Abstract:
A gaming machine comprises a spinning reel display showing a plurality of symbols on each of a plurality of rotatable reels. The reels are rotated and stopped to place the symbols of each reel in visual association with a pay line. A winning combination of displayed symbols triggers a payoff. The distribution of payoff values and probabilities results in a high volatility index, so that the distribution is similar to a state-run lottery.

Description:
FIELD OF THE INVENTION 
     The present invention relates generally to gaming machines and, more particularly, to a gaming machine with a high volatility index, i.e., most of the payoffs provided by the machine are high, and these high payoffs have a fairly high probability of occurring. 
     BACKGROUND OF THE INVENTION 
     Gaming machines such as slot machines determine the value of a player&#39;s payoff by the orientation of symbols on a display. In a typical slot machine, there are numerous payoff values each with a predetermined probability of payoff based on a variety of possible symbol orientations. The attractiveness of a slot machine to a player is based on many factors, including appearance, entertainment value, and the values and perceived chances of winning payoffs. Attempting to attract players, most slot machines currently in use employ numerous payoff levels spread fairly evenly along a spectrum from the lowest possible payoff (often simply a return of the player&#39;s bet) to the highest payoff. Slot machines have proven immensely popular with players, and casino operators typically install dozens to hundreds of the machines in a single casino. 
     The industry standard for measuring distribution of sizes and probabilities of slot machine payoffs is a mathematical value called the volatility index. Current slot machines all have low volatility indices, which means that there is a relatively steady progression of many payoff values from the lowest to the highest, with each payoff&#39;s corresponding probability decreasing as the value of the payoff increases. 
     State-run lotteries, like slot machines, are seeing great popularity. Lotteries are based on the chances of a player&#39;s chosen series of numbers matching a randomly selected series. In a lottery, there may be several smaller payoff levels based on combinations of a few numbers, but the largest payoff is reserved for the very small number of players who match all numbers. Expressed in terms used to describe slot machines, lotteries therefore have a high volatility index, though lotteries&#39; volatility indices will not necessarily be as high as the volatility indices of the present invention because large payoffs have an extremely small chance of occurring. The popularity of a lottery is directly linked to the size of the maximum payoff, so that a high maximum payoff will result in more lottery tickets being sold, even though the chances of winning remain extremely small. Players&#39; appreciation of lotteries stems from the fact that incredible wealth can be achieved with a single play. 
     Because both slot machines and lotteries are extremely popular, a slot machine employing the general payoff characteristics of a lottery would make use of each game&#39;s individual popularity to appeal to both players and casino operators. Further, the odds of winning large payoffs on a slot machine need not be so remote as in a lottery, and greater odds of winning will result in more visible large wins in a casino, increasing player interest in the slot machine. Thus, there is a need to develop a slot machine that retains the easy playability and attractive design of a slot machine, and combines this with the high volatility index seen in lotteries. The present invention is directed to satisfying this need. 
     SUMMARY OF THE INVENTION 
     In accordance with one aspect of the present invention, there is provided a payoff distribution for a slot machine with game outcomes characterized by a high volatility index. The slot machine includes a spinning reel display showing a plurality of symbols on each of a plurality of rotatable reels. The reels are rotated and stopped to place the symbols of each reel in visual association with a pay line. The pay line is associated with at least one of the stops on each of the reels. In one embodiment, the reels are rotatable about a single vertical axis so that the pay line is oriented in a vertical direction. In this embodiment, each reel is capable of displaying only one payoff symbol, though this symbol may appear several times on each reel. The machine of this embodiment only has one possible high payoff of, for example, one million U.S. dollars. The payoff of this embodiment is granted when each reel displays one of its payoff symbols so that the symbols align vertically with the pay line. 
