Title:
Games of chance involving roulette wheels
Kind Code:
A1


Abstract:
A device for playing a game of chance comprises a plurality of roulette wheels each spinnable to provide a result, and an accumulator for calculating and outputting a sum of the results of the roulette wheels. The result is a game of chance that has a bell curve of odds for the available outcomes, permitting maximum prizes which are high relative to what is currently available for this kind of game.



Inventors:
Dabosh, Eli (London, GB)
Application Number:
11/220659
Publication Date:
03/30/2006
Filing Date:
09/08/2005
Primary Class:
Other Classes:
463/17, 273/143R
International Classes:
A63F9/24; A63B71/00; A63F1/18; A63F5/00
View Patent Images:
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Primary Examiner:
DENNIS, MICHAEL DAVID
Attorney, Agent or Firm:
Martin MOYNIHAN;PRTSI, Inc. (P.O. Box 16446, Arlington, VA, 22215, US)
Claims:
What is claimed is:

1. A method of playing roulette using a plurality of wheels having discrete stopping positions, each stopping position being a discernable result, the method comprising: receiving at least one player's prediction of an accumulated result possible for the plurality of wheels, operating said plurality of wheels to cause each wheel to reach one of its stopping positions at random, thereby to give one of said discernable results, calculating an accumulated result for the plurality of wheels by adding said discernable results, and comparing said accumulated result with said at least one player's prediction to identify a winning prediction.

2. The method of claim 1, wherein said plurality comprises five wheels.

3. The method of claim 1, wherein each wheel has 37 stopping positions.

4. The method of claim 1, wherein each wheel has 38 stopping positions.

5. The method of claim 1, played using a dedicated electronic slot machine.

6. The method of claim 1, played using a dedicated mechanical device.

7. The method of claim 1, played over an electronic network, between a server and a client.

8. The method of claim 1, further comprising allowing a user to predict an individual discernable result.

9. A method of providing a game of chance having a non-linear mapping of probabilities to each of a plurality of different outcomes, the method comprising: using a plurality of wheels having discrete stopping positions, each stopping position being a discernable result, the method comprising: receiving at least one player's prediction of an accumulated result possible for the plurality of wheels, operating said plurality of wheels to cause each wheel to reach one of its stopping positions at random, thereby to give one of said discernable results, calculating an accumulated result for the plurality of wheels by adding said discernable results, said accumulated result providing said outcome, and comparing said outcome with said at least one player's prediction to identify a winning prediction.

10. The method of claim 9, wherein said non-linear mapping is a bell-shaped distribution about a median, said median being the sum of the median results of each wheel of said plurality of wheels.

11. A device for playing a game of chance comprising: a plurality of roulette wheels each spinnable to provide a result, and an accumulator for calculating and outputting a sum of the results of said plurality of roulette wheels.

12. The device of claim 11, wherein said plurality of roulette wheels is five roulette wheels.

13. The device of claim 11, wherein each roulette wheel is spinnable to provide at random any one of thirty seven results.

14. The device of claim 11, wherein each roulette wheel is spinnable to provide at random any one of thirty eight results.

15. The device of claim 11, wherein said wheels are physical wheels.

16. The device of claim 11, wherein said wheels are implemented virtually.

17. The device of claim 11, implemented virtually over a network to remote players.

18. A method of providing a game of chance having a non-linear mapping of probabilities to each of a plurality of different outcomes, the method comprising: providing a plurality of roulette wheels each spinnable to provide a result, and providing an accumulator, in association with said plurality of roulette wheels, for calculating a current one of said plurality of different outcomes, said current outcome comprising a sum of the results of said plurality of roulette wheels.

19. The method of claim 18, wherein said non-linear mapping is a bell-shaped distribution about a median, said median being the sum of the median results of each wheel of said plurality of wheels.

Description:

RELATED APPLICATIONS

The present application claims priority from GB Patent Application No. 0420125.7, filed on Sep. 9, 2004.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates to games of chance involving roulette wheels and, more particularly, but not exclusively to a game of chance involving multiple roulette wheels.

