Method for determining gaming device outcomes
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A new method for creating slot machines and other gaming devices where outcomes are fair, but players and operators realize traditional payback and hold percentages, respectively.

Taylor, William Arthur (Evergreen, CO, US)
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William Arthur Taylor (Evergreen, CO, US)
I claim:

1. A method of provided game play to a player, the method of providing game play comprising: a) offering to such player a chance game, b) said chance game having an equal probability of one or more events occurring; c) said chance game offering a pay method based on achieving one or more said events, d) said pay method being selectively altered, randomly altered or both by one or more means, e) allowing such player to play the chance game.


This application claims priority to U.S. Provisional Application Ser. No. 60/681,517 filed on May 16, 2005, which is incorporated by reference in its entirety herein.


A portion of the disclosure of this patent document contains or may contain material subject to copyright protection. The copyright owner has no objection to photocopy reproduction of the patent document or the patent disclosure exactly as appearing in the Patent and Trademark Office patent file or records, but otherwise all copyright rights whatsoever are reserved. 37 CFR 1.71(d).


The invention relates to gambling devices generally and in particular to a new modeling method for designing slot machine and gaming device mathematics.


Gambling devices, or gaming devices including slot machines, allow players to wager something of value in the hopes of winning something of greater value. Originally slot machines were mechanical devices employing 3 physical reels with various symbols painted or affixed to them. Upon inserting a coin and pulling a spring-loaded handle, the reels were set in motion and players were paid or not depending upon where the reels stopped and which symbols were displayed across the display portion of the machine.

Slot machines have evolved greatly since the original gaming devices discussed above. Most slot machines in use today are electronic computers, and the symbols are displayed in video form. Players often prefer video display slot machines over the traditional slot machines using mechanical reels. The video platform also offers more flexibility in development for manufacturers. The common term today for a gambling machine is a gaming device, which is used herein to include gambling devices such as slot machines, video poker, and other gambling games whether reel, video or otherwise.

Newer video slots typically display 5 reels side-by-side that spin on a common axis instead of the traditional 3 (or more) mechanical reels. These newer video slots usually show 3 stopping positions of each reel yielding a visible matrix of 3 rows by 5 columns. Sometimes the number of reels and reel positions displayed vary.

Players typically wager on 1 or more paylines that run in different paths through the reel positions displayed. Unlike newer models of gaming devices, early slots paid only for matching symbols straight across the center (a single payline). Traditionally the path of each payline takes 1 adjacent position of each reel, so on a 5-reel game the payline is usually 5 positions in length. However, today these payline paths may number in the hundreds, they may take any path, and they may not always span adjacent reels nor even be on contiguous positions. One newer game entitled Hoot Loot even has a special payline comprised only of symbols containing a star. Generally, players may wager on multiple paylines and may even wager multiple credits per payline. Reel symbols occurring in various combinations on the paylines are compared to a schedule of winning events commonly called a paytable to determine a win or loss. Often there are wild symbols that substitute for other symbols, and symbol combinations that trigger a bonus or feature game. Scatter pays are also common where certain symbol(s) pay anywhere in the visible display, and they don't have to be on any payline. Wins are usually rewarded with monetary awards from a coin hopper provided in the machine or tickets redeemable for cash.

Second screen features (or more) are common. A “second-screen” bonus game is usually separate and distinct from the normal reel display, and a player might select a car in a car race or scratch from a selection of video lottery tickets to earn credits, free games or anything of value. Some games even offer third screens or more, enhancing player interest and intrigue. These bonus game features typically occur randomly every 50 plays or so and are embedded in the game mathematics. Their occurrence is not conditioned upon an additional bet.

Some games let creative players play consecutive games without manual intervention. Sometimes players wedge a toothpick or folded matchbook cover in such a manner as to keep the play button depressed. Provided they have sufficient credits, consecutive games play off by themselves. Although these players have basically fashioned an autoplay device, each game is still a single, discrete event that requires a separate wager. However, in newer gaming devices a “game” might be comprised of multiple slot machines spins of a traditional nature plus other interactions and events.

