1. Field of the Invention
The invention relates in general to lottery game methods. More particularly, the present invention relates to a multi-matrix lottery game method in which matches are credited across different matrices.
2. Description of the Related Art
It is known in lottery games to utilize a selection process defined by three parameters comprising first a set of indicia; next, the game player's selection from the set of game indicia, and last the lottery authority's selection from the set of game indicia. This is the structure upon which most known types of lottery games are based. Some lottery games use more than one selection process in which the prizes awarded are based on the how the outcomes from the individual processes combine, but the outcomes for the individual processes are independent of one another.
Referring now to the drawings and the description below, many lottery games can be expressed in terms of “matrices.” As mathematically known, a matrix is a triple, (x, y, z), where x represents the number of objects selected by the player, y the number selected, or “drawn,” by the lottery authority, and z is the number of objects from which the player and lottery authority are making selections. Prizes are based on the number of matches between the player's and the lottery authority's respective selections. For example, consider a lottery game in which a player selects six numbers in the range of from 1 to 49, the lottery authority selects six numbers in the range of from 1 to 49, and prizes are based on the number of matches between the player's and the lottery authority's respective selections. This scenario could be described as a (6, 6, 49) matrix. Note, however, that the x and y in the matrices need not be the same. For example, in Keno-style game methods, the lottery authority draws 20 out of 80 numbers, and the game player may choose the size of their selection, ranging from 1 to 10 numbers. If the player chooses 6 numbers out of 80, for example, this game could be described as a (6, 20, 80) matrix.
There are also more complex “multi-matrix” lottery games, wherein the player and lottery authority make selections from more than one set of objects. A well-known example is MEGA MILLIONS®, a large-jackpot multi-state lottery game played in selected lottery jurisdictions within the United States. In MEGA MILLIONS®, players select five numbers in a range of from 1 to 52, the first set of objects, and one number in a range of from 1 to 52, the second set of numbers. Likewise, the lottery authority draws five numbers in a range of from 1 to 52, the first set, and one number in a range of from 1 to 52, the second set of numbers. MEGA MILLIONS® can thus be described as a two-matrix game, the first matrix being (5, 5, 52) and the second matrix being (1, 1, 52). Matches are tallied for the (5, 5, 52) matrix, and matches are tallied for the (1, 1, 52) matrix. Prizes are based on the number of matches for both matrices. For example, a player is awarded $5,000 according to the prize table of
“Numbers games,” e.g. lottery games based on permutations of three or four digits, can technically be considered multi-matrix games. For example, a three-digit game is composed of three identical matrices, (1, 1, 10). A player wins a “straight” bet if he matches his number with the lottery authority's for each matrix. A player wins a “box” bet if there is a one-to-one association between the player's numbers and the three matrices such that the player's numbers match those produced by the associated matrices. For example, suppose the player's selection is 1-2-2 and the lottery authority's draw is 2-1-2. Associating the player's 1st number with the 2nd matrix, the player's 2nd number with the 1st matrix and the player's 3rd number with the 3rd matrix, there are three matches.
Note that for a box bet the association between the player's selection and the matrices must be one-to-one. For example, suppose that the player's bet is 1-2-2 and the lottery authority's draw is 1-2-1. Associating the player's 1st number with the 1st matrix, the player's 2nd number with the 2nd matrix and the player's 3rd number with the 2nd matrix, would result in three matches. However, it is disallowed that both the player's 2nd and 3rd numbers be associated with the 2nd matrix.
In a multi-matrix game, such as MEGA MILLIONS®, a match is determined by comparing player indicia to lottery authority indicia within the same matrix. The number of matches is determined for each matrix separately and prizes are based on the resulting numbers of matches. The present invention allows for matches determined by comparing player indicia with regard to one matrix to the lottery authority indicia with regard to a different matrix. The matrices may have different parameterizations. This may allow for a more interesting play experience and more appealing prizes. Thus, it is to a multi-matrix lottery games with more interesting play characteristics and more appealing prizes, the present invention is primarily directed.
A multi-matrix lottery game is disclosed for which matches are allowed between a player's selection with regard to one matrix and the lottery authority's selection with regard to a different matrix. The matrices may have different parameters.