    
    
     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: 
     FIG. 1 is a perspective view of a gaming machine embodying the invention; 
     FIG. 2 is a block diagram of a control system suitable for controlling the gaming machine in FIG. 1; 
     FIGS. 3 a  and  3   b  are diagrams of reel strips used in two embodiments of the present invention; and 
     FIGS. 4 a ,  4   b ,  4   c ,  4   d , and  4   e  are math tables identifying payoff amounts and probabilities that may occur in five embodiments of the 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. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Though gaming machines have seen great popularity in casinos, up to this point they have all utilized fairly limited ranges of payoffs and probabilities. Current gaming machines have long lists of payoffs, with the probabilities gradually getting smaller for higher payoffs in the distribution. For example, a typical casino gaming machine might have ten payoff levels ranging from a few U.S. dollars to several thousand U.S. dollars, with a roughly linear progression for the intermediate values. This distribution is different from the payoff and probability distributions seen in popular state-run lotteries, where the values of the largest payoffs are much greater than smaller payoffs, with corresponding much smaller odds of winning the largest payoffs. If casino players are given the option to play gaming machines having payoff distributions similar to state-run lotteries, it is believed that such gaming machines, along with the casinos that feature them, will see great success given the combined popularity of gaming machines and state-run lotteries. While most gaming machines currently in use feature relatively low volatility indices of from 5 to 100, a gaming machine having a volatility index greater than or equal to about 150 will maintain the excitement of high payoffs being attainable within a reasonable number of spins. 
     The present invention is directed to producing a gaming machine that will make use of this combined interest in lotteries and standard casino gaming machines. FIG. 1 shows a slot machine  10  on which the present invention may be implemented. The slot machine  10  includes a display area  12  through which a player may observe five mechanical reels  14 ,  16 ,  18 ,  20 , and  22 . It will be appreciated that the game may alternatively be implemented entirely on a video display that shows video images of reels, and it may also be implemented on a display that includes more or fewer reels. 
     FIG. 2 is a block diagram of a controller system suitable for operating the slot machine  10  of FIG. 1. A coin/credit detector  34  signals a processor  36  when a player has inserted a number of coins into a coin slot  30  (see FIG.  1 ), inserted bills into a bill acceptor  28  (see FIG. 1) or played a number of credits by using the “bet” button  31 . After the player has activated a switch  38  (e.g., by pushing a spin button  26 ), the processor  36  initiates game play by randomly selecting stop positions for the reels  14 ,  16 ,  18 ,  20 , and  22  (see FIG. 1) and setting the reels  14 ,  16 ,  18 ,  20 , and  22  in motion. Then, using technology well known in the art, the processor  36  causes a reel motor and step control  40  to successively stop the reels  14 ,  16 ,  18 ,  20 , and  22  at the selected stop positions, starting with the bottom reel  22  and progressing to the top reel  14 . A rotational position detector  42  provides feedback to the processor  36  to ensure that the reels  14 ,  16 ,  18 ,  20 , and  22  are stopped at the correct stop positions. The symbols displayed on the reels at the stop positions define the game outcome. 
     A system memory  44  stores control software, operational instructions, and data associated with the slot machine  10 . In one embodiment, the system memory  44  comprises a separate read-only memory (ROM) and battery-backed random-access memory (RAM). However, it will be appreciated that the system memory  44  may be implemented on any of several alternative types of memory structures or may be implemented on a single memory structure. A payoff mechanism  46  is operable in response to instructions from the processor to grant a payoff of coins or credits to the player in response to the winning combination stored in memory  44 . This embodiment is programmed to contain only one winning combination, but other embodiments of this gaming machine having several possible winning combinations are contemplated. 
     As best observed in FIG. 1, the symbols on the reels  14 ,  16 ,  18 ,  20 , and  22  are displayed in a symbol group consisting of five symbols, with each displayed symbol aligned with a vertical pay line  32 . Under this embodiment, at most one non-blank symbol per reel is visible when the reels  14 ,  16 ,  18 ,  20 , and  22  are stopped, but it will be appreciated that alternative embodiments could be created wherein several non-blank symbols on each reel would be visible at once. The symbol group is determined to include the winning combination (e.g., the symbol combination resulting in a payment of coins or credits) if it includes the combination of symbols which corresponds to the predefined winning combination. The predefined winning combination and its associated payoff amount for the game are stored in the system memory  44  and may also be shown on a pay table printed on the slot machine cabinet. 
