US20070293308A1

US20070293308A1 - Casino gaming device with reverse pay table logic

Info

Publication number: US20070293308A1
Application number: US11/820,410
Authority: US
Inventors: Mark Jackson; Michael Martinek
Original assignee: PRECISION TECHNOLOGIES LLC
Current assignee: PRECISION TECHNOLOGIES LLC
Priority date: 2006-06-20
Filing date: 2007-06-19
Publication date: 2007-12-20

Abstract

A computerized wagering game apparatus for wagering by a player has at least a game controller having a processor, memory, a random number generator and game logic generating winning and losing outcomes with assigned probabilities. For any single wager event, the probability for a winning wager outcome is greater than the probability for a losing wager outcome while maintaining a house retention on wagers by the game apparatus which is greater than 0% of all wagers. The house retention wager is effected by the apparatus decrementing a player account or machine credit without the player specifically placing that account or credit in play for the single wager event.

Description

RELATED APPLICATION DATA

This application claims the benefit under 35 U.S.C. §119 (e) of provisional application Ser. No. 60/815,027, filed 20 Jun. 2006.

BACKGROUND OF THE INVENTION

1. Field of the Invention
This invention relates to gaming play and especially computerized casino wagering devices implementing novel wagering formats. Novel wagering formats encompass relatively high probability wins with moderated win amounts and relatively larger, lower probability losses.
2. Background of the Art
Games of chance have been enjoyed by people for thousands of years and have enjoyed increased and widespread popularity in recent times. As with most forms of entertainment, players enjoy playing a wide variety of games and new games. Playing new games adds to the excitement of “gaming.” As is well known in the art and as used herein, the term “gaming” and “gaming devices” are used to indicate that some form of wagering is involved, and that players must make wagers of value, whether actual currency or some equivalent of value, e.g., token or credit.
One popular game of chance is the slot machine, which includes both physical reels and video game play with virtual reels. Conventionally, a slot machine is configured for a player to wager something of value, e.g., currency, house token, established credit or other representation of currency or credit. After the wager has been made and the amount of the wager is placed at risk, the player activates the slot machine to cause a random event to occur. The player wagers that particular random events will occur that will return value to the player. A standard device causes a plurality of symbols to be distributed on the screen, typically by causing physical or virtual reels to spin and ultimately stop, displaying a random combination of some form of indicia, for example, numbers or symbols. If this display contains one of a pre-selected plurality of winning combinations, the machine releases money into a payout chute or increments a credit meter by the amount won by the player. For example, if a player initially wagered two coins of a specific denomination and that player achieved a payout event, that player may receive the same number or multiples of the wager amount in coins of the same denomination as wagered. If no winning event occurs, the player forfeits the amount of the initial wager. Bonus events may also occur when there is a bonus triggering event according to rules of the game.
This historical limitation of using physical coins or tokens for player wagers and the dispensing of player awards is the fundamental reason why the award values of gambling devices were historically designed to be multiples of the player wager amount (e.g., 1×, 2×, 3×, etc.). Even though this requirement of having to deal with whole coin or token amounts no longer exists for the modern day gambling device, the traditional method of awarding multiples of the wager amount remains firmly in place today.
Multi-line games exist today with the capability of awarding partial payouts but fundamentally each line operates awarding a multiple of the bet amount. The combination of multiple lines, each paying an integer multiple of the bet amount, with some lines winning and others losing can in some circumstances create an award that is not a multiple of a bet amount but this is a consequence of the multi-line capability of the machine with each pay line still paying multiples of the original bet amount as applied to individual pay lines. Because payouts include multiples of the original wager and the casino must retain an overall profit from the wagering, the frequency of wins to losses must be less than 1:1, providing a higher frequency of losing events, which is displeasing to players.
There are many different formats for generating the random display of events that can occur to determine payouts in wagering devices. The standard or original format was the use of three reels with symbols distributed over the face of the reel. When the three reels were spun, they would eventually each stop in turn, displaying a combination of three symbols (e.g., with three reels and the use of a single payout line as a row in the middle of the area where the symbols are displayed.) By appropriately distributing and varying the symbols on each of the reels, the random occurrence of predetermined winning combinations can be provided in mathematically predetermined probabilities. By clearly providing for specific probabilities for each of the pre-selected winning outcomes, precise odds that would control the amount of the payout for any particular combination and the percentage return on wagers for the house could be readily controlled. Control of the frequency and amount of winning events is effected by physical mapping of reels or electronic mapping of symbols.
Other formats of gaming apparatus that have developed in a progression from the pure slot machine with three reels have dramatically increased with the development of video gaming apparatus. Rather than have only mechanical elements such as wheels or reels that turn and stop to randomly display symbols, video gaming apparatus and the rapidly increasing sophistication in hardware and software have enabled an explosion of new and exciting gaming apparatus. The earlier video apparatus merely imitated or simulated the mechanical slot games in the belief that players would want to play only the same games. Early video games therefore were simulated slot machines. The use of video gaming apparatus to play new games such as draw poker and Keno broke the ground for the realization that there were many untapped formats for gaming apparatus. Now casinos may have hundreds of different types of gaming apparatus with an equal number of significant differences in play. The apparatus may vary from traditional three reel slot machines with a single payout line, video simulations of three reel video slot machines, to five reel, five column simulated slot machines with a choice of twenty or more distinct pay lines, including randomly placed lines, scatter pays, or single image payouts, and even fifty to 100 line plays for poker games. In addition to the variation in formats for the play of games, bonus plays, bonus awards, and progressive jackpots have been introduced with great success. The bonuses may be associated with the play of games that are quite distinct from the play of the original game, such as the video display of a horse race with bets on the individual horses randomly assigned to players that qualify for a bonus, the spinning of a random wheel with fixed amounts of a bonus payout on the wheel (or simulation thereof), or attempting to select a random card that is of higher value than a card exposed on behalf of a virtual dealer.
A video terminal is another form of gaming device. Video terminals operate in the same manner as conventional slot or video machines except that a redemption ticket is issued rather than an immediate payout being dispensed.
Casino games of chance also take the form of table games. The latter include games such as Black Jack, Roulette, Craps and Baccarat. Table games offer a very different gambling experience than the typical slot machine. With table games, it is common for the player to place multiple wagers on various game outcomes, with the intention of “spreading their odds” across multiple outcomes with the intent of covering the losing bets with the awards received from the winning bets. The game of craps takes this philosophy to a unique extreme by presenting multiple game outcome events to the player during the same base wager cycle. Unlike the single line slot machine experience, the table game experience, particularly craps, offers the player a very different perspective of expecting higher probability incremental gains from the base wager, with the possibility of losing their entire bet amount as a result of any game outcome. This is somewhat akin to the multi-line slot machine experience where although each individual award pays a multiple of the base bet amount, the overall pay per wager event may in some cases be a fractional amount due to the number of wins or losses of individual bets comprising the overall wager. The psychology of the typical slot machine as compared to that of table games is oriented towards low probability large awards balanced by high probability small, losing outcomes.
A probability distribution assigns a probability to every interval of real numbers along the real number line, such that a) every possible interval has a probability greater than or equal to zero, b) the total probability for any outcome is one, and c) the probability of the union of one or more disjoint intervals equals the sum of the probabilities of those intervals. For a random variable X derived from a given probability distribution, the mean and standard deviation can be calculated from the moments of the probability density function, and from Chebyshev's inequality (below) the probability that a certain outcome lies greater than k standard deviations from the mean is less than 1/k².
An embedded gaming device with a set of possible wagering outcomes can be viewed as a system for implementing a probability distribution for net winning or net losing game outcomes. For each game outcome, the net outcome is the game win amount minus the bet amount. Together, the net outcome (each outcome being a net win or alternatively a net loss if the win is less than the bet) amounts create a distribution from which can be obtained an expected or mean outcome and a standard deviation for possible outcomes.
From Chebyshev's inequality we know that for the embedded gaming device with mean μ and standard deviation σ,