Games of chance are highly popular and have been around for many centuries. One especially popular game of chance is roulette, which is believed to have been around in something close to its present form since the 18th century. Roulette involves a wheel traditionally having 37 or possibly 38 spaces or stopping positions, each position being assigned a unique number and one of two colors. The 37 space wheel is typically used in Europe and the 38 space wheel in the USA. The wheel is set to spin and when the wheel ceases spinning a ball comes to rest within one of the spaces. Players may bet on the numbers, or combination of numbers, or the colors, of an expected stopping position of the ball within the wheel (a betting position or prediction). The player who makes a correct prediction wins. Typically the odds the player receives for winning are slightly lower than the mathematical odds of the position he has bet on. However a disadvantage of roulette is that since the odds of any single number coming up are 37/1, the maximum prize that can be paid out is bounded above by 37 times the bet placed. Generally players are attracted by high maximum payouts, however small the odds of such a maximum payout.

Traditional roulette is based on a single wheel, and is generally played at a casino where a wheel is mounted on a table and a cloth or like marked spread is provided to enable each player to indicate his predictions. The wheel is set near the center of the table.

As indicated above, certain of the numbers and spaces on the roulette betting felt (such as 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, and 35) are colored black, while others (such as 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 32, 34 and 36) are colored red. Also included on the betting felt are spaces for such bets as: “manqué” (1 to 18 inclusive); “pass” (19 to 36 inclusive); “pair” (an even number); “impair” (an odd number); “rouge” (a red number); and “noir” (a black number). Therefore, the winning bet may be comprised of a bet on the particular winning number, a bet on a range of numbers that includes the winning number (e.g., on odd or the “2nd 12”), or a bet on a color that includes a winning number.

All bets are placed against the house and are indicated by placing stakes (e.g., chips) on the particular numbers or types of bets selected as they appear on the table. Once the bets are placed, the “croupier” spins the wheel in one direction and tosses the ball onto the wheel in the other direction. The sector where the ball finally comes to rest is the outcome, thereby indicating the winning number and color. This information is then used to manually determine which of the bets are winning bets. Various betting combinations with different odds and maximum bets are allowed depending on the rules of the gaming establishment. The standard odds and payouts for traditional roulette are well known in the art.

One way of increasing the possibilities in a game is to increase the number of balls that circulate with the roulette wheel, thus increasing the number of outcomes that can be bet on. An example is shown in U.S. Pat. No. 6,209,869 to Mathews, which discloses an apparatus and method for playing a roulette-type game. The apparatus includes a conventional roulette wheel and four tables. Each table has a lower playing field and an upper playing field, wherein each field is utilized for placing bets. During play, four balls are utilized on the one wheel, wherein each ball corresponds to one of the tables. The lower field is utilized for placing bets on the single ball that is associated with that particular table, while the upper field of each table is utilized for placing bets on all of the balls in play.

U.S. Pat. No. 5,755,440 to Sher relates to an apparatus used to play roulette using multiple balls. The apparatus includes a single roulette wheel that has multiple tracks, thereby permitting two or more balls to be propelled into the wheel simultaneously.

The mechanical systems above can be simulated electronically, and both stand alone roulette machines and computer programs for playing roulette are well known. The computer programs may be stand alone programs or can be played by remotely located participants over the Internet.

U.S. Pat. No. 5,259,616 to Bergmann discloses a coin-operated gaming machine that has a roulette-like number pan and a setting keyboard. In operation, the player inserts one or more coins into a coin insertion slot. The player then selects which numbers the player wishes to bet on using the keyboard. After the player places a bet, a random number generator randomly determines the winning number, and that number is then highlighted on the number pan. The random number generator also randomly determines a win multiplier number by which the winning payout is multiplied.

U.S. Pat. No. 6,083,105 to Ronin et al. discloses a single-player computerized roulette playing apparatus. The apparatus includes a rotatable roulette wheel that is mechanically rotated using a drive mechanism. One or more balls are put into play during the game. A roulette game field is displayed on a corresponding computer display, which provides a means by which the player can place one or more bets.

Recently, a system intended for Internet based betting or for a betting machine, provides for a series of roulette wheels and allows a player to take a betting position that takes into account the results at each of the roulette wheels in the series. The system thus allows for results with odds that are lower than 37/1 and thereby permits higher payouts, but only in a limited way. Such a system is exemplified by International Patent Application No. WO 2004/054665, which teaches a computerized multiple wheel roulette game allowing players to place bets on different wheels and on multiple numbers on the same wheel. The idea is to permit bets with lower odds and thus to permit larger prizes. The game is based on individual results produced on individual wheels and, since these are independent events, the use of the individual results does not succeed in giving a level of odds and consequent maximum prize, which can stand out against national or state lotteries and other available games of chance.