     Under this embodiment, the symbols on the reels  14 ,  16 ,  18 ,  20 , and  22  comprise blank spaces and portions of a fictional $1 million U.S. dollar bill. Only one winning combination exists, and it is displayed graphically when all portions of the $1 million U.S. dollar bill align along the single pay line  32 . Other embodiments could be developed using the present invention. For example, a gaming device similar to the first embodiment could have several payoffs instead of only one, with the distribution of probabilities and payoffs still having a high volatility index. As another example, the gaming machine could play keno, bingo, or roulette instead of slots. Another possible embodiment of the present invention is a gaming machine accepting several different wager amounts, with different volatility indices for each wager amount. All embodiments of the invention are such that the distribution of payoff probabilities and values as stored in system memory  44  exhibits a high volatility index, VI, for at least one wager amount. 
     The volatility index for a machine accepting multiple wager amounts is defined as:        VI   =         CL   F            ∑     w   =   1     WAGER              ∑     k   =   1     N              P     win                 k            (         Pay     scaled                 k         Bet     scaled   w         -       EV   w     100       )       2             WAGER                            
     where: 
     CL F  is a confidence level factor, described below (for example, CL F =2.58 for a confidence interval of 99-100% and CL F =1.65 for a confidence interval of 90-100%); 
     w progresses from one to the number of the maximum wager (i.e., if five different wagers are possible, w progresses from 1 to 5); 
     k progresses from one to the number of payoffs; 
     N is the number of different payoffs; 
     P win k  is the probability of a specified payoff occurring; 
     Pay Scaled k  is a scaled payoff (i.e., the payoff divided by the amount of money wagered) corresponding to each payoff, 
     Bet scaled w  is a scaled wager amount where magnitudes of wagers have been uniformly re-scaled so that the largest is 1 (hence, bets of 1,5 and 100 can give scaled wager amounts of {fraction (1/100)},{fraction (1/20)}and 1); 
     EV W , is the expected value of the return percentage, defined to be the percentage of the total wager that the machine will pay out over the cycle of the game, where the cycle is defined to be the set of all possible outcomes; and 
     WAGER is the maximum number of possible wagers, where different wagers alter the ratios of payoffs to bets or the probabilities associated with one or more payoffs. 
     In the present invention, at least one wager results in a high volatility index. For an embodiment having only one possible wager and several possible payoffs, the volatility index equation is simplified to:        VI   =       CL   F              ∑     k   =   1     N              P     win                 k            (       Pay     scaled   k       -     EV   100       )       2                                  
     where 
     CL F  is the confidence interval factor, described below; 
     k progresses from one to the number of payoffs; 
     N is the number of different payoffs; 
     P win k  is the probability of a win with one play; 
     Pay scaled k  is a scaled payoff (i.e., the payoff divided by the amount of money wagered) corresponding to each payoff; and 
     EV is the expected value of the return percentage, defined to be the percentage of the total wager that the machine will pay out over the cycle of the game, where the cycle is defined to be the set of all possible outcomes. 
     This simplified equation can be used to calculate the volatility index experienced by a player for a certain wager, even on a machine having multiple wagers. The expected value, scaled payoff, probability of winning, and number of different payoffs may change with each specific wager, and these values can be input into the simplified equation to give a volatility index experienced by a player for a specific wager. The present invention may be implemented on a game having multiple possible wagers, even when only one wager results in a high volatility index. 
     The confidence level is a statistical term used in the gaming industry to denote the probability that the average game outcome will occur within a predefined range, called the confidence interval, of the expected outcome for a given number of total plays. Hence, for a fixed volatility index and a given number of total plays, choosing a smaller confidence interval (e.g., 99-100% rather than 99-100%) gives a smaller confidence level. For a fixed confidence interval and a given number of total plays, a game with a higher volatility index will have a lower confidence level, since the volatility index is basically a measure of the variability of return on a given number of coins. For a game with a high volatility index to achieve the same confidence level for a given confidence interval as a game with a lower volatility index, one needs additional plays. 
     FIGS. 3 a  and  3   b  depict reel strips to be used in two embodiments of the present invention. A reel strip is a strip containing the symbols for a mechanical slot machine, and the strips are wrapped around the reels that display the game outcome. FIG. 3 a , corresponding to a first embodiment of the invention, shows a set of five reel strips  48 ,  50 ,  52 ,  54 , and  56 , with each strip having  22  possible stopping positions that could be displayed in the display area  12 . To achieve the desired win probability for this embodiment, one reel trip  48  contains seven payoff symbols that are included in the winning combination, a second reel strip  50  contains two payoff symbols that are included in the winning combination, and each of the third, fourth, and fifth reel strips  52 ,  54 , and  56  contains one payoff symbol included in the winning combination. 