- No more than ½ of the possible net outcomes are greater in magnitude than sqrt(2)*σ from the mean outcome μ. Equivalently, at least ½ of the net outcomes are less in magnitude than sqrt(2)*σ from the mean outcome.
- No more than ¼ of the possible net outcomes are greater in magnitude than 2σ from the mean outcome μ. Equivalently, at least ¾ of the net outcomes are less in magnitude than 2σ from the mean outcome.
- No more than 1/9 of the possible net outcomes are greater in magnitude than 3σ from the mean outcome μ. Equivalently, at least 8/9 of the net outcomes are less in magnitude than 3σ from the mean outcome.

In a profitable casino embedded gaming device a constraint on the overall mean net outcome μ (or expected net outcome) is that the retention of wagers by the casino gaming device must be greater than 0%, or equivalently, the mean net outcome μ for the player will be less than 0 in order to guarantee a profit for the casino.

SUMMARY OF THE INVENTION

A wagering game is provided with increased frequency of net winning events as compared to net losing events. Increased frequencies of net winning events are balanced by moderation of potential winning amounts and relatively larger losing amounts with correspondingly decreased frequency. A wagering game may be played in which frequencies of wins are increased but with amounts of potential losses increased above amounts won so that even though numerical frequencies of payouts increase, the house may maintain sufficient retention rates to continue a profit on the game.

DESCRIPTION OF THE FIGURES

FIG. 1. Example Conventional Prior Art Pay Table. Conventional pay table showing probability of a net winning outcome is less than the probability of a net losing outcome and the net win amounts greater than the net loss amounts.
FIG. 2. Example Conventional Prior Art Pay Table Chart. A chart showing the distribution of game outcomes for a conventional prior art system with outcome probability indicated along the X axis and payout along the Y axis.
FIG. 3. Example Conventional Prior Art Payout Graph. Conventional games of the prior art offset frequent small losing outcomes with relatively rare large winning outcomes.
FIG. 4. Example Reverse Logic Pay Table. Reverse logic pay table showing probability of a net losing outcome is less than the probability for a net winning outcome and the net loss amounts are greater than the net win amounts.
FIG. 5. Example Reverse Logic Pay Table Chart. Chart illustrating the distribution of game outcomes for a reverse logic pay table system with outcome probability indicated along the X axis and payout along the Y axis.
FIG. 6. Example Reverse Logic Payout Graph. The system of the invention is characterized by frequent winning outcomes offset by relatively rare large losing outcomes.
FIG. 7. Example Catastrophic Losing Outcome. Illustrates a catastrophic losing outcome consistent with the system of the invention where a player might lose the entire credit balance.

