Patent Publication Number: US-7905772-B2

Title: Gaming device having multiple round bonus scheme with residual awards

Description:
PRIORITY CLAIM 
     This application is a continuation application of, claims priority to and the benefit of U.S. patent application Ser. No. 10/241,248, filed on Sep. 11, 2002, which is a continuation-in-part of U.S. patent application Ser. No. 09/682,428, filed Aug. 31, 2001, the entire contents of which are incorporated herein by reference. 
    
    
     COPYRIGHT NOTICE 
     A portion of the disclosure of this patent document contains or may contain material which is subject to copyright protection. The copyright owner has no objection to the photocopy reproduction by anyone of the patent document or the patent disclosure in exactly the form it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
     DESCRIPTION 
     The present invention relates in general to a gaming device, and more particularly to a gaming device having multiple round bonus scheme with residual awards. 
     BACKGROUND OF THE INVENTION 
     Gaming devices such as slot, poker, blackjack and keno machines having primary games and secondary or bonus games or schemes are well known. One well known bonus game provides a player with a series of different award offers consisting of credits or dollars. The player may accept or reject any individual award offer in the series, however, the player must accept the final award offer if no previous award offer is accepted. If the player accepts an award offer, the player keeps the award and the bonus game terminates. If the player rejects the award offer, the gaming device provides a new award offer for player acceptance. The bonus game continues to provide new award offers until an award offer is accepted or the award offer is the final award offer. 
     Several implementations of this type of bonus scheme have been employed in gaming machines of various types. While this type of gaming device has achieved significant popularity in the gaming industry, players may lose interest in the game after playing the game repeatedly. Accordingly, there is a need for new gaming devices having improved award offer bonus schemes. 
     SUMMARY OF THE INVENTION 
     The present invention provides a gaming device having an award offer and termination bonus scheme, wherein the player may improve an award offer during the bonus scheme. The bonus game enables the player to select an initial choice that either is the initial award offer or that the game uses to provide an initial award offer. The gaming device then enables the player to modify the initial award offer, creating a subsequent or modified award offer, which may be more or less than the initial award offer. The game repeats this process a predetermined number of times. In one embodiment, the game sequentially increases the likelihood of decreasing the player&#39;s award offer each time the player rejects an award offer. 
     In one embodiment, to modify the award offer, the player picks a masked selection from a plurality of masked selections. The picked selection yields a modifying value. The gaming device reveals the modifying value and determines a new award offer based on the modifying value. 
     In another embodiment of the present invention, the gaming device provides a plurality of offers associated with a plurality of positions. The gaming device further provides a plurality of position changes that modify the player&#39;s position and offer. Upon the initiation of the bonus scheme, the player obtains a position and an offer. The gaming device randomly selects a position change and the player&#39;s position and offer are modified by the selected position change. The selected position change is associated with a terminator. The gaming device enables the player to either accept the provided offer or enable the gaming device to select another position change in an attempt to modify the provided offer. The bonus scheme proceeds until the player accepts the provided offer or the gaming device randomly selects a position change with an associated terminator. 
     In another embodiment of the present invention, the gaming device further provides a bonus game having a plurality of rounds, each round including a plurality of picks by the player. Upon the initiation of each round, the player obtains a position and an award. Upon an input by the player, the gaming device randomly selects position moves and the player&#39;s position and award are modified by the selected position moves. If the player reaches the first or ultimate position associated with a maximum award without using all position move points and/or picks in a round, the gaming device enables the player to carry over any residual position change points and/or residual picks from one round to another round of the bonus game. 
     It is therefore an advantage of the present invention to provide a gaming device with a bonus game that has a plurality of rounds, wherein residual awards unused during a round can be carried over to another round of the bonus game. 
     It is a further advantage of the present invention to provide a gaming device with a bonus game that has a plurality of rounds, wherein residual picks unused during a round can be carried over to another round of the bonus game. 
     Other objects, features and advantages of the invention will be apparent from the following detailed disclosure, taken in conjunction with the accompanying sheets of drawings, wherein like numerals refer to like parts, elements, components, steps and processes. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are perspective views of alternative embodiments of the gaming device of the present invention. 
         FIG. 2  is a schematic block diagram of the electronic configuration of one embodiment of the gaming device of the present invention. 
         FIGS. 3A through 3D  are front elevation views of the display of one embodiment of the improved award offer bonus scheme illustrating the selection of an initial offer from a plurality of offers. 
         FIGS. 3E through 3J  are front elevation views of the display of one embodiment of the improved award offer bonus scheme illustrating the modification of an existing offer. 
         FIGS. 4A through 4C  are front elevation views of the display of a preferred embodiment of the improved award offer bonus scheme illustrating the selection of an initial offer. 
         FIGS. 4D through 4L  are front elevation views of the display of one preferred embodiment of the improved award offer bonus scheme illustrating the replacement of an existing offer. 
         FIGS. 5A through 5F  are front elevation views of the display of another embodiment of the improved award offer bonus scheme having a varying number of selectable masked choices. 
         FIG. 6  is a front elevation view of the display of a further embodiment of the improved award offer bonus scheme having an additional offer display. 
         FIGS. 7A through 7E  are front elevation views of the display of another embodiment of the improved award offer bonus scheme having offer ranges in which the offer replacement or modification changes when the offer enters a different range. 
         FIGS. 8A through 8G  are front elevation views of the display of another embodiment of the improved award offer bonus scheme having a plurality of offers associated with a plurality of positions and a plurality of terminators associated with a plurality of position changes. 
         FIGS. 9A through 9D  are front elevation views of the display of another embodiment of the improved award offer bonus scheme having a plurality of terminators associated with a plurality of position changes and a plurality of positions. 
         FIGS. 10A through 10B  are front elevation views of the display of another embodiment of the improved award offer bonus scheme having offer ranges in which the number of offer replacements or modifications changes when the offer enters a different range. 
         FIGS. 11A through 11O  are front elevation views of the display of one embodiment of the present invention illustrating the carryover of residual points to another round of the bonus game. 
         FIGS. 11P through 11V  are front elevation views of the display of another embodiment of the present invention illustrating the carryover of residual picks to another round of the bonus game. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Gaming Device and Electronics 
     Referring now to the drawings, and in particular to  FIGS. 1A and 1B , gaming device  10   a  and gaming device  10   b  illustrate two possible cabinet styles and display arrangements and are collectively referred to herein as gaming device  10 . The present invention includes the game (described below) being a stand alone game or a bonus or secondary game that coordinates with a base game. When the game of the present invention is a bonus game, gaming device  10  in one base game is a slot machine having the controls, displays and features of a conventional slot machine, wherein the player operates the gaming device while standing or sitting. Gaming device  10  also includes being a pub-style or table-top game (not shown), which a player operates while sitting. 
     The base games of the gaming device  10  include slot, poker, blackjack or keno, among others. The gaming device  10  also embodies any bonus triggering events, bonus games as well as any progressive game coordinating with these base games. The symbols and indicia used for any of the base, bonus and progressive games include mechanical, electrical or video symbols and indicia. 
     In a stand alone or a bonus embodiment, the gaming device  10  includes monetary input devices.  FIGS. 1A and 1B  illustrate a coin slot  12  for coins or tokens and/or a payment acceptor  14  for cash money. The payment acceptor  14  also includes other devices for accepting payment, such as readers or validators for credit cards, debit cards or smart cards, tickets, notes, etc. When a player inserts money in gaming device  10 , a number of credits corresponding to the amount deposited is shown in a credit display  16 . After depositing the appropriate amount of money, a player can begin the game by pulling arm  18  or pushing play button  20 . Play button  20  can be any play activator used by the player which starts any game or sequence of events in the gaming device. 