In one embodiment, there is disclosed a lottery game method. The lottery game method includes the player receiving a first plurality of indicia selected from a first set of indicia, the player receiving a second at least one indicia selected from a second set of indicia, the lottery authority receiving a first plurality of indicia selected from the first set of indicia, the lottery authority receiving a second at least one indicia selected from the second set of indicia, determining a first number of matches by comparing the player's first plurality of indicia with the lottery authority's first plurality of indicia, determining a second number of matches by comparing the player's second at least one indicia with the lottery authority's first plurality of indicia, determining a third number of matches by comparing the player's first plurality of indicia with the lottery authority's second at least one indicia, determining a fourth number of matches by comparing the player's second at least one indicia with the lottery authority's second at least one indicia, and awarding a prize based on these first, second, third, and fourth number of matches.
In another embodiment, there is provided a system for playing a lottery game. The system includes a communication network, at least one gaming machine in communication with the communication network, and a server in communication with the at least one gaming machine through the communication network, wherein the server hosting a lottery game. The at least one gaming machine being capable of receiving from a player a first plurality of indicia selected from a first set of indicia, receiving from the player a second at least one indicia selected from a second set of indicia, and transmitting information on the first plurality of indicia and the at least one second indicia to the server via the communication network. The server being capable of receiving from the lottery authority a first plurality of indicia selected from the first set of indicia, receiving from the lottery authority a second at least one indicia selected from the second set of indicia, determining a first number of matches by comparing the first plurality of indicia received from the player with the first plurality of indicia received from the lottery authority, determining a second number of matches by comparing the second at least one of indicia received from the player with the first plurality of indicia received from the lottery authority, determining a third number of matches by comparing the first plurality of indicia received from the player with the second at least one indicia received from the lottery authority, and determining a fourth number of matches by comparing the second at least one indicia received from the player with the second at least one indicia received from the lottery authority.
In one embodiment the present invention is a multi-matrix game for which matches are allowed between a player's selection from one matrix and the lottery authority's selection from a different matrix. Moreover, this invention differs from a “box” bet in at least three ways: at least one matrix in this game is non-trivial, i.e., x and y in the triple (x, y, z) are not both one for at least one of the matrices; the matrices do not have to be symmetric, i.e., if (x1, y1, z1) and (x2, Y2, Z2) are both matrices for the game, it is not required that (x1, y1, z1)=(x2, y2, z2); and there does not have to be a one-to-one association between the player's selections and the matrices for which comparisons are made to the lottery authority's selections. One exemplary ticket for a multi-matrix game is shown in
The following embodiment is an extension that may be used with the current MEGA MILLIONS® game. The extension game is known to those skilled in the art as an add-on game to a base or parent game. As discussed above, MEGA MILLIONS® is based on two matrices of (5, 5, 52) and (1, 2, 52).
For example, consider the player's and the lottery authority's selections as illustrated in
An exemplary prize table for this game extension game is illustrated in
Another example of the game method is shown
With regard to this embodiment of the present invention, at least one of the matrices is non-trivial, i.e., for the first matrix, (5, 5, 52) more than one number is selected by both the player and the lottery. The matrices are not symmetric as the two matrices are different from one another, i.e., (5, 5, 52)≠(1, 2, 52). The association between the matrices is not one-to-one. The game player is allowed matches between his selection for the 1st matrix with the lottery authority's selection for both the 1st and 2nd matrices. Similarly, the game player is allowed matches between his selection for the 2nd matrix with the lottery authority's selection for both the 1st and 2nd matrices.
In an alternative embodiment, the lottery authority may institute one prize according to the number of matches between a player's selection for the 1st matrix and the lottery authority's selection for both the 1st and 2nd matrices, and a different prize according to the number of matches between the player's selection for the 2nd matrix and the lottery authority's selection for both the 1st and 2nd matrices.