DETAILED DESCRIPTION OF THE INVENTION

As discussed above, the characteristics of prior art casino slot machine gaming devices include: they are based on a bet amount wagered per game, a pay table that pays back a fixed percentage over time, single line win amounts that are multiples of the wager amount, and the potential for a big win either in the base game pay table or in some forms by adding a plurality of bonus screens on top of the base game. The present technology includes systems, methods, apparatus and rules that effectively reverse probabilities or frequencies of winning and losing events and shifts scales of potential winning and losing amounts so that the “house” still statistically returns less than 100% even with higher frequencies of winning events as compared to losing events, even with nominally consistent or constant amounts of wagers. These reverse probabilities and payouts can be effected in a number of alternative manners, both in physical games (by applying game rules that impact probabilities) and in computerized games (with random number generators, mapped symbol provisions, and pay tables impacting the reverse payback events).
The following descriptions will provide enablement for numerous alternatives for practice of the present technology.
A first format for enabling practice of the present technology can be described as establishing probabilities and amounts of payouts and losses such that ΣWn·An−ΣLn·Sn<0 wherein Wn is the frequency (probability) of a net winning event for each probable winning event within the total set of events n, A is the payout amount of each winning event within all of the probable events n, Ln is the frequency (probability) of a net losing event for each losing event within all probable events n, and S is the loss amount for each losing event within all probable events n, wherein ΣWn>ΣLn. In non-mathematical terms, the sum all of the individual probabilities for each winning event multiplied by the individual payout for each winning event is less than the sum all of the individual probabilities for each losing event multiplied by the individual loss effect for each losing event, and wherein the total probability of winning events W is greater than the total probability of losing events.
One embodiment of the present technology consists of an embedded casino gaming device with a set of possible wagering outcomes viewed as a system for implementing a probability distribution for net winning or net losing game outcomes. For each game outcome, the net win is the net increase in the player's monetary or credit balance due to the game's outcome, taking into account the wager, outcome and any bonusing or side bets. Together, the net win (or alternatively net loss if the player's monetary or credit balance decreases due to the game's outcome) amounts create a distribution from which can be obtained a mean or expected net outcome μ and a standard deviation σ for all possible outcomes. The total set of net outcomes is divided into a set of relatively large magnitude outcomes consisting of those net outcomes greater than or equal in magnitude to μ+sqrt(2)*σ (that is √2*σ) or less than or equal in magnitude to μ−sqrt(2)*σ, and a set of relatively small magnitude outcomes consisting of those net outcomes greater than μ−sqrt(2)*σ and less than μ+sqrt(2)*σ. A fundamental requirement for the casino gaming device is the expected net outcome μ for the entire distribution (including bonusing) must be less than zero for the casino to make a profit. Using Chebyshev's inequality as a basis (choosing k=√2) the teachings of the present technology predict that the expected net outcome for the set of relatively small magnitude outcomes is greater than zero. Correspondingly, the expected net outcome for the set of relatively larger magnitude outcomes must be less than zero to result in an overall mean for the gaming device that is less than zero.
Another alternative embodiment consistent with this technology would be the Paid-to-Play format described herein. In the Paid-to-Play format, here exemplified with a poker variant against a pay table, it will be assumed that a player begins play with 100 credits. The gaming system or casino table will “pay” the player 5 credits to play, so that as the first set of cards is dealt, the player immediately has 105 credits, as opposed to normal play where the player has 5 credits at risk and 95 credits in reserve. If the player attains a hand over a certain rank (e.g., over a rank of at least queen high in five card stud (which will occur about 56% of the time), the player will be paid an amount proportional to the wagered amount (e.g., if paid 1:1, the player could receive 5 credits and the reserve would be 110 credits). Higher ranked hands would receive higher payouts (higher odds) based on the amount of the payment to the player.
At the same game event, low ranking hands would effect losses to the player out of the player reserve. For example, a perfect “low” hand of 6, 4, 3, 2 and Ace (of more than one suit) could cause a loss of the entire 100 credits. Even though the frequency of winning events (a non-loss is a “net win” due to the “reverse” wager of 5 credits paid to the player by the casino) significantly exceeds then frequency of losing events, the house advantage can be retained within acceptable ranges because of larger absolute loss amounts. Again, some capability of assuring credits that will cover maximum losses, or “wagers” for the Paid-to-Play format payment may be limited within ranges of multiples of available credit, just as wagers are limited to available credits. For example, if the largest catastrophic loss is 20×, the maximum wager (payment) allowed would be 5 units with 100 credits available, 4 units for 80-99 credits available, 3 units for 60-79 credits, 2 units for 40-59 credits available, and 1 unit for 0-39 credits. It is also possible to grant some leeway in the range of available credits as gratis for losses so that a player with 75 credits available may wager 4 credits, even if a catastrophic loss cannot be fully covered by the available credits. It is also possible that such games may be limited in play to players with an account which may be drawn down, over the amount in play on the device or on the table. Other ways to allow play for players with a small credit balance is to offer an “insurance” cover bet which for a fixed wager amount (or deduction in the “paid to play” amount) would “insure” the player in the event of a catastrophic loss.
A general description of the apparatus and methods according to the present technology can be provided as a computerized wagering game apparatus for use by a player, comprising: a game controller having a processor, memory, and a random number generator; the game controller generating symbols and outcomes for wagering events in the game; events in the game providing statistically expected numbers of observed (net) winning events that are greater in frequency for the player than statistically expected numbers of observed (net) losing events for the player; wherein statistical retention of wagers by the gaming apparatus is greater than 0% for the game. This means that the statistical return to a player (always considered over a theoretic infinite number of plays) is less than 100%.