     As shown in  FIGS. 1A and 1B , gaming device  10  also includes a bet display  22  and a bet one button  24 . The player places a bet by pushing the bet one button  24 . The player can increase the bet by one credit each time the player pushes the bet one button  24 . When the player pushes the bet one button  24 , the number of credits shown in the credit display  16  decreases by one, and the number of credits shown in the bet display  22  increases by one. A player may cash out by pushing a cash out button  26  to receive coins or tokens in the coin payout tray  28  or other forms of payment, such as an amount printed on a ticket or credited to a credit card, debit card or smart card. Well known ticket printing and card reading machines (not illustrated) are commercially available. 
     Gaming device  10  also includes one or more display devices. The embodiment shown in  FIG. 1A  includes a central display device  30 , and the alternative embodiment shown in  FIG. 1B  includes a central display device  30  as well as an upper display device  32 . The display devices display any visual representation or exhibition, including but not limited to movement of physical objects such as mechanical reels and wheels, dynamic lighting and video images. The display device includes any viewing surface such as glass, a video monitor or screen, a liquid crystal display or any other static or dynamic display mechanism. In a video poker, blackjack or other card gaming machine embodiment, the display device includes displaying one or more cards. In a keno embodiment, the display device includes displaying numbers. 
     The slot machine base game of gaming device  10  preferably displays a plurality of reels  34 , preferably three to five reels  34 , in mechanical or video form on one or more of the display devices. Each reel  34  displays a plurality of indicia such as bells, hearts, fruits, numbers, letters, bars or other images which preferably correspond to a theme associated with the gaming device  10 . If the reels  34  are in video form, the display device displaying the video reels  34  is preferably a video monitor. Each base game, especially in the slot machine base game of the gaming device  10 , includes speakers  36  for making sounds or playing music. 
     Referring now to  FIG. 2 , a general electronic configuration of the gaming device  10  for the stand alone and bonus embodiments described above preferably includes: a processor  38 ; a memory device  40  for storing program code or other data; a central display device  30 ; an upper display device  32 ; a sound card  42 ; a plurality of speakers  36 ; and one or more input devices  44 . The processor  38  is preferably a microprocessor or microcontroller-based platform which is capable of displaying images, symbols and other indicia such as images of people, characters, places, things and faces of cards. The memory device  40  includes random access memory (RAM)  46  for storing event data or other data generated or used during a particular game. The memory device  40  also includes read only memory (ROM)  48  for storing program code, which controls the gaming device  10  so that it plays a particular game in accordance with applicable game rules and pay tables. 
     As illustrated in  FIG. 2 , the player preferably uses the input devices  44  to input signals into gaming device  10 . In the slot machine base game, the input devices  44  include the pull arm  18 , play button  20 , the bet one button  24  and the cash out button  26 . A touch screen  50  and touch screen controller  52  are connected to a video controller  54  and processor  38 . The terms “computer” or “controller” are used herein to refer collectively to the processor  38 , the memory device  40 , the sound card  42 , the touch screen controller and the video controller  54 . 
     In certain instances, it is preferable to use a touch screen  50  and an associated touch screen controller  52  instead of a conventional video monitor display device. The touch screen enables a player to input decisions into the gaming device  10  by sending a discrete signal based on the area of the touch screen  50  that the player touches or presses. As further illustrated in  FIG. 2 , the processor  38  connects to the coin slot  12  or payment acceptor  14 , whereby the processor  38  requires a player to deposit a certain amount of money in to start the game. 
     It should be appreciated that although a processor  38  and memory device  40  are preferable implementations of the present invention, the present invention also includes being implemented via one or more application-specific integrated circuits (ASIC&#39;s), one or more hard-wired devices, or one or more mechanical devices (collectively or alternatively referred to herein as a “processor”). Furthermore, although the processor  38  and memory device  40  preferably reside in each gaming device  10  unit, the present invention includes providing some or all of their functions at a central location such as a network server for communication to a playing station such as over a local area network (LAN), wide area network (WAN), Internet connection, microwave link, and the like. 
     With reference to the slot machine base game of  FIGS. 1A and 1B , to operate the gaming device  10 , the player inserts the appropriate amount of tokens or money in the coin slot  12  or the payment acceptor  14  and then pulls the arm  18  or pushes the play button  20 . The reels  34  then begin to spin. Eventually, the reels  34  come to a stop. As long as the player has credits remaining, the player can spin the reels  34  again. Depending upon where the reels  34  stop, the player may or may not win additional credits. 
     In addition to winning base game credits, the gaming device  10 , including any of the base games disclosed above, also includes bonus games that give players the opportunity to win credits. The gaming device  10  preferably employs a video-based display device  30  or  32  for the bonus games. The bonus games include a program that automatically begins when the player achieves a qualifying condition in the base game. 
     In the slot machine embodiment, the qualifying condition includes a particular symbol or symbol combination generated on a display device. As illustrated in the five reel slot game shown in  FIGS. 1A and 1B , the qualifying condition includes the number seven appearing on three adjacent reels  34  along a payline  56 . It should be appreciated that the present invention includes one or more paylines, such as payline  56 , wherein the paylines can be horizontal, diagonal or any combination thereof. 
     Offer Modification 
     Referring now to  FIGS. 3A through 3J , one embodiment of the improved award offer bonus scheme of the present invention includes modifying such as by increasing or decreasing an existing offer by mathematically altering it, as discussed in more detail below. The gaming device includes a screen or display  100  which preferably includes a touch screen. The display and particularly the touch screen enables the player to select an award offer from a plurality of award offers. A plurality of masked selections  102 ,  104  and  106  are illustrated in  FIGS. 3A through 3D . It should be appreciated that while three selections are illustrated, two or more selections are contemplated. Appropriate messages such as “MAKE A SELECTION” or “SELECT AN AWARD OFFER” are preferably provided to the player visually, or through suitable audio or audiovisual displays in conjunction with the plurality of selections. 
     The player picks one of the masked initial award offers or selections  102 ,  104  or  106 , and the game provides or generates an initial award offer  108 ,  110  or  112 , respectively. The gaming device also preferably reveals each of the available initial award offers  108 ,  110  and  112  associated with selections  102 ,  104  and  106 , respectively, as illustrated in  FIG. 3D , so that the player knows whether the player has made a good or bad selection. In one example, the player chooses the selection  104 , and the game reveals the initial award offer  110  having a value of 50 credits as illustrated in  FIGS. 3B and 3C . The gaming device preferably includes an award offer display  113 , which displays the initial award offer  114  as illustrated in  FIGS. 3C and 3D . 
     In one embodiment, the gaming device selects and distributes the plurality of masked initial award offers from a larger pool (not illustrated) of initial award offers available during the bonus game. The pool of initial award offers may, for example, include nine possible initial award offers ranging from +10 to +100 credits, although any size pool is contemplated by the present invention. The pool may alternatively include negative initial award offers. The gaming device preferably randomly selects the plurality of initial award offers from the pool of initial award offers (not illustrated) each time the bonus game is initiated. It is also contemplated that the gaming device may assign a weight factor or probability to each initial award offer in the pool such that award offers having higher weight factors or probabilities have a greater chance of being selected. This weight factor or probability may be consistent throughout the entire bonus game or change from play to play during the bonus game. 