The computation of the probabilities for this embodiment is now described. It is noted that there are two basic cases for a player selection as it relates to this invention: (1) the “distinct” case, wherein the number the player selected for the 2nd matrix is distinct from the 5 numbers the player selected for the 1st matrix, and (2) the “indistinct” case, wherein the number the player selected for the 2nd matrix is one of the 5 numbers the player selected for the 1st matrix. For example, the player selection of Matrix 1: 1, 2, 3, 4, 5, Matrix 2: 6, would be a distinct case, as the 6 is not included among the numbers the player selected from Matrix 1. As another example, consider the player selection of Matrix 1: 1, 2, 3, 4, 5, Matrix 2: 5. This would be an indistinct case, as 5 is one of the numbers the player selected for Matrix 1. The probabilities for these two cases are different and must therefore be computed separately.
First, it is computed the probabilities for the distinct case as it is the more straightforward. Observe that the lottery authority selects either 5 or 6 distinct numbers depending on whether or not the number drawn from the 2nd matrix is one of the numbers drawn from the 1st matrix. Moreover, the probability that the lottery authority's selection comprises five distinct numbers is 5/52 while the probability that the lottery authority's selection comprises six distinct numbers is 47/52. The probabilities for the number of matches can be computed using the hypergeometric distribution, as known. For example, the probability of 6 matches is:
47/52×hypgeomdist(6, 6, 6, 52)=0.00000004439645680758
where hypgeomdist is the hypergeometric distribution with the standard parameters. The probability of 5 matches is:
47/52×hypgeomdist(5, 6, 6, 52)+5/52×hypgeomdist(5,5,5,52)=0.00001247540436292860.
The other probabilities for the distinct case are computed similarly and are displayed in the “distinct” column in
To compute the probabilities for the indistinct case, consider 4 matches as an illustrative case. It is useful to note that for the indistinct case one of the player's numbers for the 1st matrix must be the player's number for the 2nd matrix. Four matches can be attained in two ways: (1) 4 of the player's numbers for the 1st matrix match the lottery's numbers for the 1st and/or 2nd matrix, but these 4 numbers do not include the player's number for the 2nd matrix, and (2) 3 of the player's numbers for the 1st matrix match the lottery authority's numbers for the 1st and/or 2nd matrix, and these 3 numbers include the player's number for the 2nd matrix, which would be an additional match. The probability for 4 matches can be computed by computing and adding the probabilities for these two cases. Thus the probability of 4 matches is:
1/5×[5/52×hypgeomdist(4,5,5,52)+47/52×hypgeomdist(4,6,6,52)]+4/5×[5/52×hypgeomdist(3,5,5,52)+47/52×hypgeomdist(3,6,6,52)]=0.00460902556288788000.
The other probabilities for the indistinct case are computed similarly and displayed in the “indistinct” column in
As the probabilities for indistinct and distinct selections are different, a prize structure wherein prizes are awarded based on the number of matches may produce a higher return for one type of selection than the other. For example, in
One remedy is for a lottery terminal to quick-pick the player selection for the 2nd matrix, i.e., the player selection is generated by a random number generator. In this case, the player has a 47 out of 52 chance of getting a distinct selection and 5 out of 52 chance of getting an indistinct selection. The game is fair to all players as a player has no control over whether or not his play is distinct or indistinct. Nonetheless, some tickets would be worth more than others by chance. For this reason it is recommended that the game be non-cancelable.
The present invention can be described economically in terms of cross-matches. A “cross-match” is defined as a match between a player's first set of numbers and the lottery's at least one second number or a match between a player's at least one second number number and the lottery's first set of numbers. The player is awarded a number of “cross-matches” which are incorporated into the prize structure.
We disclose such an embodiment: The price is $2 for two plays. The game is based on two matrices with different parameters: the 1st matrix's parameters are 4/4/31 and the 2nd matrix's parameters are 1/1/31. For convenience, we refer to the 1st matrix as “regular” and the 2nd matrix as “special” (e.g., each play and draw is composed of 4 “regular” numbers and 1 “special” number). Also, plays are distinguished by types: “Type A” and “Type B.” For a Type A play, the special number does not repeat any of the regular numbers (e.g., regular numbers: 01, 02, 03, 04, special number: 05). For a Type B play, the special number repeats one of the regular numbers (e.g., regular numbers: 01, 02, 03, 04, special number: 03, the special number repeats a regular number). This game without (or before) consideration of the cross-matches is referred to as the “base game.”