In general, the more interactive a gaming device is, the more entertaining it is, and the greater its entertainment value the more players will play it. Accordingly, more play normally translates to greater profits for gaming device operators.

Other types of gaming devices offer side bets. For example, in one game players play blackjack, but may wager separately who gets closest to a “21” point score. In another a gaming device is provided that offers a side bet to participate in a super jackpot game.

Side bets have also been around for a very long time. Aristocrat, a major slot machine manufacturer headquartered in Australia, makes games that offer side bets embedded within a video slot machine. Their Cashman series offers bonus features that can only be achieved when a side bet is made. This side bet is only offered when the player has first bet the maximum number of lines offered on the machine. For example, after a player bets the maximum 20 paylines they are offered the chance to make a side bet that costs the equivalent of betting another 5 paylines. Thus, these games entice the player to raise their bet. Since casinos and operators normally retain a percentage of the bet, this side bet usually results in greater revenues and profits. While this is a somewhat creative means to offer a side bet, it is still just an additional bet. Side bets are separate wagers on separate events.

Some gaming devices offer multiple bets. Triple Play Poker permits player's held cards to be played as multiple poker hands with each draw performed independently, usually resulting in 3 different outcomes. Each additional hand requires an additional wager that can become expensive, since it costs 3 times as much to play.

Regardless of the type or form of gaming device—whether reel slot, video game, some other type or combination—the basic method of wagering has remained largely the same for years. The player inserts coins or otherwise obtains credits on a machine, commits a wager, plays the game and then is paid or not depending on the outcome.

Slot machines today play in many different denominations. Credits on one machine might be worth 1 cent (or less), while others are worth $100. Some machines even allow you to select the denomination at the machine and to change it between games. One advance in slot machine development was the use of a credit meter. With a credit meter, a player could insert more coins than were needed to play a single game, and thus have a pool of funds to draw upon. Ten nickels inserted would yield ten credits, for example. Then, the player could play one game that required ten nickel credits, ten games that required one nickel credit each, or anything in between. The use of a credit meter also allowed winnings to be accumulated on the machine, instead of always being paid out in coins each time the player won. A player could rack up credits and then choose to cash out at their leisure by the use of a special button on the machine for this purpose.

In 1990s, most slot machine manufacturers began offering currency acceptors with their machines. Players could obtain machine credits by simply inserting paper currency. In recent years, manufacturers have even added devices that could dispense currency instead of, or in addition to, coins. (These are known as note hoppers and operate similar to bank cash machines or ATMs). Many new machines pay players in paper tickets or scripts that may be redeemed elsewhere or reinserted into similar machines that read and accept such paper. These are often called ticket-printer machines. Some machines may even accept credit cards or other cards that have value.

A traditional video slot machine commonly has 2 rows of bet buttons plus a service and cashout button. The top row dictates the number of paylines, often from 1 to 9 or more. (In the case of the Cashman example cited earlier, the top row also contains the side bet button.) The bottom row has the credit per line bet buttons, which are commonly from 1 to 10. These limits change depending on the game. A typical one-cent game today may offer up to 20 paylines and 20 credits per line for a total bet of 400 credits or $4.00 per play, or more. Play is commonly initiated by pressing the credit per line button, which is multiplied by the number of currently selected paylines to arrive at the total bet.

As a promotion, casinos sometime configure certain slot machines for tournament play. Slot tournaments are player versus player competitions administered by casino staff. Players gain entry through a variety of means, such as achieving VIP status in the casino's players club, paying an entry fee or simply for signing up. In these tournaments, players do not wager anything directly or at all, but person(s) with the highest credit scores receive something of value from the casino. Since there is no wager, the slot machines are set to a free play mode where the goal is to get more credits than the other players. Players are not paid directly for credits earned. Tournaments are marketing programs that rely on gaming devices for implementation.

