
0.0001447.
The computation of probability of one, two, three, four or five COW symbols
appearing on the combination of reels 14, 16, 18 in a single spin is somewhat
more
complicated than that for zero or six COW symbols because there are multiple
combinations of 0, 1 or 2 COW symbols on each respective reel that will
support those
combinations. After the combinations supporting a particular number of COW
symbols are
determined, one must compute the probability of each combination and then sum
the
probabilities to determine the probability of that number of COW symbols
occurring in a
single spin. Consider, for example, the probability of one COW symbol
appearing on the
combination of reels 14, 16, 18. There are three combinations of 0, 1 or 2 COW
symbols
on each respective reel that will support a total of one COW symbol in a
single spin. These
combinations include: l, 0 and 0 COW symbols, 0, l and 0 COW symbols and 0, 0
and 1
COW symbols on respective reels 14, 16, 18. The probabilities per reel
associated with 1,
0 and 0 COW symbols on respective reels 14, 16, 18 are 0.416667, 0.58333 and
0.41667
and the probability of that combination is therefore 0.101274. The
probabilities per reel
associated with 0, 1 and 0 COW symbols on respective reels 14, 16, 18 are
0.541667,
0.33333 and 0.41667 and the probability of that combination is 0.07523. The
probabilities
per reel associated with 0, 0 and 1 COW symbols on respective reels 14, 16, 18
are
0.541667, 0.58333 and 0.541667 and the probability of that combination is
0.171. The
probability of one COW symbol appearing in a single spin, 0.3476563, is the
sum of the
probabilities of the three aforementioned combinations.
The probability of two, three, four or five COW symbols appearing in a single
spin
is computed in similar fashion and will not be described in detail herein.
Suffice it to say
that the probability of two COW symbols is 0.3294271, the probability of three
COW
symbols is 0.1507523, the probability of four COW symbols is 0.0364583 and the
probability of five COW symbols is 0.0039063.
CA 02278949 1999-07-23
FIG. 8 summarizes the probabilities and expected values associated with
various
combinations of collection symbols which may appear in a single spin. The
"Award"
column identifies the normalized value of each possible outcome. As has been
heretofore
described, in one embodiment of the JACKPOT STAMPEDET"' game, the normalized
5 value of each COW symbol is one coin or credit. Thus, in a 1-c~~n game, the
appearance of
six COWs in a single spin will result in an award of 6 coins or credits, five
COWs will
award 5 coins, and so on. The value of a CASH COW symbol in a 1-coin game, on
average, is 11.833 coins or credits. In one embodiment, the actual award
values for COW
and CASH COW symbols are doubled relative to the normalized values in a 2-coin
game
10 and tripled in a 3-coin game. In one embodiment, the award values are
doubled still further
for bonus rounds entered with "Round Up Double Wild" combinations. Thus, the
actual
award values may be up to six times the normalized award values, in a 3-coin
game entered
with a "Round Up Double Wild" combination.
The "Pulls/Hit" column of FIG. 8 identifies, on average, the number of bonus
15 spins that would be required to "hit" each respective combination of
collection symbols.
This is computed for each combination by taking the inverse of the probability
value
associated with that outcome. Specifically, the "Pulls/Hit" value is 6912
(i.e., 1
0.0001447) for the "Six Cows" combination, 256 (i.e., 1 = 0.0039063) for the
"Five
Cows" combination, 27.42857 (i.e., 1 = 0.0364583) for the "Four Cows"
combination,
20 6.633397 (i.e., 1 = 0.1507523) for the "Three Cows" combination, 3.035573
(i.e., 1
0.3294271 ) for the "Two Cows" combination, 2.876404 (i.e., 1 = 0.3476563) for
the
"Single Cow" combination, 7.595604 (i.e., 1 = 0.1316551) for the "No Cows"
combination and 8 (i.e., 1 = 0.125) for a combination including the "Cash Cow"
symbol.
The "EV" column of FIG. 8 identifies the normalized expected value per spin
25 associated with each respective combination of collection symbols, computed
as the
product of the probability of that combination (i.e., the value in the left
hand column of
FIG. 8) and the normalized award value of that combination. Specifically, the
normalized expected value per spin is 0.000868 (i.e., 0.0001447 x 6) for the
"Six Cow"
combination, 0.019531 (i.e., 0.0039063 x 5) for the "Five Cow" combination,
0.145833
(i.e., 0.0364583 x 4) for the "Four Cow" combination, 0.452257 (i.e.,
0.1507523 x 3) for
the '"Three Cow" combination, 0.658854 (i.e., 0.3294271 x 2) for the "Two Cow"
CA 02278949 1999-07-23
. , 26
combination, 0.347656 (i.e., 0.347656 x 1) for the "Single Cow" combination, 0
for the
"No Cows" combination and 1.479167 (i.e., 0.125 x 11.8333) fir a combination
including a "Cash Cow" symbol. The sum of each respective EV value, 3.104167,
is the
normalized expected value per spin of any combination of collection symbols.
In a
bonus round consisting of five bonus spins, the contribution to expected value
from
COW or CASH COW symbols is five times the expected value per spin, or
15.52083.
The normalized expected value per spin including contributions from both
collection symbols and standard winning combinations is computed by summing
the
normalized expected value from standard winning combinations (FIG. 6) and the
normalized expected value from collection symbols (FIG. 8). Thus, for example,
in a 3-
coin game, where the normalized expected value from standard winning
combinations is
0.788122, the normalized expected value per spin including contributions from
both
collection symbols and standard winning combinations is 3.892289 (i.e.,
0.788122 +
3.104167). In a bonus game consisting of five bonus spins, the normalized
expected
value is five times the expected value per spin, or 19.461445. It is noted
again, however,
that the actual award values for the bonus round are doubled relative to the
normalized
values in a 2-coin game and tripled in a 3-coin game, and doubled still
further for bonus
rounds entered with "Round Up Double Wild" combinations. Thus, the actual
award
values for the bonus round may be up to six times the normalized award values,
or
116.76867, in a 3-coin game entered with a "Round Up Double Wild" combination.
While the present invention has been described with reference to one or more
particular embodiments, those skilled in the art will recognize that many
changes may be
made thereto without departing from the spirit and scope of the present
invention. Each
of these embodiments and obvious variations thereof is contemplated as falling
within
the spirit and scope of the claimed invention, which is set forth in the
following claims.