     The bonus game as described above reveals or unmasks the remaining initial award offers  108  and  112  as illustrated in  FIG. 3D . If the player would have chosen the selection  102 , the player would have obtained the initial award offer  108  worth 100 credits, and if the player would have chosen the selection  106 , the player would have obtained the initial award offer  112  worth 75 credits. 
     After establishing the initial award offer, the gaming device enables the player to modify the initial award offer and form a subsequent or new award offer. The subsequent or new award offer is based on or dependent on the initial award offer. It should be appreciated that the subsequent or new award offer may be of lesser, greater or equal value than the selected award offer, adding an element of risk to the bonus game. It should be appreciated that the initial award offer is preferably positive as discussed above. 
     Referring now to  FIGS. 3E through 3J , after establishing an initial award offer, the gaming device provides the player with a second display  116 . The second display  116  includes the initially selected award offer  114  in the award offer display  113 , a value display  118  and a plurality of masked selections  120 ,  122  and  124 . It should be appreciated that the number of masked selections may vary in accordance with the present invention. 
     The value display  118  includes a plurality of positions or points  126  or a ranking of positions or points and a plurality of associated offer modifiers  128 . In this embodiment, the ranking of positions or points and modifiers or offer modifiers are displayed in a tabular format although other suitable displays are contemplated. Each position, point or number of points has an associated offer modifier. The offer modifier in one embodiment is measured in credits. The offer modifiers  128  are not new award offers. Rather, the gaming device uses the offer modifiers  128  to modify the initially selected award offer  114  (and subsequent award offers) to produce a new or modified award offer. The points  126  which the player chooses or obtains as described below, correspond to or determine which offer modifiers  128  the game uses to modify the award offer. 
     The player picks one of the masked selections  120 ,  122  or  124 . The gaming device reveals and provides a number of points associated with the selection. The gaming device may select the points for this portion of the bonus game from a larger pool of points (not illustrated). The gaming device preferably randomly selects points from the pool and randomly assigns the points to each of the selections  120 ,  122  and  124 . The point pools (not illustrated) may be weighted via a weight factor or probability associated with each point. The weight factor or probability may be consistent throughout the bonus game or vary from play to play in the bonus scheme. 
     In one example, the player chooses selection  124 , which reveals the point  136  having a value of “1” as illustrated in  FIG. 3F . The gaming device preferably reveals or unmasks the remaining, non-chosen points  132  and  134  as illustrated in  FIG. 3G . The gaming device also highlights or otherwise indicates the offer modifier associated with the selected point in the value display  118 . In this embodiment, the value display  118  highlights the offer modifier of twenty-five, which is associated with the selected point value of “1” as illustrated in  FIG. 3G . 
     The gaming device modifies the award offer and specifically adds the designated offer modifier  128  of “25” to the initial or previous offer of “50.” Another embodiment includes multiplying the modifier by the initial or previous offer. Other suitable mathematical operations or calculations may be performed or desired by the implementor. The addition of the modified offer  128  creates a modified or subsequent award offer  138  of 75 credits, which is displayed in the award offer display  113  as illustrated in  FIGS. 3G and 3H . 
     The present invention includes enabling the player to accept the modified award offer  138  or reject it and continue to play the bonus game.  FIG. 3H  includes accept and reject indicators or buttons  140  and  142 , respectively, enabling the player to register his or her decision. That is, the game enables the player to accept or reject an offer award after the first modified award offer. Another embodiment includes enabling the accept or reject function after the initial award offer, second or any subsequent modification. In the illustrated embodiment, the accept and reject buttons are labeled “STOP” and “GO.” 
     If the player accepts the subsequent award offer  138 , the gaming device provides the player with the award offer and updates the player&#39;s total credits with the accepted or provided award offer. The gaming device preferably does not enable the player to obtain any more award offers and thereby terminates the bonus game. If the player rejects the modified award offer  138 , thereby risking it for the chance at receiving a modified award offer of greater value, the gaming device enables the player to obtain a modified or subsequent award offer as illustrated in  FIGS. 3I and 3J . The new or second subsequent award offer  144  is based on the immediately previous award offer  138  as illustrated in  FIG. 3J , and a selected point  132  of “−1” which yields an offer modifier of “−25” credits, which decreases the previous award offer by 25 to award offer  144  of “50.” 
     Thus, after the player rejects the first subsequent award offer  138 , the gaming device enables the player to generate another offer modifier  128  in the same manner as described above. When the player selects a point  132  with a value of “−1”, the game generates the offer modifier  128  of “−25” credits. The gaming device thereby reduces or modifies the player&#39;s previous award offer  138 , resulting in a third award offer  144  of “50” credits as illustrated in  FIG. 3J . The gaming device enables the player to accept this offer, terminating the bonus scheme, or continue as described previously. The game preferably ends after a predetermined number of award offers are rejected such as after three rejections or four total award offers made to the player. 
     In one preferred embodiment, the gaming device of the present invention further includes structuring the point pools such that later point distributions yield a greater chance of generating a negative number of points and thus credits for the player and generating a relatively high positive number of points and thus credits for the player. That is, the present invention includes later offers being potentially riskier and potentially yielding higher award offers. 
     Offer Replacement 
     Referring now to  FIGS. 4A through 4L , another embodiment of the improved award offer bonus scheme of the present invention includes replacing award offers with related award offers. The award offers are related by an order of their values. The gaming device of this embodiment enables the player to individually select an initial award offer, similar to the above embodiment, from a plurality of masked award offer selections and thereafter receive a new or replaced award offer, which is based on the initial award offer. The replaced award offer may be greater than, less than or equal to the value of the previous award offer. 
     In this embodiment, the display  200  includes the value display  218  and a plurality of masked selections  202 ,  203 ,  204 ,  205  and  206 . The value display  218  includes a ranking of positions  226  and associated award offers  228 , which differ from the offer modifiers  128  in the previous embodiment, which mathematically modify previous offers. The display  200  enables the player to select an initial number, ranking, point or position  226  which is associated with an initial award offer. The player picks from the five masked selections as illustrated in  FIGS. 4A through 4C , although any suitable number of selections may be employed. In this embodiment, the ranking, points or positions  226  which are initially player selected designate award offers  228 , and the award offers  228  replace the previously selected award offers instead of modifying the previous award offers. 
     In one preferred embodiment, the value display  218  is similar to a chart used to record and display best sellers such as book or record sales. The current number or position  226  represents the rank, place or spot on the chart (i.e., number 1 meaning a number one best selling book or record) and the award offers  228  are the game credits associated with that position on the chart. The object is to move to or as close to the number 1 rank or position as possible and thereby receive the highest number of credits. After establishing the initial rank or position on the chart that the game generates from the player&#39;s initial pick, as indicated above, the game enables the player to modify the player&#39;s current position on the value display  218 . A positive number moves the player&#39;s position a number of positions closer to the number 1 position and a negative number moves the player&#39;s position  226  a number of positions away from the number 1 position. 
     After the player picks one of the masked initial positions or selections to generate an initial position such as position  209  of “18”, the gaming device preferably reveals the other possible initial positions  208 ,  210 ,  211  and  212  associated with the selections  202 ,  204 ,  205  and  206 , respectively (best seen in  FIG. 4C ). In this example, the player chooses the selection  203  which reveals the associated initial position  209  of “18” as illustrated in  FIGS. 4B and 4C . The initial positions  208  through  212  may be any of the illustrated possible positions  226  including positions “1” to “25.” The possible positions  226  in one implementation are weighted so that the game more likely generates less valuable positions, such as “18” or “24” than middle valued positions, such as “12” or high valued positions, such as “3.” 