An alternative description is a computerized wagering game apparatus for use by a player, comprising: a game controller having a processor, memory, a random number generator; the game controller providing a total set of event outcomes consisting of a set of possible net tying event outcomes, net winning event outcomes and net losing outcomes; wherein the total set of event outcomes comprises a probability distribution for possible game outcomes wherein for k>=√(2) (that is, square root of 2) there is a greater probability of losing outcomes than winning outcomes considering only those outcomes that lie greater than k standard deviations from the overall distribution's mean outcome. Bonusing events (e.g., a triggering event where there may or may not be any implication on the underlying value placed at risk in the basic game) are inherently included with the tying, winning and losing events. The mean outcome is the statistical expected value of game outcomes and may lie very close to a net tying event (such as with a game with a 98% payback). For example purposes, pay tables given in the figures show a game with expected 100% return in which case the tying event is equal to the expected value, but it should be understood that in reality the mean outcome for a casino game is designed to be weighted in favor of the casino.
The unique orientation of winning events and losing events in their probabilistic relationship offers an opportunity for a unique gaming event, as part of an automatic bonus event or as a side bet bonus event. The bonus event, because of the higher probability of winning events, has an especially attractive feature. Bonuses can be paid on the basis of extended numbers of consecutive winning events, again either as an automatic bonus event or as a side bet bonus event. For example, with 10 consecutive non-loss events (pushes as well as wins) in a row, there could be an automatic win of $10.00, or if based on a side bet bonus event, where the system is receiving higher revenue inputs and so higher payouts might be available, a $25 bonus might be available. Similarly with fifteen consecutive wins, $15 or $50, respectively, with twenty consecutive wins, $100 and $500, respectively and the like, up to actuarially tolerable award amounts. Additionally, players might elect to enter such a bonus event midstream if they feel they are in a hot streak, with attendant reduced awards for the bonus. For example, after three consecutive wins, the player may be able to place the $0.25 side bet entry fee, and if seven more consecutive non-loss events occur, the player could receive a educed amount, such as $6 or $7, the basis of the bonus still being the ten consecutive non-loss events, but with the lower payback because of the later entry into the event. One point of attractiveness of the bonus event is that because of the higher frequency of winning events versus losing events in the game, there is a clearly higher probability for such consecutive win events to occur. The video system could, for example, make a running display of the count of consecutive wins for present and/or recent play (as with a baccarat display (showing Banker or Player wins) or roulette display (showing Red or White, Odd or Even) to further entice players into making a side bet wager or at least playing the game. The display could also provide information on the number of bonus winning streaks occurring in the past twenty-four hours and how long those streaks were and the theoretic payouts for those streaks.
Another alternative apparatus description may be as a computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator; the game controller providing a set of possible game outcomes consisting of net tying outcomes, net winning outcomes and net losing outcomes, wherein the set of total game outcomes consists of a probability distribution for all possible game outcomes; wherein for k=√(2) there is a greater probability of a winning outcome than losing outcome considering only those outcomes that lie less than k standard deviations from the overall distribution's mean outcome.
A still further alternative description could be as a computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator and game logic generating winning and losing outcomes with assigned probabilities, wherein for any single wager event the probability for a net winning wager outcome is greater than the probability for a net losing wager outcome while maintaining a house retention on wagers by the game apparatus which is greater than 0% of all wagers.
Yet another alternative description may be as a computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator, game logic capable of generating winning and losing outcomes with assigned probabilities, and accounting logic capable of tracking the player's credit balance, wherein for a single wager event the probability of a player's credit balance increasing as a result of a game round is greater than the probability of a player's credit balance decreasing as a result of a game round while maintaining a house retention on wagers by the game apparatus which is greater than 0% of all wagers.
Yet another alternative description may be a player credit-banked computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator, game logic capable of generating winning and losing outcomes with assigned probabilities, and accounting logic capable of tracking the player's credit balance to sources within local apparatus and within external wagering game apparatus credit-processing apparatus, wherein initiating play of a round of a game adds a wager amount to the player's credit balance and the game logic assigns varying probabilities and amounts for losing outcomes to the player's credit balance such that house retention on wagers on the game apparatus is greater than 0% of all wagers.
What is meant by the terminology external wagering game apparatus credit-processing apparatus is that a processor other than the game control apparatus and a processor outside the physical confines of the terminal or slot machine or game table manages credit. As opposed to machines where credit is directly established by monetary input, ticket input, voucher input or the like, credit here may include or consist of access to an account, such as one managed by the casino or a chain of casinos. In those environments where wagering is allowed directly on credit cards, debit cards, cash cards or to bank accounts, this would suffice for the external wagering game apparatus credit-processing apparatus.