There is thus a widely recognized need for, and it would be highly advantageous to have, a game of chance based on roulette wheels which is devoid of the above limitations.

SUMMARY OF THE INVENTION

According to one aspect of the present invention there is provided a method of playing roulette using a plurality of wheels having discrete stopping positions, each stopping position being a discernable result, the method comprising:

    • receiving at least one player's prediction of an accumulated result possible for the plurality of wheels,
    • operating the plurality of wheels to cause each wheel to reach one of its stopping positions at random, thereby to give one of the discernable results,
    • calculating an accumulated result for the plurality of wheels by adding the discernable results, and comparing the accumulated result with the at least one player's prediction to identify a winning prediction.

In a particularly preferred embodiment the method uses five roulette wheels, as this gives a level of odds that are seen as an ideal balance between the level of the prize and the chances of actually winning.

The wheel being used may be the traditional European version having 37 stopping positions, or it may be the traditional USA version having 38 stopping positions. As a further alternative the wheel may make use of any other suitable format. There exist for example various historical formats of the roulette wheel which are not in widespread use today.

The method may use a dedicated electronic slot machine.

Alternatively, the method may use a dedicated mechanical device, for example a device in which a given number of wheels are arranged in a column. A single spin action by the operator sets all of the wheels spinning but they come to rest independently. Preferably the stopping positions are electronically detected and the sum of the stopping positions is indicated at an output.

Alternatively the method may be played using a computer program, which simulates the spin of the roulette wheels.

The computer program may be stand alone or support play with one or more remote users over an electronic network, say between a server and a client.

According to a second aspect of the present invention there is provided a device for playing a game of chance comprising:

    • a plurality of roulette wheels each spinnable to provide a result, and
    • an accumulator for calculating and outputting a sum of the results of the plurality of roulette wheels.

A preferred number of roulette wheels is five roulette wheels, again for providing a trade off between the ability to provide a large prize and a reasonable possibility of actually winning.

As above, the wheels concerned may be in the US format or the European format. Alternatively they may be in any other suitable format.

The wheels may be physical wheels, irrespective of whether the accumulation is carried out electronically, mechanically or left to the users.

In an alternative device the wheels are implemented virtually.

As discussed above, the virtual implementation may be provided over a network, such as the Internet, to enable participation by remotely located participants or players.

According to a further aspect of the present invention, there is provided a method of providing a game of chance having a non-linear mapping of probabilities to each of a plurality of different outcomes, the method comprising:

    • providing a plurality of roulette wheels each spinnable to provide a result, and
    • providing an accumulator, in association with the plurality of roulette wheels, for calculating a current one of the plurality of different outcomes, the current outcome comprising a sum of the results of the plurality of roulette wheels.

According to a further aspect of the present invention there is provided a method of providing a game of chance having a non-linear mapping of probabilities to each of a plurality of different outcomes, the method comprising:

    • using a plurality of wheels having discrete stopping positions, each stopping position being a discernable result, the method comprising:
    • receiving at least one player's prediction of an accumulated result possible for the plurality of wheels,
    • operating the plurality of wheels to cause each wheel to reach one of its stopping positions at random, thereby to give one of the discernable results,
    • calculating an accumulated result for the plurality of wheels by adding the discernable results, the accumulated result providing the outcome, and
    • comparing the outcome with the at least one player's prediction to identify a winning prediction.

The non-linear mapping is typically a bell-shaped distribution about a median, the median being the sum of the median results of each wheel of the plurality of wheels.

Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The materials, methods, and examples provided herein are illustrative only and not intended to be limiting.

Implementation of the method and system of the present invention involves performing or completing certain selected tasks or steps manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of preferred embodiments of the method and system of the present invention, several selected steps could be implemented by hardware or by software on any operating system of any firmware or a combination thereof. For example, as hardware, selected steps of the invention could be implemented as a chip or a circuit. As software, selected steps of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In any case, selected steps of the method and system of the invention could be described as being performed by a data processor, such as a computing platform for executing a plurality of instructions.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only, and are presented in order to provide what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the invention may be embodied in practice.