     The value display  218  preferably indicates or designates the initial position as illustrated in  FIG. 4C . The value display also highlights or otherwise marks an associated award offer of eight credits. The value display  218  may display a label  250  such as “WEEK 1” which enhances the theme of the game by showing different positions at different times or stages of the game. 
     After establishing the initial position, the gaming device provides a second selection display  216  as illustrated in  FIGS. 4D through 4L , which includes value display  218  and a plurality of masked selections  219 ,  220 ,  221 ,  222 ,  223  and  224 . Although six selections are illustrated, two or more selections are contemplated. 
     The player picks one of the masked selections. The gaming device reveals a number, rank or position move or point associated with such selection. In this example, the player chooses selection  224  revealing position move or point of “+3” as illustrated in  FIG. 4E . It should be appreciated that the selected point  236  is not a new award offer or credit amount. Rather the point  236  is used to determine the modification of the player&#39;s current position or spot on the value display  218 , which corresponds to an award offer that replaces the original offer. The position could also be associated with an award modification as explained above. 
     In this example, the player selected an initial position of “18”, which has a corresponding award offer of eight as illustrated in  FIG. 4C . The player subsequently selects the move  236  of “+3.” The game accordingly changes the initial position by three places or positions closer to position 1, creating a new position of 15 and a new offer of twelve as illustrated in  FIG. 4F . That is, the player&#39;s position changes three spots towards the number 1 position. The new award offer  228  of twelve is displayed by the value display  218  and marked by the label  252  as “WEEK 2” as illustrated in  FIGS. 4E and 4F . It should be appreciated that the value display  218  may display the initial and new position  250  and  252 , respectively, simultaneously or only the new position  252 . The gaming device preferably reveals or unmasks the remaining non-chosen points  231 ,  232 ,  233 ,  234  and  235  associated with the remaining selections  219 ,  220 ,  221 ,  222  and  223 , respectively, as illustrated in  FIG. 4F . 
     The preferred embodiment includes enabling the player to accept the new award offer or reject the award offer and continue to play the bonus game. The gaming device provides the previously described accept and reject indicators or buttons  240  and  242  respectively labeled “STOP” and “GO”, as illustrated in  FIG. 4G . 
     If the player accepts the new award offer, the gaming device provides the player with the new award offer and terminates the bonus game. If the player rejects the new award offer, the bonus game continues in like fashion, wherein in this example: (i) the player picks one of the masked selections from the group of selections  219  through  224  as illustrated in  FIGS. 4G and 4H ; and (ii) the gaming device reveals position move  235  of zero as illustrated in  FIG. 4H , such that the player&#39;s position on the display does not change after the third offer as illustrated by position  253  in  FIG. 4I . The game also reveals the other position moves as illustrated in  FIG. 4I . At this point, again the player may accept or reject the award offer as illustrated in  FIG. 4J . 
     In one embodiment of the present invention, the game automatically rejects the award offer  228  if there is no risk to the player, e.g., when the current award offer is the lowest possible offer illustrated here as one credit in association with the twenty-fifth position. This auto-executing feature occurs only when the current award offer is not the final offer, that is, when the game will provide another award offer to the player. 
     As illustrated in  FIG. 4K , the player selects selection  219  which provides a +4 position move  231 . The game changes the position by four places or positions closer to position 1,creating a new position of 11 and a new offer of 30 as illustrated in  FIG. 4L . The offer of 30 is displayed by the value displayed  218  and marked by the label  254  as “WEEK 4” as also illustrated in  FIG. 4L . The gaming device also reveals the remaining non-chosen points associated with the remaining masked selections as further illustrated in  FIG. 4L . The player may then either reject the offer if there are any more remaining offers or accept the offer and end the bonus game. If there are no more remaining offers, the player&#39;s award is 30. It should be appreciated that this multi-step bonus game provides an interesting and exciting bonus game for players. 
     It should also be appreciated from previous example that the present invention includes positive position moves, negative position moves and no position moves. The present invention further includes assigning the masked selection values to make advancement more difficult or less difficult or more hazardous or less hazardous as the game advances. That is, the implementor may make advancement more difficult by increasing the number of negative moves and/or lower positive moves. The implementor may make advancement more hazardous by increasingly placing larger positive and negative moves or points in the selection groups, whereby the average value of the points stays the same, but the potential for obtaining high negative position moves as well as high positive position moves increases with each selection. It should also be appreciated that the gaming device may provide the player a replay of the game if the player achieves a certain level such as the first position. In such instance, the player would get the awards achieved in both the initial play and any replays. 
     In the embodiment of  FIGS. 4A to 4L , the number of masked selections increased from 5 in  FIGS. 4A to 4C  to 6 in  FIGS. 4D to 4L . It should be appreciated that the number of masked player selections can remain constant throughout the bonus scheme. In a further embodiment illustrated in  FIGS. 5A through 5F , the number of player selectable choices or masked selections may decrease or otherwise vary during the bonus game. In  FIG. 5A , the gaming device provides a display  300  having seven masked selections  319 ,  320 ,  321 ,  322 ,  323 ,  324  and  325 . The player picks one of the masked selections. The gaming device reveals the position associated with such selection. In  FIG. 5B , the player chooses the selection  319  revealing the initial position  336  of 12 as illustrated in  FIG. 5B . The gaming device preferably reveals or unmasks the remaining non-chosen positions  337  to  342  associated with the remaining selections  320 ,  321 ,  322 ,  323 ,  324  and  325 , respectively, as illustrated in  FIG. 5C . 
     In the next round of the bonus game illustrated in  FIGS. 5D through 5F , the gaming device provides six masked selections  319 ,  320 ,  321 ,  322 ,  323  and  324 . The player picks one of the masked selections. The gaming device reveals the position moves or points associated with such selection. In the illustrated example, the player chooses selection  324  revealing the position move point  341  having a value of −1 as illustrated in  FIG. 5E . The gaming device preferably reveals or unmasks the remaining non-chosen position moves or points  336 ,  337 ,  338 ,  339  and  340  associated with the remaining selections  319 ,  320 ,  321 ,  322  and  323 , respectively, as illustrated in  FIG. 5F . 
     A further alternative embodiment is illustrated in  FIG. 6 . This embodiment includes the value display  418 , the positions  426 , the associated offers  428  and the accept and reject buttons  440  and  442  as described previously. However, in this embodiment, the bonus game includes an award offer display  412  showing the various replaced positions  426  and offers  428  associated with the positions  426 . 
     It should be appreciated that the alternative embodiments of the improved award offer bonus scheme of the present invention can be simultaneously implemented in a single bonus round or each implemented individually in different bonus rounds. The determination of when to implement such alternative embodiments could also be randomly determined. 
     Offer Ranges 
     Referring now to  FIGS. 7A through 7E , in another embodiment of the present invention, the game is adapted to: (i) replace or modify a player&#39;s current offer with higher award offers when the player&#39;s offer resides within a particular offer range; and (ii) replace or modify a player&#39;s current award offer with higher or lower award offers when the player&#39;s offer resides within another award offer range. In one preferred implementation, the player upgrades the award offers through the range where the award offers can only increase until obtaining an award offer in a second range, wherein the player has to decide whether it is worth risking the current award offer and potentially receiving a lower award offer. The multiple ranges may be implemented with an award offer modification embodiment illustrated in  FIGS. 3A through 3J , or with an award offer replacement embodiment illustrated in  FIGS. 4A through 4L . For purposes of illustration, only an award offer replacement embodiment is illustrated and described below. 