An exemplary playslip is in
An exemplary corresponding ticket is in
The top prize is a progressive, pari-mutuel jackpot that starts at $50,000 and increments a minimum of $5,000 per draw. The jackpot is won by matching the 4 regular numbers and the 1 special number with the lottery draw. 20.0% of the sales are reserved for the jackpot. (A certain level of sales is required to support this jackpot scheme, e.g., $50,000 sales per draw is sufficient.)
Prizes for the lower tiers and their associated inverse probabilities are described in
Example: The lottery draws 02, 05, 17, 25 for the regular numbers and 19 for the special number. The player's ticket is as in
For the 1st play, 2 regular numbers (02 and 05) match 2 of the lottery's regular numbers. The special number for the 1st play, 31, does not match the lottery's special number, 19. As the player's outcome is 2 regular matches and 0 special matches he is awarded $2 by the prize table in
For the 2nd play, 2 regular numbers (17 and 25), match 2 of the lottery's regular numbers. Also, the special number (18) does not match the lottery's special number (19). As the player's outcome is 2 regular matches and 0 special matches he is awarded $2 by the prize table in
Example: The lottery draws 02, 05, 19, 31 for the regular numbers and 02 as the special number. The player's ticket is as in
For the 1st play, none of the player's regular numbers match any of the lottery's regular numbers. Nor does the player's special number (11) match the lottery's special number, 02. Nor are there any cross-matches. This play does not win a prize for the 1st play.
For the 2nd play, 3 of the regular numbers (02, 19 and 31) match 3 of the lottery's regular numbers. The special number (31) does not match the lottery's special number (02). As the player's outcome is 3 regular matches and 0 special matches he is awarded $5 by the prize table in
Those skilled in the art of Mathematics can confirm that this embodiment pays out 62.3% (which includes 20.0% for the jackpot) and has an overall win rate of 1 in 7.4.
It should be noted that this game exhibits short term volatility. The lottery's special number repeats one of its regular numbers about 1 in 7.75 draws. When this happens, the payout is on average 111.5%, vs. 55.0% for other draws.
Another variation on this embodiment is to incorporate set prizes based on cross-matches. For example, in the above embodiment, the prize for 2 cross-matches could be revised to be the greater of $5 and the multiplier (i.e., whatever value is obtained by applying the multiplier, which could be $0). This enhancement would increase the overall win frequency to 1 in 6.2 (as opposed to 1 in 7.4) and the payout to 69.3% (as opposed to 62.3%).
To elaborate on design details, it is recalled that in the above embodiment it is required that the two plays be of different types: Type A and Type B. This is done so that the value of a ticket is uniform. This discourages retailer theft as all tickets are of equal value. Also, it allows for tickets to be non-cancelable as no ticket has an advantage over another.
Also, it is recalled that in the above embodiment the player is allowed to select the regular numbers for the 1st play (e.g. on the playslip in
Another embodiment is described that is conceived to be an enhancement of Embodiment 1 for a higher price. It may be run concurrently with Embodiment 1 using the same draw.
Embodiment 2: The player pays $5 for 4 plays. The base game prize table is the same as for the above disclosed embodiment, in
Those skilled in the art of Mathematics can confirm that the probabilities and other calculations in this description and in the related figures, whether explicitly mentioned in the description or not, are correct.
The invention can be based on a standalone gaming machine or a server. A standalone gaming device may include a display unit, a scanning unit (also known as a player input device) for scanning play slips containing player selection, and a ticket issuing unit for issuing tickets to players. The gaming device has a controller with a random number generator capable of performing quick picks for the player. The controller also takes player bets from the scanning device and issues a ticket to the player. After issuing the ticket, the controller generates a set of winning numbers, and determines if the player has a winning ticket according to the predefined rules. The gaming device may also be connected to a server as illustrated in
In the context of
While the invention has been particularly shown and described with reference to one embodiment thereof, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the spirit and scope of the present invention as set forth in the following claims. Though, the method in
This application claims the benefit of U.S. Provisional Application No. 60/641,969, “Multi-Matrix Lottery”, filed on Jan. 7, 2005, and U.S. Provisional Application No. 60/722,826, “Lottery Game Having Enhanced Winnings with Predefined Threshold”, filed on Sep. 30, 2005, the entirety of all of which is hereby incorporated herein by this reference.
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