In the drawings:

FIG. 1 is a simplified diagram showing a traditional roulette wheel;

FIG. 2 is a simplified block diagram showing a system for playing multiple wheel roulette according to a first preferred embodiment of the present invention;

FIG. 3 is a simplified flow chart showing a procedure for playing a multiple wheel roulette game according to a first preferred embodiment of the present invention;

FIG. 4 is a simplified block diagram illustrating a system for playing multiple wheel roulette according to a second preferred embodiment of the present invention; and

FIG. 5 is a simplified block diagram illustrating a mechanical implementation of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present embodiments comprise a system and method for playing multiple wheel roulette in which a final result on which players place bets is an accumulated or otherwise combined total taken from the results of the different wheels.

In a further aspect the present embodiments provide a game with a plurality of possible outcomes and a non-linear probability curve defining the likelihood of the different outcomes. More specifically but not exclusively the non-linear probability curve is a bell curve or a Gaussian distribution or like statistical distribution about a median or mode.

The system and method may be played using multiple standard roulette wheels used together or it may be played using a dedicated mechanical machine including the multiple wheels needed for the game or it may be played using an electronic slot machine or it may be played over the Internet or like electronic network, for example using a server-client type connection.

The principles and operation of a multiple wheel roulette system or method according to the present invention may be better understood with reference to the drawings and accompanying description.

Before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting.

Reference is now made to FIG. 1, which illustrates a standard roulette wheel 10. The roulette wheel has 37 or 38 different stopping positions, each associated with a different number and one of two colors, and players bet on the different stopping positions in various ways. The highest odds available in the game are 36/1 or 37/1 depending on the table and thus the maximum win for any given bet is limited.

Reference is now made to FIG. 2, which is a simplified diagram illustrating a device 12 for playing a game of chance, in this case roulette. The device has several 10 roulette wheels 14.1 . . . 14.n and each wheel has some kind of indicator for showing the winning or stopping position. In the traditional roulette wheel a small ball travels around the wheel as it spins and the number that the ball rests on at the end of the spin is the determined stopping position. In the device of the present embodiments it is possible to have several horizontal wheels each working the same way or the wheels can be placed vertically, in which case the stopping position is simply a particular angular position defined by the device, see marked positions 16.1 . . . 16.n shown on the device. Alternatively the wheels may in fact be virtual wheels in which case the stopping position is determined by a software algorithm. In addition to the wheels there is an accumulator 18 which adds up the numbers from each of the stopping positions 16.1 . . . 16.n and outputs a sum of the results of the roulette wheels 14.1 . . . 14.n.

The number of roulette wheels can be selected according to the desired maximum odds it is intended to provide. Thus a game provider wishing to provide odds of a million to one so that he can advertise a million dollar maximum prize, would select an appropriately large number of roulette wheels. A typical application would include say five roulette wheels, although herein, at least partial probability tables are given for all possibilities between two and nine wheels.

Reference is now made to FIG. 3, which is a simplified flow chart illustrating a method of playing roulette using a plurality of wheels having discrete stopping positions, in short roulette wheels or virtual implementations thereof. Each stopping position provides a discernable result. The method comprises a stage S1 of first of all receiving the different players' predictions of an accumulated result for the plurality of wheels. There is a further stage S2 of operating the wheels to cause each wheel to reach one of its stopping positions at random, thereby to give one of the discernable results. Preferably a single action on the part of the operator is able to initiate all of the wheels simultaneously. In a virtual device this is relatively straightforward. In a mechanical device some kind of mechanical linkage has to be provided which starts all of the wheels together with a single motion. Preferably, however the energy transferred is not identical for all wheels so that the relative behavior between the wheels is also random.

It is of course appreciated that stages one and two need not be successive. It is common in roulette to continue to place bets up to a certain point in the spin of the wheel.

Once the wheels have settled at their stopping positions then the numbers of the different stopping positions are taken in stage S3 and used in calculating an accumulated result in stage S4.

In a final stage S5, the accumulated result is compared against the bets that have been placed and correct predictions are rewarded, as with any other game of roulette.

It is pointed out that as well as placing bets on the accumulated total, it is also possible to place bets on individual outcomes, for example will a three appear on any of the wheels, or will a three appear on any specific wheel.