Time on a particular device is a huge factor in the gaming industry today. Time on device is important not only for direct profits to gaming device operators, but also indirectly. The more time spent in one gambling property means more profit opportunities for the casino. Restaurants, shows, gift shops, hotel rooms, etc., all give the casino the chance for more profits. In general, the more time a player spends in a gaming establishment, the greater the likelihood they will return and spend even more. Operators strive to keep you in their establishment, which generally means more profits, and typically provide numerous incentives such as free or inexpensive food and drinks specifically for this purpose.

Marketing studies have revealed that players do not mind losing so much, as long as they can have a good time playing. Most casino gamblers don't really expect to win, but they do expect to play for a reasonable amount of time. This is consistent with newer trends in gaming where gambling for the typical patron is more of an entertainment experience. With the proliferation of casinos in America in recent years, casino gambling has become mainstream entertainment. Perhaps the most important part of that entertainment value is “time on device”, or how long you get to play for your money. Time on device is critical to a positive gambling experience.

Accordingly, recent attempts have been made to ensure greater time on device for players. Perhaps the most common method today on slot machines is to offer more winners of lesser amounts. To this end slot makers design games with a greater mathematical win frequency and a reduced paytable. Especially in newer video slots these win or hit frequencies reach 50% or more. In practice, this means you might bet 10 coins per line on 9 paylines (90 coins total) only to win 20 coins. Even though this is clearly a net loss for the player, the 20 award is still advertised as a win. This trickling back of credits to the player takes their money more slowly, recognizes them as winners (even if they're losing) and extends their playtime for a given amount of money to bet.

One problem with high hit frequencies is that player returns become meaningless. While time on device is generally lengthened, betting 90 to win 20 eventually becomes tedious and boring. Players soon realize that with these gaming products they are not really winning even if the machine displays “winner”, but rather, they have simply lost less. The reduced payable means the allure of big winners is diminished. The tradeoff of more common winners is smaller winners.

Other enticements also keep players playing longer. As mentioned occasional bonus features or second-screen events that award free plays or credits are common ways to motivate players. Random payouts and mystery jackpots (typically paid anywhere on a bank of networked gaming machines) are also popular. Progressive awards, where certain outcomes pay an amount that increases with credits played until won, also give players something special to play for. Qualifying for progressive awards is often conditioned on players first wagering the maximum allowable bet.

Some less common gaming devices employ a hold and re-spin feature. In these games the reels are spun once, then desirable symbols are held similar to draw poker and the rest are spun again in order to make more favorable combinations. Still other esoteric and non-traditional concepts let players buy a predetermined amount of time and play remotely without even being near the machine. But, this lesser involvement detracts from the experience.

Different jurisdictions impose different regulations onto casino operators and gaming machine manufacturers. For example, riverboat casino legislation in Mississippi resulted in casinos being built in the mud that don't even float. These riverboats don't navigate and can't even move. In other markets, riverboat casinos are required to cruise some distance periodically to qualify under the regulations.

Similarly, different states place different requirements onto gaming devices. One common rule requires a skill component. Thus in some markets video draw poker games are the standard. Skill is needed to make the best choice as to cards retained and cards replaced on the “draw.”

Some states don't allow traditional slot machines, but only bingo or lottery games that resemble slot machines. These games, often called “Class II” games, usually require another button press or two to set the reels spinning. Commencing with the bet, a bingo card is selected. The next button push selects a series of bingo balls, and a win or loss outcome is determined in accordance with the rules of bingo. The next press sets slot machine reels spinning and the resulting outcome is that commensurate with the bingo game. As an example, a bingo winner paying 10 is represented as a slot machine result paying 10. Thus clever manufacturers have fashioned a bingo game simulating a slot machine that is legal in some markets.