     In  FIG. 7A , the display  500  includes an award offer display  518  that has a plurality of ranks or positions  526  and a displayed award offer  528  associated with each rank or position. This example provides twenty-two ranks positions  526  and award offers  528  spanning from one to one thousand. As illustrated, the same award offer  528  may be associated with two or more positions  526 . The display  500  also includes an accept button  540  and a reject button  542 , which have the functionality described above. The display  500  also includes an offers or moves remaining indicator  544 , which shows the player how many more times the player may reject a current award offer and obtain a new award offer. 
     In one implementation, the award offer display  518  includes a trail or path that a marker  550 , representing the player, moves along as the player generates new award offers. This particular trail includes an upward slope, wherein the marker  550  moves upwardly, and a downward slope, wherein the marker  550  moves downwardly. The slopes are differentiated by different audio, visual or audiovisual messages  520  and  522 . 
     This embodiment may provide messages, such as messages  520  and  522 , which describe the different risks of playing while the player&#39;s offer exists in a particular range. Alternatively, the game does not provide this information. The message  520 , corresponding to the nine positions on the upward slope (not including the top position), informs the player that the player&#39;s offer  528  only moves up if the player selects to keep moving while the marker  550  resides in one of the upward slope positions. The message  522 , corresponding to the thirteen downward slope positions  526  (including the top position), informs the player that the player&#39;s offer  528  can move up or down if the player selects to keep moving while the marker  550  resides on the top position or on one of the downward slope positions  526 . 
     In one embodiment of the present invention, the gaming device includes an area in the memory device  40  that stores one or more tables having position changes  546  one through twelve, move changes  548  that add or subtract moves from the moves remaining indicator  544  and an offer plus/minus indicator  560 , which the game generates when the player&#39;s current offer resides on the downward slope. When the player picks the keep moving button  542 , an input is sent to the processor  38 , whereby the processor randomly generates either a position change  546  or a move change  548 . If applicable, the processor also generates an offer plus/minus indicator  560 . 
     The display  500  may be adapted to inform the player of the actual values stored in the memory device  40 . Either or both the position  546  or move change  548  generation or the plus/minus indicator  560  generation may be weighted so that, e.g., the game generates one of the move changes  548  less than 1/7th of the time, or the game generates an offer increase fifty-five percent of the time, etc. 
     As illustrated in the display  500  of  FIG. 7A , in one implementation the player begins with three moves and at the start position. The message  520  informs the player that the player can only increase the offer by selecting the keep moving button  542 . In the display  502  of  FIG. 7B , after the player picks the keep moving button  542  a first time, the game generates a position change  546  of four from the memory device  40  but does not generate a plus/minus indicator  560 . The marker  550  moves four positions upward along the path of the offer display  518  so that the player&#39;s new award offer is three. The moves remaining display  544  shows one less move. Since the player&#39;s award offer still resides on the uphill side of the display  518 , the player would wisely pick the keep moving button  542  again. 
     In the display  504  of  FIG. 7C , after the player picks the keep moving button  542  a second time, the game generates a move change  548  of “add move” from the memory device  40 . The plus/minus indicator  560  is inapplicable here because the game does not generate a position change. That is, even on the downhill side the game does not generate an indicator  560  when it generates a move change  548 . The marker  550  stays in the same position  526  so that the player&#39;s award offer remains three. The moves remaining display  544  shows one additional move. Since the player&#39;s offer still resides on the uphill side of the display  518 , the player would again wisely pick the keep moving button  542  again. 
     In the display  506  of  FIG. 7D , after the player picks the keep moving button  542  a third time, the game generates a position change  546  of six from the memory device  40 , but does not generate a plus/minus indicator  560 . The marker  550  moves six positions  526  upward along the path of the offer display  518  so that the player&#39;s new award offer is ten. The moves remaining display  544  shows one less move. Since in this implementation, the uppermost position  526  is considered to be on the downhill side of the display  518 , the player has to weigh the risk of picking the keep moving button  542  again. In alternative implementations as discussed below, the uppermost position  526  may be considered to be on the uphill side of the display  518  or as a separate range altogether in which the offer  528  always decreases, so that the player has to backtrack positions  526  to move past the top position. 
     In the display  508  of  FIG. 7E , after the player picks the keep moving button  542  a fourth time, the game generates a position change  546  of eleven from the memory device  40  and additionally generates the plus indicator  560 . The marker  550 , therefore, moves eleven positions downward, i.e., creating a positive change in the player&#39;s offer  528 , which is now five hundred. If the game had generated a minus eleven position  526  change, the marker would move ten positions to the start position and stop. 
     Likewise, if the player generates a position change  546  that exceeds the last and most valuable position, e.g., corresponding to the one thousand offer  528 , the game in one implementation just provides the last offer. Thus, in the player&#39;s current position  526  having an associated offer  528  of five hundred, any positive position change  546  results in the player&#39;s achievement of the highest offer  528 . The moves remaining display  544  again shows one less move. Since in this implementation, the position  526  associated with the five hundred award  528  is on the downhill side of the display  518 , the player again has to weigh the risk of picking the keep moving button  542 . 
     In another implementation, the game may be adapted to weight the position moves  546  as a function of the player&#39;s current position  526 . That is, the game has, e.g., one weighting system for when the player keeps moving after achieving one of the offers  528  fifteen through fifty and another weighting system for when the player keeps moving after achieving one of the offers  528  one hundred through five hundred. In this implementation, the offer plus/minus indicator  560  can be weighted to generate negative changes  546  more often than positive changes  546 , and/or the changes  546  can also be weighted to generate higher numbers so that the game tends to set the player back further to a lesser position  526 . In any of these weighting systems, the move changes  548  may be weighted as desired by the implementor. 
     Although one implementation for providing varying offer ranges has been illustrated, the varying offer ranges may be combined differently than as illustrated in  FIGS. 7A to 7E . As described above, in one implementation, a third range having only decreasing offers is mixed in with one or more increase only and/or increase/decrease ranges. In another implementation, an increase/decrease range occurs first, followed by an increase only range. In another implementation, a decrease only range occurs at the end of the positions, so that the player must back up to try for a higher position. Any type of range may be adapted to include one, more than one or all of the positions  526 , so that each position  526  in one implementation includes a different type of range. In any of these combinations, a positive and or negative move changes  548  may be included in the selection pool as desired by the implementor. 
     Referring now to  FIGS. 8A through 8G , in another embodiment of the present invention the game is adapted to: (i) replace or modify a player&#39;s current offer with a higher award offer; (ii) replace or modify the maximum award offer with a higher maximum award offer; (iii) replace selected position changes with termination symbols or terminators; and (iv) enable the player to accept or reject each modified award offer. This modified award offer embodiment may be implemented with an award offer modification embodiment as illustrated in  FIGS. 3A through 3J  or with an award offer replacement embodiment as illustrated in  FIGS. 4A through 4L . For purposes of this application, only an award offer replacement embodiment is illustrated and described below. 
     In  FIG. 8A , the display  600  includes an award offers display  618  which has a plurality of ranks or positions  626  and a displayed award offer  628  associated with each rank or position. This examples provides twenty-four positions  626  and award offers  628  initially spanning from one to twenty. It should be appreciated that any suitable number of positions and award offers are contemplated by the present invention. As illustrated, the same award offer may be associated with two or more positions. In this embodiment, the display  600  includes an offer display  644  which displays the current award offer, an accept award offer indicator or button  648 , and a reject award offer indicator or button  642  which have the functionality described above. 
     In one embodiment of the current invention, the award offer display  618  includes a trail or path having a marker  650  representing the player. The marker moves along as the player generates modified award offers. The illustrated trial includes an upward slope wherein the marker  650  moves upwardly toward a peak position associated with the maximum award offer  620  and a downward slope wherein the marker  650  moves downwardly. It should be appreciated that the maximum award offer  620  may be associated with any position of the trail, path or sequence. In this embodiment, the award offers associated with the plurality of positions increase up the upward slope and decrease down the downward slope. The slopes may be differentiated by different audio, visual or audiovisual messages. 
     In one embodiment of the present invention, the gaming device includes an area in the memory device  40  that stores one or more tables having a plurality of position changes  646  which are illustrated on the display  646 . Each position change represents the number of positions along the award offer path or sequence  618  that the marker  650  will be moved. It should be appreciated that these position changes may or may not be display. It should also be appreciated that weighted probabilities may be associated with the position changes. At the initiation of the bonus scheme and when the player uses the reject award offer indicator  648 , an input is sent to the processor  38 , whereby the processor randomly selects one of the position changes  646 . In the illustrated embodiment, the gaming device displays the plurality of position changes and indicates to the player the selected position change. 
     In this embodiment, upon the triggering of the bonus scheme, the gaming device randomly selects a position change from the plurality of position changes  646 . The marker  650  is subsequently moved along the path the number of positions corresponding to the selected position change. After the gaming device has moved the marker  650  the number of positions corresponding to the selected position change, the selected position change is associated with a termination symbol or terminator. The player is offered the offer associated with the current position indicated by the marker as the players initial award offer. In one embodiment, the maximum award offer  620  is modified by combining the initial offer with the prior maximum award offer. The player may either accept or reject the initial award offer. If the player accepts the initial award offer, the gaming device provides the player the award offer, the player cannot obtain any more award offers and the bonus game ends. If the player rejects the award offer, the gaming device selects another position change. If the gaming device subsequently selects a position change with an associated termination symbol or terminator, the bonus game ends and the player may receive a consolation award. If the subsequently selected position change is not associated with a termination symbol or terminator, the marker is moved the number of positions corresponding to the selected position change. As described above, after the marker  650  is moved, the randomly selected position change is associated with a termination symbol or terminator. The players award offer is modified by combining the prior award offer with the offer associated with the markers current position. The maximum award offer  620  is further modified by combining the prior modified maximum award offer with the offer associated with the markers current position. The player may accept the modified award offer, thereby ending the bonus game or reject the modified award offer in an attempt to obtain a higher award offer or the maximum award offer. The game proceeds as described above until either the player obtains the maximum award offer or the gaming device selects a position change associated with a termination symbol or terminator. If the marker is moved to the peak position, the gaming device provides the player the maximum award offer, the player cannot obtain any more award offers and the bonus scheme ends. 
     In one example, as illustrated in the display  600  of  FIG. 8A , the player begins at the start position  624 . In the display  602  of  FIG. 8B , upon the initiation of the bonus scheme, the gaming device randomly selects a position change of five  652  from the plurality of position changes  646 . The marker  650  moves five positions upward along the path of the offer display  618  so that the player&#39;s initial award offer is one as illustrated in  FIG. 8B . The initial award offer is indicated in the award offer amount display  644 . The maximum award offer  620  is modified by combining the players initial award offer with the initial maximum award offer. As illustrated in  FIG. 8B , the maximum award offer is modified to twenty-one by combining the players initial award offer of one with the initial maximum award offer of twenty. Furthermore, as described above, the position change of five positions is associated with a termination symbol or terminator  654  for subsequent position change selections. In an alternative embodiments, the maximum award offer does not have to be modified, the modification could be randomly determined or could be modified based on number of moves. 
     In this embodiment, the player may either accept the initial award offer using the accept indicator  648  or reject the initial award offer using the reject award indictor  642 . In an alternative embodiment the player is not able to accept the initial award offer. In this embodiment, the gaming device will automatically select another position change and the game will proceed as described above. In another embodiment, the gaming device automatically rejects any award offer if subsequent or potential award offers are at least of an equal value to the initial award offer. 
     Referring to the display  604  of  FIG. 8C , upon the player using the reject indicator  642  to reject the initial award offer, the gaming devices randomly selects another position change from the plurality of position changes  646 . The gaming device randomly selected the position change of eight  652 . The marker  650  moves eight positions upward along the path of the offer display  618  over the peak position and downward along the path to a position with an associated award offer of three. As described above, the position change of eight is associated with a termination symbol or terminator for subsequent position change selections. It should be appreciated that the prior selected position change remains associated with a termination symbol or terminator. The player&#39;s award offer is modified to four by combining the prior award offer of one with the award offer of three associated with the markers current position. The gaming device displays the modified award offer  644 . The maximum award offer  620  is also modified to twenty-four by combining the prior maximum award offer of twenty-one with the award offer of three associated with the markers  650  current position. The player may either accept or reject the modified award offer of four as described above. 
     As seen in the display  606  of  FIG. 8D , using the reject indicator  642 , the player rejected the modified award offer. The gaming device randomly selected another position change from the plurality of position changes. The gaming devices selects the position change of thirteen  652 , and the marker  650  is moved thirteen positions downward along the path of the offer display to a position with an associated award offer of one. The position change of thirteen is associated with a termination symbol or terminator for subsequent position change selections. The players award offer is modified to five by combining the prior award offer of four with the current award offer of one. The offer display  644  displays the new modified award offer. The maximum award offer  620  is also modified to twenty-five by combining the prior maximum award of twenty-four with the current award offer of one. 
     As illustrated in the display  608  of  FIG. 8E , the player chose to reject the award offer of five. Accordingly, the gaming device randomly selected the position change of one. Having completed the download slope of the path of the offer display  618 , the marker  650  circles back to the upward slope of the path. The position change of one is associated with a termination symbol or terminator for subsequent position change selections. 
     In one embodiment, for completing one cycle of the offer display path the award offers  628  associated with each position on the path are modified. In this embodiment, the award offers associated with the non-peak positions increase by one, and the maximum award offer associated with the peak position increased by five to thirty. It should be appreciated that the award offer associated with each position may be randomly increased or increased according to some pre-determined mathematical formula. In an alternative embodiment, the award offers associated with a plurality of positions may increase. In another embodiment, the offers associated with a plurality of positions may increase, decrease, remain the same or any combination thereof. 
     As illustrated in  FIG. 8E , the award offer associated with marker&#39;s new position  626  is two. Accordingly, the player&#39;s award offer is further modified to seven by combining the prior modified award offer of five with the current award offer of two. The offer display  644  reflects this modification. Additionally, the maximum award offer  620  is further modified to thirty-two by combining the prior modified maximum award offer of thirty with the current award offer of two. The player may either accept or reject the award offer of seven as described above. 
     As seen in display  610  of  FIG. 8F , the player rejected the award offer of seven and the gaming device randomly selected another position change. The selected position change is associated with a termination symbol or terminator  654  and the bonus game ends. In this embodiment, with the selection of a position change with an associated termination symbol or terminator, the player receives a consolation prize of two credits. 
     In an alternative embodiment, when a position change with an associated termination symbol or terminator is selected, the bonus game ends and the player obtains no award. In another embodiment, the player obtains the award offer associated with the marker&#39;s  650  last position. In another embodiment, as illustrated in  FIG. 8G , the player obtains the last modified award offer, in this case seven. In this embodiment, since the player does not risk losing a modified award offer by the selection of a termination symbol or terminator, the player is motivated to continue rejecting award offers until either a terminator symbol is obtained or the maximum award offer is obtained. 
     Referring to  FIGS. 9A through 9D , in an alternative embodiment of the present invention, when the player rejects the offer associated with the markers current position  626 , the rejected position is associated with a termination symbol or terminator. In this embodiment, if the marker is subsequently moved to a prior visited position with an associated termination symbol or terminator, the bonus game ends. The additional feature of this embodiment provides increased risks and entertainment to the player because the player must avoid termination symbols or terminators not only in the plurality of position changes but also on the path of award offers itself. 
     Referring now to  FIG. 9A , upon the initiation of the bonus scheme, as described above, the gaming device randomly selects the position change of seven. Accordingly, the marker  750  moved from the start position, upward along the path of the offer display  718  to a position seven moves away as illustrated in  FIG. 9B . The selected position change of seven is associated with a termination symbol or terminator. The award offer of two associated with the seventh position of the offer display  718  is the players initial award offer. The award offer of two is displayed in the award offer display  744 . The maximum award offer  720  is modified to twenty-two by combining the initial maximum award offer of twenty with the players initial award offer of two. As described above, the player may either accept or reject the initial award offer. 
     As also illustrated in  FIG. 9B , the initial award offer is rejected. As described above, the gaming device selects another position change from the plurality of position changes and, if no termination symbol or terminator is selected, moves the marker  750  the corresponding number of positions on the path of the offer display. After the marker  750  is moved, the prior visited position is associated with a termination symbol or terminator. Accordingly, as illustrated in  FIG. 9C , the seventh position on the path is no longer associated with an award offer of two, but is now associated with a termination symbol or terminator  756 . 
     As illustrated in  FIG. 9C , the gaming device selected a position change of three and the marker  750  moved three positions upward along the path to the tenth position of the offer display. The tenth position is associated with an award offer of two. As described above, the player&#39;s initial award offer is modified to four by combining the prior award offer of two with the current award offer of two. The modified award offer is displayed in the award offer display. Additionally, the maximum award offer  720  is modified to twenty-four as described above. The player may either accept or reject the modified award offer. In this case, the player rejects the modified award offer and the gaming device randomly selects another position change. A terminator becomes associated with the markers  750  prior visited position. 
     As illustrated in  FIG. 9D , the gaming device randomly selected the position change of twenty and the marker was moved twenty positions. As described above, as the player completes one cycle of the award offer path, the offer amount associated with each position is increased. It should be appreciated that the increase in the associated offer amount has no effect on the positions that have become associated with termination symbols or terminators. As illustrated in  FIG. 9D , the position the marker  750  landed on had an associated termination symbol or terminator and the bonus game ends. In this embodiment, the player obtains the last modified award offer. 
     Referring to  FIG. 10A , in another embodiment of the present invention, the gaming device provides the player a plurality of marker moves. Each marker move represents one time the player may move the marker along the path to a new position. The number of marker moves remaining is displayed in the moves remaining indicator  852 . In this embodiment, each time the player rejects a current award offer, the marker moves remaining is decreased by one. If the player has no marker moves remaining, then the gaming device provides the last modified offer, the player cannot obtain any more offers and the bonus game terminates. It should be appreciated that in this embodiment, the bonus game terminates when either the player accepts an award offer, the player obtains the maximum award offer, or the player has no marker moves remaining. 
     In a further embodiment including marker moves, as illustrated in  FIG. 10B , a plurality of positions are associated with a plurality of move changes that modify the number of remaining marker moves. The modified number of marker moves is displayed in the moves remaining indicator. It should be appreciated that the move changes, if any, associated with each position may be masked or displayed to the player. If the move change is masked, then the move change is revealed when the marker is moved to that position. In this embodiment, the positions are separated into two ranges. The first range begins at the marker start position and proceeds up the upward slope of the path and ends at the peak position. The second range includes positions on the downward slope of the path. In this embodiment, the plus move changes  830  are associated with the positions from the first range and the minus move changes  832  are associated with the positions from the second range. In an alternative embodiment, the minus move changes  832  are associated with positions from the first range and the plus move changes  830  are associated with the positions from the second range. In an alternative embodiment, plus move changes  830  and minus move changes  832  may be associated with positions from either range. In this embodiment, if the marker current position is associated with a move change, the players number of moves remaining is modified according to the associated move change. 
     In a further alternative embodiment of the present invention, a reverse could be associated with one or more of the positions. If the marker lands on a position having an associated reverse, the direction of the marker movements changes or reverses. 
     Residual Points and Residual Picks 
     Referring now to  FIGS. 11A  though  11 V, one embodiment of the present invention includes carrying residual award upgrade points over from one round of the bonus game to another or different round. In this embodiment, the bonus scheme includes a number of rounds, such as four rounds, and each round allows a number of picks, such as four picks, by the player. Any suitable number of rounds and picks may be employed. In one embodiment, a player&#39;s advancement to the next round may be conditioned upon the attainment of a designated position, e.g., the first or ultimate position, during the previous round. Alternatively, the advancement to the next round may be automatic after the player has completed a number of picks in the round. 
     It is contemplated that the gaming device may generate an initial position in each round automatically at random without an input by the player. Gaming device alternatively generates an initial position depending on an input by the player or generates an initial position depending on the outcome of a preceding round. The initial position in a subsequent round can also be effected by an outcome of any one, some or all of the preceding rounds. In an alternative embodiment, the starting position can be fixed or predetermined or otherwise suitably determined. For instance, the starting position could be based on the player&#39;s wagers in a primary game. 
       FIGS. 11A through 11C  illustrate a first pick during a first round of the bonus game. In  FIG. 11A , gaming device provides a display  900  having a value display  918  and five masked selections  902 ,  903 ,  904 ,  905  and  906  that mask initial positions, although any suitable number of selections may be employed. Selections  902  to  906  show one possible arrangement of the selections in the game. Selections  902  to  906  include any suitable type of arrangement desired by a game implementor and in accordance with a theme of the game. To make a pick, the player activates an input device such as by pushing an electromechanical button, touching a touch screen selection displayed on the screen, or clicking a mouse, etc. 
     As illustrated in  FIG. 11A , the gaming device provides a display  981  indicating that there are four picks left in that round and a display  982  indicating that there are three rounds left unplayed. In  FIG. 11A , the gaming device provides a message  991  that asks the player to “go ahead and make a pick of one of the masked selections to move up the chart!” Such a message could be a visual message, an audio message, or an audiovisual message. The gaming device may also provide a paid display  985  showing the amount of awards the player has received, as illustrated in  FIG. 11A . 
     In  FIG. 11B , the player picks the selection  903 , revealing the initial position of sixteen. Display  981  indicates that there are now three picks left in that round. The gaming device records the selection by the player on the value display  918 , for example, by displaying “pick 1”, as illustrated in  FIG. 11C . In one embodiment, the gaming device reveals or unmasks the remaining non-picked positions associated with the remaining selections  902 ,  904 ,  905  and  906 , respectively, as illustrated in  FIG. 11C . Alternatively, the gaming device does not reveal or unmask the remaining non-picked selections and either prompts the player to pick within the remaining non-picked selections in the same group or provides a new group of selections. 
     After the first pick by the player, the gaming device provides a second pick display  916  as illustrated in  FIGS. 11D through 11F . As illustrated by  FIG. 11D , the gaming device provides again a number of masked selections associated with position moves. The position moves of the present invention can be of positive, negative or zero value to move forward, move back or to not move the position obtained by the player during a previous pick. The position moves in one preferred embodiment are each of a positive value in order to provide the player with higher awards. This embodiment, unlike certain of the previous embodiments described herein (see  FIGS. 5D ,  6 ,  7 A to  7 E,  8 A to  8 G,  9 A to  9 D and  10 A to  10 B) is not an offer/acceptance game. Therefore, the gaming device preferably does not lower the player&#39;s amount without a player input indicating willingness to assume the risk of such lowered award. 
       FIG. 11D  illustrates six masked selections  919 ,  920 ,  921 ,  922 ,  923  and  924 , although any suitable number of selections may be employed. Selections  919  to  924  show one possible arrangement of the selections in the game. As illustrated in  FIG. 11D , display  981  indicates that there are three picks left for this round and display  982  indicates that there are three rounds of the bonus game left. In  FIG. 11D , the gaming device provides a message  991  asking the player to “go ahead and make a pick of one of the masked selections to move up the chart!” 
     In the example illustrated by  FIG. 11E , the player picks the selection  922 , revealing the position move points having a value of +6 associated with such selection. In  FIG. 11E , display  981  indicates that there are now two picks left in that round. The game accordingly changes the initial position by six places or positions closer to the first or ultimate position, creating a new position of ten and a new award of thirty-five, marked as “pick 2”, as illustrated in  FIG. 11F . 
     A player&#39;s third pick during the first round of the bonus game continues in like fashion, as illustrated in  FIGS. 11G to 11I . Here, the player picks one of the masked selections, the selection  919 , from the group of selections  919  through  924 , and the gaming device reveals position move points of +8, as illustrated in  FIG. 11H , such that the player&#39;s position moves by eight places or positions closer to the first or ultimate position, creating a new position of two and a new award of two hundred, marked as “pick 3” in  FIG. 11I .  FIG. 11G  presents a new set of selections associated with position move points.  FIG. 11H  shows the pick by the player resulting in a position move of +8.  FIG. 11I  shows the result of the pick wherein the player&#39;s position changes. 
       FIGS. 11J through 11L  illustrate the fourth or final pick by the player during the first round of the bonus game. In this example, the player picks one of the masked selections, the selection  924 , from the group of selections  919  through  924  as illustrated in  FIG. 11J , wherein the gaming device reveals position move points of +3 as illustrated in  FIG. 11K . In  FIG. 11K , display  981  indicates that there are now no picks left in that round. In  FIG. 11L , the player only needs to move one place or position to reach the first, activation, target, ultimate, designated, or predetermined or reset position and the award of five hundred, marked as “pick 4.” The gaming device accordingly changes the awards shown in display  985  from zero to five hundred, as illustrated in  FIG. 11L . Alternatively, the gaming device pays the player at the end of all the rounds. In one preferred embodiment, the gaming device also provides the player an additional award for obtaining the highest, best, or most favorable, designated, target, predetermined, or randomly determined position. In one alternative embodiment, a multiplier or other award can be determined from a mechanical device such as a wheel, die or reel upon the occurrence of the trigger or designated position. 
     In one embodiment, the gaming device saves the residual +2 position move points as indicated by an additional display  983 , as illustrated by  FIG. 11L . The gaming device applies the residual points to the result of the first pick during the next round of the bonus game, as illustrated by  FIGS. 11M through 11O . That is, the gaming device uses the residual points in determining the player&#39;s initial position in the next round, whether that position is determined via a player&#39;s pick or automatically and randomly by the gaming device. 
     In another embodiment, the gaming device may enable the player to hold the residual points and not automatically apply the residual points to the first pick during the next round, wherein the player selectively uses the residual points in a desired round. The player can thereby command the gaming device to apply the residual points to the final pick of a round instead of to the initial or “come out” position of a round. In yet another embodiment, the gaming device accumulates residual points to be applied in a subsequent round. Here, the gaming device may accumulate residual points over multiple rounds of the bonus game and let the player use the residual points as needed. 
       FIGS. 11A through 11L  illustrate an embodiment with residual points.  FIGS. 11M through 11V  on the other hand illustrate another embodiment of the bonus game having residual picks instead. In  FIG. 11M , display  981  indicates that there are four picks left for this round, display  982  indicates that there are now two rounds of the bonus game left unplayed, and display  983  indicates that there are +2 residual position move points carried over from the previous round of the bonus game. The player chooses the selection  906 , revealing the initial position of fifteen as illustrated in  FIG. 11N . In  FIG. 11N , display  981  indicates that there are now three picks left in that round. Since there is a carryover of residual position move points of +2, the game accordingly changes the initial position of fifteen by two places or positions closer to the first or ultimate position, creating a new position of thirteen and a new award of twenty, marked as “pick 1”, as illustrated in  FIG. 11O . 
     For the second pick during the second round of the bonus game as illustrated in  FIGS. 11P through 11R , the player picks one of the masked selections, the selection  921 , from the group of selections  919  through  924 , and the gaming device reveals position move points of +4, as illustrated by  FIG. 11Q , such that the player&#39;s position moves by four places or positions closer to the first or ultimate position, creating a new position of nine and a new award of forty, marked as “pick 2” in  FIG. 11R . 
     The player proceeds to make the third pick during the second round of the bonus game as illustrated in  FIGS. 11S through 11U . In this example, the player picks the selection  920  revealing position move points of +8 as illustrated in  FIG. 11T . In  FIG. 11T , display  981  indicates that there are now two picks left in that round. The game accordingly changes the previous position of nine by eight places or positions, creating a new position of one and a new award of five hundred, marked as “pick 3”, as illustrated in  FIG. 11U . In  FIG. 11U , the paid display  985  shows the accumulated awards the player has received, here, one thousand. 
     In the example illustrated by  FIG. 11U , the gaming device saves one residual pick as indicated by display  981 , and will enable the player to use the residual pick automatically during the next round of the bonus game or selectively during any subsequent round. As illustrated in  FIG. 11V , the first pick of the next round of the bonus game provides a total of five picks instead of four picks, as indicated by the four picks in the picks left display  981  and the one pick in Residual Picks display  983 . In addition to message  991 , the gaming device may provide a message display  992 , e.g., “Hey, you get an extra pick in this round saved from last round”, as illustrated in  FIG. 11V . 
     It should be appreciated that the gaming device may accumulate residual picks over multiple rounds of the bonus game. It should also be appreciated that the player may receive both residual position move points and residual picks in the same round or in the same game and that each of the various embodiments described above for the residual move points is applicable to the residual picks. It should further be appreciated that the gaming device may provide the player with an additional award based on residual points and/or residual picks or provide an award in lieu of providing the additional move points or additional picks. 
     In an alternative embodiment of the present invention, credits or awards are not associated with the sequential position numbers. In this embodiment, an award or prize is provided to the player for completing the round and getting to the designated, predetermined or target position. A consolation award may be provided to the player for not obtaining the designated, predetermined or target position. In one embodiment, the award provided to the player associated with the designated, predetermined or target position is determined through another game or event such as the selection of one or more of the plurality of selections or the activation of a mechanical device such as a wheel, reel, die or set of objects such as balls. Thus, in this embodiment, the primary goal of the player is obtain the number one or target selection. 
     It should be appreciated that in one preferred embodiment of the present invention, each subsequent round includes higher awards or higher average awards. In such embodiment, the probability of reaching subsequent rounds may decrease with each round. 
     While the present invention is described in connection with what is presently considered to be the most practical and preferred embodiments, it should be appreciated that the invention is not limited to the disclosed embodiments, and is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the claims. Modifications and variations in the present invention may be made without departing from the novel aspects of the invention as defined in the claims, and this application is limited only by the scope of the claims.