Reference is now made to FIG. 4, which is a simplified block diagram illustrating a further preferred embodiment for playing multiple wheel roulette with accumulation according to a further preferred embodiment of the present invention. In FIG. 4, the multiple wheel roulette machine is implemented on server 20. The server 20 is connected via network 22 to remotely located users 24.1 . . . 24.n. Each user makes predictions or places bets over the network and the wheels spin. The accumulated number is then compared against the predictions and correct predictions are rewarded.

Reference is now made to FIG. 5, which illustrates a mechanical implementation of the present invention. Device 28 includes an accumulator 30 connected to a column 32 having five roulette wheels 34.1 . . . 34.5. A single spin action by the operator sets all of the wheels spinning but they come to rest independently. Preferably the stopping positions are electronically detected and the associated numbers added at the accumulator 30. The sum of the stopping positions is indicated at an output, thus screen 36 of accumulator 30.

It will be appreciated that for any given number of wheels, possible summation results range from zero to the number 36 multiplied by the number of wheels used. It will further be appreciated that sums towards the center of the range are more likely to occur since there are more combinations of stopping positions that give these results than there are for the sums at the extremities of the range. For example the summed result zero is highly improbable since there is only one way it can be achieved on the European formatted wheel, namely that each wheel stops on zero. However the median or mode result has a maximal number of combinations that will achieve it and hence the odds of such a summed result are correspondingly higher.

The importance of the above is that the summed roulette game as described here is very different from traditional roulette because the graph of the odds is essentially a bell curve, whereas with the traditional game it is a flat curve. This enables the game designer to offer different odds for different sums and thus advertise a maximum prize which is in fact extremely high, even though the overall chances of wins of some kind occurring is not that small.

As explained above, the idea of using multiple roulette wheels is to provide the possibility of predictions with lower odds, so that larger prizes can be paid. In the following tables, odds are given for different results using different numbers of wheels.

Tables 1 to 8 below represent the probabilities for the most likely outcomes when spinning a number of roulette wheels and calculating the sum of all the individual outcomes. For each number of wheels the Mode sum is given, indicated by shading, as well as the corresponding probability of occurrence. Also given are the probabilities of obtaining the five closest sums to the Mode, 5 on each side. It is noted that the probabilities for getting mirroring sums around the Mode are the same as the distribution is symmetric.

The calculations were carried out using a counting algorithm that works in a recursive fashion and counts the number of times each sum occurs when adding an additional roulette wheel. The probabilities are obtained by dividing the number of observations by the size of the population of possible results.

TABLE 1
2 roulettespopulation size = 37{circumflex over ( )}2 = 1369
Sum of
resultsnumber of observationsprobability
31320.023374726
32330.024105186
33340.024835646
34350.025566107
35360.026296567
36370.027027027
37360.026296567
38350.025566107
39340.024835646
40330.024105186
41320.023374726

TABLE 2
3 roulettespopulation size = 37{circumflex over ( )}3 = 50653
Sum of
resultsnumber of observationsprobability
4910020.019781652
5010110.019959331
5110180.020097526
5210230.020196237
5310260.020255464
5410270.020275206
5510260.020255464
5610230.020196237
5710180.020097526
5810110.019959331
5910020.019781652

TABLE 3
4 roulettespopulation size 37{circumflex over ( )}4 1874161
Sum of
resultsnumber of observationsprobability
67329160.017563059
68332190.017724731
69334600.017853322
70336360.017947231
71337440.018004857
72337810.018024599
73337440.018004857
74336360.017947231
75334600.017853322
76332190.017724731
77329160.017563059

TABLE 4
5 roulettespopulation size = 37{circumflex over ( )}5 = 69343957
Sum of
resultsnumber of observationsprobability
8511016510.015886763
8611092650.015996563
8711152150.016082367
8811194800.016143872
8911220450.016180862
9011229010.016193206
9111220450.016180862
9211194800.016143872
9311152150.016082367
9411092650.015996563
9511016510.015886763

TABLE 5
6 roulettespopulation size = 37{circumflex over ( )}6 = 2565726409
Sum of
resultsnumber of observationsprobability
103375235620.014624927
104377484870.014712592
105379243980.014781154
106380505780.014830333
107381265020.014859925
108381518470.014869803
109381265020.014859925
110380505780.014830333
111379243980.014781154
112377484870.014712592
113375235620.014624927