Still other markets require “central determination.” Unlike traditional slot machines that stand alone independent of each other, centrally determined gaming devices are networked to a central server. This server dishes random numbers or gaming device outcomes to each device on the network. Thus a central accounting point may be maintained in a government office that controls each device statewide. While imposed by regulation, this also helps with accounting controls, general security and the verification process over large jackpot payouts. These are sometimes called video lottery games. Many other variations exist on gaming devices and the systems that work with them.

As indicated lower denomination games have become very popular recently. In the early 1990s games were generally nickel, quarter and dollar denomination. Today one-cent games are among the most popular. Since the denomination has fallen, so have average bets. Thus, manufacturers and gaming device operators are striving for ways to keep the bets high to maintain profitability. To these ends, some gaming device makers incorporate elaborate second- and third-screen bonuses with multiple bonus features embedded within their video slots. But, irrespective of the wagering method, games that are too complicated are generally less successful, since most players prefer new games that are easy to learn and play. So, it is a balancing act to keep games interesting and engaging, but simple. Likewise, keeping the bets high enough to return traditional or better profits while offering lower denominations is also a major objective of game designers today.

Almost all gaming devices retain a portion of wagers for the operator or house. This is called the hold percentage. This percent of the wager is used to cover operator expenses and contribute to profits. What is not retained is returned to players in the form of winnings, and this proportion of wagers is called the payback percentage. Note player returns or winnings may be in the form of prizes, accrued payouts, annuities or other things of value that are normally paid for or arranged by the device operator.

Hold and payback percentages are predetermined at the gaming device design stage. The casino game The Big Wheel yields a straightforward example. The Big Wheel is typically a single large spinning wheel with approximately 54 dollars bills pinned to its perimeter in different denominations. The player makes a wager, spins the wheel and receives the bill indicated when it stops. Assuming the example shown below having 40 equally likely positions, the expected value of playing this game is $9.55. (The award is multiplied times its possibility, which yields a contribution to the total. Dividing by the total number of possibilities yields an expected value. Alternatively, as in the case of slot machines, each award is multiplied by its probability yielding a contribution, which is then summed to find the expected value of play and ultimately the payback percentage.) If it costs $10 to play, the casino on average keeps $0.45 or 4.5% of bets. Thus the hold percentage in this case would be 4.5% and the payback percentage would be 95.5% as illustrated below (for demonstration purposes only).

AwardPossibilitiesContributionExpected Value
 $1 bill12$12
 $2 bill5$10
 $5 bill10$50
$10 bill6$60
$20 bill5$100 
$50 bill1$50
$100 bill 1$100 
Total40$382 $382/40 = $9.55

As discussed slot machine percentages are found similarly, being typically a function of symbol occurrences and the paytable. The paytable (containing the awards) is predominantly fixed and unchanging during game play, while the symbols (the possibilities) vary. Symbols are ultimately dictated by a computer algorithm acting as a random number generator that determines where the reels stop.

Hold and payback percentages on slot machines have been determined in largely the same way for many years. Winning outcomes (usually symbol combinations) are predetermined and listed in a paytable, or published schedule of pays. A higher value award or payoff is typically given to scarcer symbols or symbol combinations. The reels are then mapped with symbols, with the number of symbols and total positions ultimately determining the odds of getting any particular outcome or combination. For example, with one reel containing 1 each of 10 symbols and a random spin, the odds of getting any particular symbol are 1 in 10. With 2 such reels, the odds of getting a particular symbol on reel 1 and a particular symbol on reel 2 at the same time are 1 in 100, and so on. Using math or statistical methods, game developers ascertain the chances of each outcome and fashion a paytable accordingly to assure the house retains a mathematical advantage—it's desired hold percentage. One hundred percent less the hold percentage is equal to the payback percentage.