A method of playing a wagering game may be described as comprising: a player initiating play of the wagering game by placing value at risk. The risk may be achieved by placing a wager, by the system “paying” the player to play (as described elsewhere herein) or just by initiating a game which automatically places money/credits at risk and increments or decrements money/credits based on results, independent of defining a single round wager amount. At least the player receives randomly provided sets of symbols for use in the game. A dealer (real or virtual) may also receive a set of symbols if the game includes a player-versus-dealer competition as opposed to or in addition to a player-versus-paytable event. The player's received randomly provided set of symbols is evaluated (e.g., compared to a dealer's hand and/or against ranking or designated count or designated order, or designated numbers of specific symbols, such as 1 cherry, two cherries, three bars, etc.) according to at least one of predetermined rules of count (e.g., as in baccarat, Twenty-One, 7.5 and 21.5 poker), order (e.g., three jackpot symbols in a single line, a name spelled out in order, etc.), sets (e.g., any three bars, a flush, etc.), matching symbols, rank of symbols (e.g., poker hands), rank of combination of symbols (poker hands), alignment of symbols (e.g., sequences of numbers is hierarchal order, a scene formed in logical order, etc.), and numbers of triggering symbols (e.g., three bonus symbols in any position on a screen). The evaluation assigns net tying outcomes with tying effect (no credit adjustment from before starting round of play of the game), net winning outcomes with winning effects (e.g., the positive change in total credit position, and inclusive of the common use of returning the credit position to the total credit available before start of the game when credit has been reduced to allow start of the game) and net losing outcomes with losing effects (e.g., a reduction in total credit available comparing credit after conclusion of a round of play to credit available before the round of play) to all possible received randomly provided sets of symbols. Frequency of net winning outcomes for the player exceeds frequency of net losing outcomes for the player, and statistical magnitude of winning effects and magnitude of losing effects under the rules for the game statistically assure house retention on wagers that is greater than 0% of all wagers. In this method, symbols are randomly provided by physical playing cards, spinning of a physical reel on a slot machine, and/or by a random number generator providing symbols on a display screen. The player may place value at risk by placing a wager of a player-selected amount on a round of play of the wagering game, and/or by a processor allotting a player-selected amount of credit to the player's credit while placing at risk an amount of credit greater than the player-selected wager amount. A system may have an automatic default amount at risk and reward (e.g., a player may not be able to select amounts at risk, except for underlying credit units placed at risk, as in playing a $1.00 machine with all factors of wins and losses being based on the unit amount of $1.00). Similarly, the player may select an automatic $0.25 wagering device or a $5.00 wagering unit device. The player may or may not be able to alter the number of unit credits wagered within the system. That is, if a player is on a $5.00 unit credit machine, he may be required to stay at the $5.00 level for all wagers, or he may be able to alter the unit credits at risk in any round of play by increasing the $5.00 amount or decreasing the $5.00 amount at any time before initiation of play. The method may use a statistical basis for game play wherein summation of probabilities of net winning events multiplied by winning payback odds for each winning event is less than summation of probabilities of net losing events multiplied by losing deduction odds for each losing event. It is possible, if not preferred to have a frequency of net winning events plus frequency of net tying events that exceeds 60% of all wagering outcomes, such that in at least 60% of rounds of play, the player will not lose any value. The method may also be provided such that the frequency of net winning events exceeds 60% of all wagering outcomes (e.g., ties may or may not be considered in this comparison). The method may be practiced with at least one net losing event having a magnitude or loss effect that exceeds at least the magnitude of at least 90% of all net winning events. That is, even though a nominal wager of for example $5.00 is placed, and 90% of all winning outcomes returns $50.00 or less, at least one losing outcome at the $5.00 nominal unit credit wagering amount will cause a net loss of greater than $50.00, such as at least $51.00.
As noted, the system may be provided as a processor-based or computer system with direct input into a terminal, hand-held devices for interfacing with the processor, television input from rooms, or internet play. Buttons or touch screens or keyboards may be used for player input. In a further non-limiting configuration, one or more of the players can be located in separate locations, and the player terminals or hand-held devices or player screens in rooms can be connected to the controller via communication links (e.g., hardwired or wireless). Standard protocols, software, hardware and processor languages may be used in these communication links, without any known limitation. There are hundreds of available computer languages and formats that may be used, among the more common being Ada; Algol; APL; awk; Basic; C; C++; Cobol; Delphi; Eiffel; Euphoria; Forth; Fortran; HTML; Icon; Java; Javascript; Lisp; Logo; Mathematica; MatLab; Miranda; Modula-2; Oberon; Pascal; Perl; PL/I; Prolog; Python; Rexx; SAS; Scheme; sed; Simula; Smalltalk; Snobol; SQL; Visual Basic; Visual C++; and XML.
Any commercial processor may be used either as a single processor, serial or parallel set of processors in the system. Examples of commercial processors include, but are not limited to Merced™, Pentium™, Pentium II™, Xeon™, Celeron™, Pentium Pro™, Efficeon™, Athlon, AMD and the like.
Display screens may be segment display screen, analog display screens, digital display screens, CRTs, LED screens, Plasma screens, liquid crystal diode screens, and the like.
A pay table can typically be presented as game outcomes in tabular format by rows where each row in the table has a probability of occurrence and an associated amount. An simplified example pay table for conventional prior art casino slot machine gaming devices is presented in FIG. 1. In the figure, for purposes of example the bet amount is assumed to be 1, and the outcomes are ordered from lowest payout to highest payout in multiples of the bet amount. The net win amount is the payout amount minus the bet amount (and may be a net loss if the result is negative). Note that in this particular example, there is an outcome with net parity (bet equals payout) but there is nothing requiring such a row in any pay table.
It can be seen that the expected net win for the pay table in FIG. 1 is zero (assuming a bet amount of $1 and summing the net outcome amounts weighted by probability of occurrence as shown in column 4) In a typical casino however, the pay tables will be offset such that there will be a house advantage that will result in the expected payout to the player being less than even money. Typical values for the house advantage in a typical casino may range from 80% to 98% for example, but is variable based on gaming jurisdiction and casino. Another way of stating this is the expected net win amount will be less than zero, or alternatively, the retention of wagers by the casino will be greater than 0 on a percentage basis.
In the pay table in FIG. 1, it can be seen that the payout structure has been designed so that the game will play with a frequent amount of losing outcomes interspersed with relatively rare large wins. In general, this is what gives the prior art casino slot machines their characteristic look and feel of play.
It can be seen from FIG. 1 that the probability of a win outcome is 13% (4%+3%+2%+2%+1%+1%) while the probability of a net loss is 80%. 7% of the possible outcomes result in a net even outcome (bet equals win amount). Using this terminology, “net win” refers to the increase in the player's credit balance derived from the combination of the bet amount and the outcome of the wager, i.e., the win amount of the wager minus the amount of the wager itself. If a player bet $1 and won $10, the net win would be $10 payed−$1 wagered=$9 net win. If the wager did not result in a win, the net loss would be the amount of the wager itself, i.e., the $1 that was risked by the player for the wager.
FIG. 2 illustrates the example conventional pay table in graphical form. The winning outcomes 201 are relatively rare events indicated by the width of the winning outcomes in the graph. These wins are offset by the losing outcomes 202 that have a much higher probability of occurrence but a smaller payout magnitude. Together, the winning outcomes and the losing outcomes can be averaged to obtain a mean outcome, and this mean outcome gives the expected win (loss) for the pay table (and hence the gaming device). For example purposes, the illustrative pay table of FIGS. 1 and 2 has been designed to have a mean outcome of zero, but in an actual casino the mean outcome will be shifted in the casino's favor. Nothing in the system of the invention requires the overall mean outcome to lie in any certain range with respect to the individual potential wagering outcomes (although to be profitable for the casino the mean outcome of the pay table should be less than zero), rather, here we are talking about the manner in which the relatively rarer, larger magnitude outcomes relate to the properties of the distribution as a whole.
The mean net outcome and standard deviation can be calculated from the pay table in FIG. 1 using well known formulas to yield 0 for the mean and 3.0364 for the standard deviation. The set of net outcomes with magnitude greater than μ−√2σ and less than μ+√2σ (greater than −4.2942 and less than 4.2942) consists of the first four lines of the pay table. The mean value of these outcomes is −1*0.8+0*0.07+1*0.04+4*0.03=−0.64 and we see that the pay table of FIG. 1 is not consistent with the system of the invention because the resultant mean value of the relatively lower magnitude outcomes is not greater than zero. Similarly, the mean net outcome for the set of relatively large outcomes (with magnitude greater than or equal to sqrt(2)*σ from the mean) is +0.64 and is not less than zero as required by the system of the invention.
FIG. 3 gives a sample payout graph over time for a game implementing a conventional pay table. Each point on the graph indicates the player's balance at a particular point in time, with time being indicated indirectly on the x-axis through the number of wagers. It can easily be seen from the chart that the most likely payout is a loss, indicated by the tendency for the payout line segments connecting sequential dots in the graph to be directed with a negative slope. Interspersed with the high probability losses are low probability high magnitude winning outcomes 301 that infrequently boost the player's credit balance with large wins, bonuses or jackpots.
The system of the invention introduces a reverse or in some embodiments a partial pay paradigm to provide for a gaming device with unique characteristics and certain advantages over prior art systems. It does this by reversing the high and low probability events to result in a pay table that consistently rewards the player with small wins at the risk of low probability large (potentially catastrophic) losses.
FIG. 4 gives an example reverse logic pay table consistent with the system of the invention. A quick comparison to the pay table of FIG. 1 reveals that the pay table has simply been “reversed”—the wins have been replaced with losses, and vice-versa, to illustrate that most existing slot machines could potentially be converted to a reverse logic pay table (assuming that the mean outcome is adjusted to result in a net win for the casino and not the player. For these examples the mean is already at zero and so such an adjustment does not need to be performed. This does not affect the validity of the examples however). FIG. 5 shows a chart illustrating the pay table from FIG. 4. Characteristic of such a pay table are there are fewer large winning outcomes, and mainly large losing outcomes.
Psychologically, a game machine built with a pay structure of the system of the invention rewards the player with constant positive reinforcement because the credit balance on the machine has a higher probability of increasing with each spin. For players used to seeing their credit balance decrease with each spin at conventional gaming devices in a casino, the result is potentially a refreshing break from the steady drain on credits associated with those conventional prior art gaming devices. Comparing FIG. 2 and FIG. 5 clearly illustrates the fundamental difference in payout characteristics as they relate to the system of the invention and prior art gaming devices. In FIG. 2, the wins are the low probability (thin) high magnitude (tall) events. In FIG. 5, this is reversed with the losses being the low probability high magnitude events.
The mean net outcome and standard deviation can be calculated from the pay table in FIG. 4 using well known formulas to yield 0 for the mean and 3.0364 for the standard deviation. The set of net outcomes with magnitude greater than μ−√2σ and less than μ+√2σ (greater than −4.2942 and less than 4.2942) consists of the first four lines of the figure. The mean value of these outcomes is 1*0.8+0*0.07+−1*0.04+−4*0.03=0.64 and we see that the pay table of FIG. 4 is consistent with the system of the invention because the resultant mean value of the relatively lower magnitude outcomes is greater than zero. Similarly, the mean net outcome for the set of relatively large outcomes (with magnitude greater than or equal to sqrt(2)*σ from the mean) is −0.64 and is less than zero as required by the system of the invention.
FIG. 6 illustrates a payout graph for a reverse logic pay table. It can be seen during game play the player's credit balance has a high probability of increasing with incremental wins, interspersed with large low probability losing outcomes 601.
In one embodiment of the system of the invention, a casino game is provided that does not require the player to wager any amount to play, rather, the player adds a base amount of credits into the machine that represent the credit amount the player wants to risk. This amount becomes the player's credit basis for the wagering session. With each spin in a reel game (or equivalent terminology applied to non-reel games), the casino pays the player what is termed a “reverse wager”. The reverse wager is an amount the casino or house pays to the player every time the spin button is pressed and in some embodiments is based on or derived from the player's credit basis in the machine. In essence the player and the casino's roles have reversed and the casino is paying the player to play, and the casino wins (the player loses) when an infrequent rare event happens with a large payout.
Instead of a steady series of losses and the possibility of a large win associated with systems of the prior art, the casino game of the system of the invention provides for the probable guarantee of a relatively steady credit increase but provides for the possibility of a catastrophic loss. Instead of the traditional mentality when playing a slot hoping for the lucky rare event, a player playing a reverse pay table device hopes for the random outcome because the (un)lucky low probability events are usually losses.
In some embodiments of the system of the invention there are no winning awards. Instead there is only the possibility of various loss amounts to be subtracted from the player's credits. Other embodiments provide for a variety of wins and/or losses combined into a single pay table whereby adding the possibility of a large loss into the payout structure of the game allows the game designer to simultaneously provide for correspondingly larger wins on the same machine. Such a machine has the reverse pay table of the system of the invention combined with a traditional prior art pay table, although win amounts will be less frequent or less in magnitude than losing amounts consistent with the system of the invention.
Other embodiments of the system of the invention that may be more palatable in certain jurisdictions provide for a gaming device that requires a base buy-in amount from the player equal to the amount of the largest possible loss and with each wager that base buy-in amount is risked by the player. Wins are awarded using a pay structure based on the base buy-in amount and the probability structure of the pay table such that most of the time the total buy-in amount is awarded back to the player including an incremental amount determined from the base wager amount, but, in relatively infrequent occasions there is a large loss and only a fraction of the wager is awarded to the player. When considered in light of net game outcomes there is no difference in the net win/loss structure between the two forms, but in this embodiment the wager is presented in a manner that may conform better to the current letter of the law in certain gaming jurisdictions requiring a player bet and casino payout.
To further illustrate this type of embodiment of the system of the invention, the pay table of FIG. 4 shows that there are several ways to implement the actual game. For example, Game A might have the casino pay the player $1 per spin event, with the player losing up to $20 in one spin. Thus, for Game A, the casino pays the player a $1 reverse bet on every wager. The maximum $20 outcome is a loss (win for the casino) based on the wager outcome. Alternatively, for Game B implemented using traditional wagering terminology, the player bets $20 per spin and the max win for the player is $21. The catastrophic loss where the player loses the entire $20 bet can only happen 1% of the time for this example pay table. Game B uses traditional wagering terminology that may be in some cases more acceptable to certain jurisdictions. It can be easily seen that the differences between the two games are due purely to terminology, with no discernible differences in the payouts for net winning or net losing outcomes between the two games. It is important to note that in order to implement Game B, a fractional payout must be assigned to the wager ($21 pay for $20 bet, etc.). In any case, these two embodiments of the system of the invention present here are equivalent when viewed in terms of the net win and net loss for the various outcomes and the respective probabilities for such.
Most existing game formats can be adapted for use with the system of the invention. For example, a game device of the system of the invention can take the form of a one line reel spinning game, either mechanical or video, a multi-line reel spinner, mechanical or video, a keno video apparatus, or other form. The actual presentation comprising video, sound or other multimedia can be implemented in any of a multitude of choices and still have the pay table characteristics of the system of the invention.
Taking a single line reel spinning game as a specific embodiment for example purposes only, a game implemented using a pay table of the system of the invention might have bombs or other symbols with a negative connotation. The player, when playing such a device, would hope for a random no-pattern wager outcome, which means he would keep the casino's “bet”. In the event where three bombs lined up in a row (a catastrophic outcome as shown in FIG. 7), the player might lose a) his entire credit balance on the device, b) a maximum percentage (e.g., 50% of total credits available above a threshold minimum amount, for example above a minimum number of credits such as 100), or in c) some embodiments, the loss might be limited to the initial buy-in amount on the game machine. Example c) may operate such that if a player has from 1-100 credits available, all credits will be lost, and if 101 to 200 credits are available, only 100 credits will be lost, and for a number X>200 credits, some specific percentage such as 50% X will be lost. Such a catastrophic outcome in pay table structure does not exist in casino slot machine devices currently operating on casino floors but adds a compelling, exciting feel and an entirely new psychology to the game. As such, it is expected that a game consistent with the system of the invention will likely appeal to a different segment of player.
Some embodiments of the system of the invention might include a combination of both reverse pay tables and regular pay tables in a multi-game format. A player might play for the big win for a period of time, then switch to play for the incremental win as a refreshing change in odds structure. This could be done by a player exercising an option on underlying probability strategies. For example, the gaming apparatus might display to selectable play formats with the same symbols, and the selection of one format of a given game versus another format of the same game would alter the game format from the higher frequency win event with reduced average size payout to a lower frequency win event with higher average size formats as compared to the other format (with the higher win frequency).
It is to be noted that although numerous specific examples have been given to assist in an appreciation and understanding of the generic concepts of this disclosure and inventions included therein, the examples are not intended to be limiting with respect to the claims and the scope of the invention.

Claims

1. A computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator and game logic capable of generating at least one net winning or net losing outcome with assigned probabilities,

wherein for any single wager event the probability for a net winning game outcome is greater than the probability for a net losing game outcome while maintaining a house retention on wagers by the game apparatus which is greater than 0% of all wagers.

2. The wagering game apparatus of claim 1 with accounting logic capable of tracking the player's credit balance,

wherein for a single wager event the probability of a player's credit balance increasing as a result of the single wager is greater than the probability of a player's credit balance decreasing as a result of the wager.

3. The wagering game apparatus of claim 2 wherein the probability of a player's credit balance increasing as a result of the single wager is greater than 60 percent.

4. A player-banked computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator, game logic capable of generating game outcomes with assigned probabilities, and accounting logic capable of tracking the player's credit balance, wherein initiating play of a round of a game adds a wager amount to the player's credit balance and the game logic may assign at least one losing outcome to the player's credit balance after the completion of a round such that long term statistical house retention on wagers on the game apparatus is greater than 0% of all wagers.

5. A method of playing a wagering game comprising:

a player initiating play of the wagering game by placing value at risk;

at least the player receiving randomly provided sets of symbols for use in the game;

evaluating a player's received randomly provided set of symbols according to at least one of predetermined rules of count, order, sets, matching symbols, rank of symbols, rank of combination of symbols, alignment of symbols, and numbers of triggering symbols;

assigning, tying outcomes with net tying effects, winning outcomes with net winning effects and losing outcomes with net losing effects based on received randomly provided sets of symbols;

wherein frequency of net winning outcomes for the player exceed frequency of net losing outcomes for the player and magnitude of winning effects and magnitude of losing effects under the rules for the game statistically assure house retention on wagers that is greater than 0% of all wagers.

6. The method of claim 5 wherein symbols are randomly provided by playing cards.

7. The method of claim 5 wherein symbols are randomly provided by spinning of a physical reel on a slot machine.

8. The method of claim 5 wherein symbols are randomly provided by a random number generator providing symbols on a display screen.

9. The method of claim 8 wherein a player places value at risk by placing a wager of a player-selected amount on a round of play of the wagering game.

10. The method of claim 8 wherein a player places value at risk by a processor allotting a player-selected amount of credit to the player's credit while placing at risk an amount of credit greater than the player-selected wager amount.

11. The method of claim 8 wherein summation of probabilities of net winning events multiplied by winning payback odds for each net winning event is less than summation of probabilities of net losing events multiplied by losing deduction odds for each net losing event.

12. The method of claim 8 wherein frequency of net winning events plus frequency of net tying events exceeds 60% of all wagering outcomes.

13. The method of claim 8 wherein frequency of net winning events exceeds 60% of all wagering outcomes.

14. The method of claim 8 wherein at least one net losing event has a magnitude of loss effect that exceeds at least the magnitude of 90% of all winning events.

15. A computerized wagering game apparatus for wagering by a player, comprising: a game controller having a processor, memory, a random number generator and game logic capable of generating at least one net winning or net losing outcome with assigned probabilities,

wherein all possible net outcomes for the player comprise a probability distribution with an overall mean μ and an overall standard deviation σ,

wherein there exists a subset S of relatively small magnitude net outcomes consisting of those net outcomes that are greater than μ−√2σ and are less than μ+√2σ,

wherein there exists a subset L of relatively large magnitude net outcomes consisting of those net outcomes that are less than or equal to μ−√2σ or are greater than or equal to μ+√2σ,

wherein the mean of net outcomes calculated over subset S is greater than zero or the mean of net outcomes calculated over subset L is less than zero.