TABLE 6
7 roulettespopulation size = 37{circumflex over ( )}7 = 94931877133
Sum of
resultsnumber of observationsprobability
12112929038150.01361928
12212996012190.01368983
12313048325430.013744936
12413085811480.013784423
12513108350990.013808166
12613115872150.013816088
12713108350990.013808166
12813085811480.013784423
12913048325430.013744936
13012996012190.01368983
13112929038150.01361928

TABLE 7
8 roulettespopulation size = 37{circumflex over ( )}8 = 3.51248E+12
Sum of
resultsnumber of observationsprobability
139449475230240.012796523
140451536887400.012855218
141453146657520.012901048
142454299858720.012933879
143454993129200.012953617
144455224444690.012960202
145454993129200.012953617
146454299858720.012933879
147453146657520.012901048
148451536887400.012855218
149449475230240.012796523

TABLE 8
9 roulettespopulation size = 37{circumflex over ( )}9 = 1.29962E+14
Sum of
resultsnumber of observationsProbability
157 1.5734E+120.012106613
1581.57986E+120.012156363
1591.58491E+120.012195191
1601.58852E+120.012222999
1611.59069E+120.012239712
1621.59142E+120.012245288
1631.59069E+120.012239712
1641.58852E+120.012222999
1651.58491E+120.012195191
1661.57986E+120.012156363
167 1.5734E+120.012106613

TABLE 9
Complete Summed Results and corresponding
probabilities for the five wheel case.
p(sumx)sum(x)
1.44209E−080
7.21043E−081
2.16313E−072
 5.0473E−073
1.00946E−064
1.81703E−065
3.02838E−066
4.75889E−067
7.13833E−068
1.03109E−059
1.44353E−0510
1.96845E−0511
 2.6246E−0512
3.43217E−0513
4.41279E−0514
5.58953E−0515
6.98691E−0516
8.63089E−0517
0.00010548918
0.00012769719
0.00015323620
0.00018242421
0.00021559222
0.00025308623
0.00029526724
0.00034251 25
0.00039520426
0.00045375327
0.00051857428
0.00059010229
0.00066878230
0.00075507731
0.00084946132
0.00095242633
0.00106447634
0.00118613135
0.00131792336
0.00146032937
0.00161376738
0.00177859839
0.00195512440
0.00214359 41
0.00234418442
0.00255703643
0.00278221844
0.00301974445
0.00326957146
0.00353159847
0.00380566748
0.00409156149
0.00438900550
0.00469767 51
0.00501716452
0.00534704153
0.00568679754
0.00603586855
0.00639363656
0.00675942157
0.00713248958
0.00751204659
0.00789724260
0.00828716861
0.00868085762
0.00907728763
0.00947537564
0.00987398265
0.01027191266
0.01066790967
0.01106066168
0.01144879969
0.01183089470
0.01220546271
0.01257095872
0.01292578473
0.01326842474
0.01359745 75
0.01391152276
0.01420938577
0.01448987178
0.01475189879
0.01499447280
0.01521668381
0.01541771 82
0.01559681783
0.01575335584
0.01588676385
0.01599656386
0.01608236787
0.01614387288
0.01618086289
0.01619320690
0.01618086291
0.01614387292
0.01608236793
0.01599656394
0.01588676395
0.01575335596
0.01559681797
0.01541771 98
0.01521668399
0.014994472100
0.014751898101
0.014489871102
0.014209385103
0.013911522104
0.01359745 105
0.013268424106
0.012925784107
0.012570958108
0.012205462109
0.011830894110
0.011448799111
0.011060661112
0.010667909113
0.010271912114
0.009873982115
0.009475375116
0.009077287117
0.008680857118
0.008287168119
0.007897242120
0.007512046121
0.007132489122
0.006759421123
0.006393636124
0.006035868125
0.005686797126
0.005347041127
0.005017164128
0.00469767 129
0.004389005130
0.004091561131
0.003805667132
0.003531598133
0.003269571134
0.003019744135
0.002782218136
0.002557036137
0.002344184138
0.00214359 139
0.001955124140
0.001778598141
0.001613767142
0.001460329143
0.001317923144
0.001186131145
0.001064476146
0.000952426147
0.000849461148
0.000755077149
0.000668782150
0.000590102151
0.000518574152
0.000453753153
0.000395204154
0.00034251 155
0.000295267156
0.000253086157
0.000215592158
0.000182424159
0.000153236160
0.000127697161
0.000105489162
8.63089E−05163
6.98691E−05164
5.58953E−05165
4.41279E−05166
3.43217E−05167
 2.6246E−05168
1.96845E−05169
1.44353E−05170
1.03109E−05171
7.13833E−06172
4.75889E−06173
3.02838E−06174
1.81703E−06175
1.00946E−06176
 5.0473E−07177
2.16313E−07178
7.21043E−08179
1.44209E−08180