Note the term reel mapping refers to the fashioning of a reelstrip. A reelstrip is a way of laying out symbol possibilities on a reel. Commonly reelstrips are mapped such that identical symbols are not in adjacent positions. Symbols are normally at least 2 positions away from identical symbols on a reel when a typical 3 row by 5 reel array is used. (The term reelstrip developed from machines where these plastic “strips” were affixed to mechanical reels.)

There are some simple enhancements to the above method. Wild symbols often substitute for other symbols. They may even substitute for other symbols on other reels, for other symbol positions on the current reel or for multiple positions at the same time. Other games treat each displayed symbol position independently. That is, there is no reel in the traditional sense and each symbol or position is determined individually without any deference to a reel or to which symbol(s) is adjacent.

The term reel as used herein is a convenient way to reference the action, method and means of finding symbols and displaying outcomes, and it stems from the old mechanical machines. However, since most gambling devices today are based on computer platforms, physical reels are now less common. Virtual reels that simulate a physical reel are most common today. Instead of using springs and reels to achieve or simulate randomness, a computer means generates a random or pseudo-random number that determines either which symbol(s) is displayed and in which position or some other outcome, which is then displayed or otherwise used in the course of play.

Some special cases effectively modify one or more paytable awards between games. Progressive awards usually have a reset value and increase as a percentage of the bet. For example, a progressive jackpot might start out at $1 million and increase with 1% of monies wagered on all networked machines. This is how IGT's Megabucks works. The odds or winning are remote, but with hundreds of machines linked to the progressive system Megabucks has paid awards well over $20 million. Once paid, the progressive jackpot resets to its starting value and the cycle repeats.

Unlike progressives, random pays and mystery awards are paid when no advertised winning event or symbol combination occurs. Both are usually smaller paytable values paid frequently. The timing of their payouts is often based on some random or other event with pre-set limits. For example, the operator may specify that ½% of bets are accumulated in a hidden pool, and that a mystery award always pays between $25 and $75. The gaming device selects a random value between these limits. Whoever's wager causes the hidden pool to reach this value is then paid this amount. Since the player never knows in advance what the selected random value is, the win is a mystery. It has nothing to do with achieving any winning outcome on the game, and it may be paid with or without any coinciding win on the machine. Random pays are similar, although the internal method that determines when they're paid and how much may vary. Both random pays and mystery awards are triggered separately from advertised paytable events, and both are paid from some reserved portion of the payback percentage that is typically influenced, directly or indirectly, by the cumulative wager.

Some games modify the paytable's schedule of winning events between games. In IGT's Hoot Loot one special symbol combination pays an award, and that combination changes with each play.

Regardless, with the traditional means of using reelstrips and paytables to determine gaming device payback percentages, it is necessary that some symbols occur less frequently than others. For example, if 5 “red sevens” pays 10000, and 5 “bars” pays 10, it follows that red sevens won't occur as often. After all, the operator must normally retain a mathematical advantage. In practice this means that some symbols or combinations are elusive and rare.

Higher paying symbols are the most sought after. Game designers usually make them the most ornate, the most animated or otherwise the most attractive. But, they occur least frequently. Players know these are the most valuable, but get frustrated when they don't get them very often. Thus it's obvious to players that the reels do not contain an equal number of symbols, or that the game is somehow designed with a bias towards lower paying symbols. This restricts naturally expected symbol combinations, and clearly reinforces that the odds are stacked against players with every play. The present invention overcomes these problems with a new and novel means for determining slot machine hold and payback percentages.


Accordingly it is one aspect of the present invention to provide a new and novel means for developers to obtain traditional gaming device hold and payback percentages required for commercial viability while also providing fair device outcomes to players.

The present invention accomplishes these goals. The preferred embodiment is entitled Fair Game (“FG”). Instead of predominantly fixing the paytable and weighting or otherwise varying the likelihood of winning events, FG takes the opposite approach. In FG the wins are equally likely and the paytable is varied to achieve the required percentages.

Some new benefits include:

1. As the name implies FG games have an equal chance of hitting each combination. Traditional biases and symbol weightings are removed and outcomes are fair. In the case of slot machines, less desirable symbols do not occur more frequently.

2. More suspense equals more excitement and potentially more fun. When you don't know exactly what your winning combination pays, the knowledge of a win coupled with the suspense of its worth creates anticipation.

3. Most play methods can remain as is traditional in the art.

4. This new method can be used with traditional equipment and with existing game themes.

5. This new invention can be used with new games and play methods. Consider a game where one or more paylines change each game. (A) The “repeater” may offer a payline or paylines based on prior game events. Thus the current game options depend on a previous game or games. For example, if payline at coordinates 1,3-2,2-3,1-4,2-5,3 won last game it might pay double in this game. (The first digit being the reel, from 1 to 5 left to right, and the second digit being its position, from 1 to 3, top to bottom respectively.) (B) Alternatively, patterns such as four corners and keno-type payline group selections may be offered. (C) In another embodiment, players may choose their paylines by simply making touch selections onscreen and may thus play any positions and length. While it's traditional to have 5 reels, players could have fewer or more positions to wager upon, perhaps selecting 6, 7, 8 or more positions.

In a typical embodiment of the present invention the paytable varies, but the reel symbols are weighted equally. Referring now to FIG. 1, a traditional reelstrip would usually contain fewer of the highest-paying Red 7 symbols and more of the lower-paying Bar symbols. As shown in a typical embodiment of a Fair Game reel, all symbols are equally likely. (Note there is no requirement that each of multiple reels contain the same number of reel positions or number and/or type of symbols. Further, there is no requirement that all symbols be ordered in the same repeating fashion as shown.)

In a typical embodiment of the present invention the paytable varies. The method of this variation may be accomplished by any means and may take any form. One means is for the outcome (the award) to be found in advance, typically at the time of wager, and then both the win and paytable amount is displayed from a set of one or more possibilities. Alternatively a random number generator may be called once or multiple times—first to find the reel spin outcomes and again to find its value as if from a corresponding paytable, for example. The paytable presentation to the player may also be accomplished by any means and take any form if, for example, once the winner is determined the paytable amount or amounts are indicated by a scrolling pointer appearing to land randomly or otherwise as depicted in FIG. 2. Other means of paytable determination include, but are not limited to, a spinning arrow which points to the pay or paytable, alternating arrows, other indicators or highlights per FIG. 3. While not shown, some or all paytable events, combinations, pays, wins or options may be determined in whole or part by the wager, additional bet, side bet or other means.

Multiple paytables or single paytables with multiple awards may be selected from. It may be possible to incorporate a side bet or an additional bet in any fashion. This may be appropriate to qualify for certain options, awards, paytables or other features or bonuses. There may or may not be a bias in the paytable towards rewarding certain symbol occurrences with greater awards.

As described, the mathematics involved in finding payback percentages and contributions of any particular winning outcome generally differ from that which is traditional in the art. One way, when playing a gambling device, one or more events are fair in that any probability of occurrence is equally weighted with all possible events. In the case of slot machines one or more reels are fair, in that there is no bias towards a particular outcome. In this invention it is the award related to a particular outcome that may vary from time to time.

Any subset or combination of the above methods, means or forms of wagering, finding winners and losers and/or displaying or otherwise presenting outcomes may be used.

There are numerous variations falling within the scope of the present invention. This invention may be employed with any combination of options including, but not limited to, bonuses, any skill game or games having a player skill components, feature games, side bets, wagering or play methods. This invention may be employed in whole or in part, or itself as a bonus, add-on or otherwise in conjunction with traditional gaming devices or methods. Thus, these and all embodiments described should be viewed as illustrative, rather than limiting.


FIG. 1 compares a traditional reel strip to a sample reel strip per the present invention.

FIG. 2 shows a sample means to determine a payoff associated with a spin result.

FIG. 3 shows a paytable selected from 4 samples and the payoff associated with a spin result thereunder.