     FIG. 3 b , corresponding to a second embodiment of the invention, shows a set of five reel strips  58 ,  60 ,  62 ,  64 , and  66 , with each strip having  18  possible stopping positions that could be displayed in the display area  12 . Reel strip  58  contains five payoff symbols that are included in the winning combination, and each of reel strips  60 ,  62 ,  64 , and  66  contains one payoff symbol that is included in the winning combination. 
     FIG. 4 a  shows a math table corresponding to the first embodiment having only one possible payoff and five reel strips with  22  positions on each strip. The “Wager Amount” column indicates the amount of money that the player bets with each play. The “Payoff” column identifies the pay value of the sole winning outcome. The “Probability” column indicates the probability of hitting the respective winning combination in a single spin. This number is the same as the “hit frequency” in the volatility index equations. The “Plays/Hit” column identifies, on average, the number of plays that would be required to “hit” the game&#39;s winning symbol combination. This value is the inverse of the probability. For example, in a game having the reel strips shown in FIG. 3 a , the probability of hitting the winning combination in a single pull is 0.00000272. The plays/hit value is thus {fraction (1/0.00000272+L )}, or approximately 367,423. In this first embodiment, it would take approximately 367,423 plays, on average, to hit the winning combination. 
     The “Expected Value of $3 Play” column of FIG. 4 a  identifies the expected value of each play of the first embodiment, which is computed by finding the product of the “Payoff” value and the “Probability” value. Thus, for the first embodiment with reel strips as shown in FIG. 3 a  having a payoff of $1,000,000, a wager amount of $3, and a probability of 0.00000272, the “expected value” of each $3 play is computed as: $1,000,000×0.00000272=$2.72. The “Volatility Index” column gives the volatility index for this embodiment with a confidence interval of 99-100%. 
     The volatility index for the machine of this embodiment is calculated according to the simplified equation, above. The probability of a win, P win , is 2.71653E-06. The scaled payoff, Pay scaled , is $1,000,000 divided by the wager amount, $3, or 333,333.33. The expected value percentage, EV, is thus the scaled payoff multiplied by the probability of a win, or 333,333.33×2.71653E-06=0.9055, or 90.55% of the money wagered. Hence, using the volatility index equation given above for games having one wager amount, the volatility index for the embodiment shown in FIG. 4 a , VI, is calculated as:        VI   =       2.58          0.00000271653          (       333   ,   333.33     -   .9055     )     2           ≈   1417.                            
     FIG. 4 b  shows a math table corresponding to a second embodiment having only one possible payoff and five reel strips with  18  positions on each strip. Each column in FIG. 4 b  contains the same information depicted in the corresponding column in FIG. 4 a , with the values being slightly modified because this embodiment has a different reel strip configuration. In a game having the reel strips shown in FIG. 3 b , the probability of hitting the winning combination in a single pull is 0.00000265. The plays/hit value is thus {fraction (1/0.00000265+L )}, or approximately 377,358. In this second embodiment, it would take approximately 377,358 plays, on average, to hit the winning combination. Further, for the second embodiment with reel strips as shown in FIG. 3 b  having a pay value of $1,000,000, a wager amount of $3, and a probability of 0.00000265, the expected value of each $3 play is computed: $1,000,000×0.00000265=$2.65. The volatility index is given for a confidence interval of 99-100%. 
     FIG. 4 c  is a math table for a third embodiment having multiple payoff possibilities with a single wager. Each column contains the information explained above for each payoff. The two expected values are added to arrive at the “Total Expected Value” as shown in the bottom row. 
     FIG. 4 d  is a math table for a fourth embodiment having multiple payoff possibilities with a single wager. The mathematical basis for this table is described above. 
     FIG. 4 e  is a math table for a fifth embodiment of the present invention, having multiple payoffs with a maximum payoff of $1 million and a volatility index of approximately 884. 
     While the present invention has been described with reference to one or more preferred 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 which is set forth in the following claims.