It is clear from table 9 that the best odds available to the player are for the sums about the mode. The game designer is able to offer a flat level of odds over the entire table or he can offer a curve of odds, thus offering a very high maximum prize for the sums towards the ends of the table.

TABLE 10
Individual Results The US Wheel
The
probs#s012345
10.9471-364.04E−073.63E−050.0013090.0235530.2119790.763123
20.6321-240.0067880.058180.1994750.3419570.2931060.100494
30.4741-180.0403860.1817370.3271270.2944150.1324870.023848
40.02610.8751660.1182660.0063930.0001732.33E−061.26E−08
50.05320.7631230.2119790.0235530.0013093.63E−054.04E−07
60.07930.6628610.2840830.04870.0041740.0001793.07E−06
70.10540.5734250.3373090.0793670.0093370.0005491.29E−05
80.13250.4939140.3741780.1133870.017180.0013023.94E−05
90.15860.4234790.3970120.1488790.0279150.0026179.81E−05
100.18470.3613190.4079410.1842310.0416010.0046970.000212
110.21180.3066820.4089090.2180850.0581560.0077540.000414
120.23790.2588640.4016860.2493220.0773760.0120070.000745
130.263100.2172060.3878680.2770490.0989460.0176690.001262
140.289110.1810930.3688920.3005790.1224580.0249450.002033
150.316120.1499510.346040.3194220.1474250.0340210.00314

TABLE 11
Individual Results The European Wheel
The
probs#s012345
10.9731-361.44E−082.6E−060.0001870.0067280.1211080.871975
20.6491-240.0053540.0494250.1824920.3369080.3109920.114828
30.4861-180.0357070.1691410.3204770.303610.1438150.027249
40.02710.8719750.1211080.0067280.0001872.6E−061.44E−08
50.05420.7574110.2164030.0247320.0014134.04E−054.61E−07
60.08130.6552180.2890670.0510120.0045010.0001993.5E−06
70.10840.5643660.342040.0829190.0100510.0006091.48E−05
80.13550.4838840.3780340.1181360.0184590.0014424.51E−05
90.16260.4128570.3995390.154660.0299340.0028970.000112
100.18970.3504270.4088320.1907880.0445170.0051940.000242
110.21680.2957890.4079840.2250950.0620950.0085650.000473
120.24390.2481880.3988740.2564190.082420.0132460.000852
130.270100.2069240.3831920.2836460.1051280.0194680.001442
140.297110.171340.3624490.3066880.1297530.0274480.002322
150.324120.1408290.3379890.324470.1557450.0373790.003588

Tables 10 and 11 show for the two separate cases of the European and the US format of roulette wheel the probability that a given number from 1 to 36 will appear on no wheels, on exactly one wheel etc up to five wheels. The second row shows the chances of a number from 1 to 24 will appear on no wheels, on exactly one wheel etc up to five wheels. The third row shows the same calculation for numbers from 1 to 18 and then the remaining lines are for individual numbers.

Winning Table 5 Roulettes

TABLE 12
012345
1/10000000100001/20001/1001/7No1
1/1501/181/51/31/31/7
1/251/51/2.51/31/61/33
No11/71/1201/40001/300001/10000000
No11/41/361/5001/200001/1500000
No11/31/171/2001/40001/200000
1/1.51/2.51/101/901/10001/50000
1/1.51/21/7.51/491/5001/18000
1/21/21/61/301/3001/5000
1/2.51/21/51/201/1501/2500
1/31/21/41/141/1001/1500
1/3.51/21/3.51/111/501/1000
1/41/2.51/31/91/451/600
1/51/2.51/31/71/301/380
1/61/2.51/2.51/61/241/250

It is expected that during the life of this patent many relevant random devices and systems and ways of implementing random selections will be developed and the concepts herein are intended to include all such new technologies a priori.

It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable subcombination.

Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention.