Abstract:
A set of N game dice, each of the N dice having at least N faces with each of N faces of each die bearing one of a group of N 2  design markings. The group of N 2  design markings is formed by the combination of each of N values of a first attribute series with each of N values of a second attribute series. The N 2  design markings are divided into N subgroups such that each attribute value of each attribute series comprises only one design marking in each of the subgroups. The N design markings of each subgroup are borne by a multiple of N faces of a different die. Each design marking is borne by the same multiple of faces.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of provisional patent application Ser. No. 61/352,764, filed Jun. 8, 2010, by the present inventor. 
     
    
     BACKGROUND 
     Prior Art 
       [0002]    The following is a tabulation of some prior art that presently appears relevant: 
       U.S. Patents 
       [0003]      
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 U.S. Pat. No. 
                 Issue Date 
                 Patentee 
               
               
                   
                   
               
             
             
               
                   
                 4,258,919 
                 1981 Mar. 31 
                 Martelli 
               
               
                   
                 4,436,306 
                 1984 Mar. 13 
                 Sanders 
               
               
                   
                 5,125,660 
                 1992 Jun. 30 
                 Stahl 
               
               
                   
                 5,169,148 
                 1992 Dec. 08 
                 Wheeler 
               
               
                   
                 7,871,077 B2 
                 2011 Jan. 18 
                 Culvert 
               
               
                   
                 6,764,075 B2 
                 2004 Jul. 20 
                 Nigale 
               
               
                   
                 4,585,232 
                 1986 Apr. 29 
                 Sheppard and Darnell 
               
               
                   
                 6,659,868 B2 
                 2003 Dec. 09 
                 Stern 
               
               
                   
                 4,930,788 
                 1990 Jun. 05 
                 Roccanova 
               
               
                   
                 5,249,808 
                 1993 Oct. 05 
                 Batté 
               
               
                   
                 4,312,508 
                 1982 Jan. 26 
                 Wood 
               
               
                   
                 5,364,101 
                 1994 Nov. 15 
                 Spooner and Spooner 
               
               
                   
                   
               
             
          
         
       
     
         [0004]    Dice have often been used as elements of games. Such games take many forms, including those where the dice are elements of a stand-alone dice game and others where, for example, the dice are one element of a game consisting of many elements. 
         [0005]    Dice have usually been used to randomly generate outcomes for use in a game by throwing or rolling the dice onto a surface. The use of dice for this purpose is so familiar to game players that many computer and video games provide the digital equivalent of rolling dice. 
         [0006]    Decks of playing cards are also commonly used to randomly generate outcomes for use in games. There is a significant difference in the nature of the probability distributions of the outcomes between rolling dice and dealing cards. Each card in a deck and, equivalently, each die face in a set of dice is a possible outcome. When a card is dealt from a deck, its outcome is removed from the set of remaining possible outcomes. When one die from a dice set is rolled, the upper horizontal face presents the outcome. However, not only is this outcome removed from the set of remaining possible outcomes, but so are the potential outcomes present on the other faces of the rolled die. This physical difference in how the outcomes are grouped and generated for dice on the one hand and cards on the other is the source for the difference in the nature of the probability distributions or statistics of cards and dice. 
         [0007]    Playing cards and the faces of dice have design markings or indicia that convey information relevant to the various games. These design markings typically have one or more attributes. The design markings on conventional dice faces have one attribute type: the number of dots. For conventional dice the series of attribute values or elements is R={one dot, two dots, three dots, four dots, five dots, six dots}. Conventional playing cards, often used for the game of poker, having design markings with two attribute types: rank and suit. For such a deck of cards, the series of attribute values for rank is R={A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2} and the series of attribute values for suit is S={spade, heart, clubs, diamond}. The familiar playing card design markings are formed with a value selected from each of the two attribute series, rank and suit. Forming every possible combination of the thirteen rank attribute values with the four suit attribute values results in the familiar set of fifty-two different design markings. 
         [0008]    Conventional dice are cubical blocks bearing a pattern of dots on each face to indicate a numerical value from one to six. As discussed, this single attribute of die face markings is to be contrasted with conventional playing cards that bear markings with two attribute types such as suit and rank or color and numerical value. The use of a single attribute limits the complexity and variety of games based on conventional dice compared to games based on conventional playing cards, where two attributes contribute to game play. 
         [0009]    A set of dice have an advantage over a deck of cards in that it is easier and quicker to generate new random outcomes. The set of dice only need to be rolled, where as a deck of cards needs to be shuffled prior to cards being dealt. This has prompted the creation of dice games that are analogs to familiar card games. 
         [0010]    In attempts to combine the advantages of cards and dice, prior art includes examples of incorporating a second attribute type into dice face design markings. Many of these examples are poker-related or best-hand dice games, which include the dice game Yacht and its variations. 
         [0011]    U.S. Pat. No. 4,258,919 to Martelli (1981) disclosed a set of five six-sided poker dice with design markings comprised of six ranks and five suits. The rank attribute values are distributed uniformly across the dice, in that each rank attribute value is present on one of the faces of each die, while the suit attribute values are not distributed in a uniform manner. A similar distribution of design markings, comprised of six numerical values and five colors, across five machine equivalent six-sided dice, is used in the Ultimate Yahtzee™ computer game (Hasbro, 1996). U.S. Pat. No. 4,436,306 to Sanders (1984) disclosed a set of five eight-sided Yacht dice with design markings comprised of eight numerical values and five colors. The numerical values are distributed uniformly across the dice, while the colors are not. U.S. Pat. No. 5,125,660 to Stahl (1992) disclosed a set of five six-sided poker dice with design markings comprised of seven rank values and four suit values on twenty-eight faces and ‘joker’ on the remaining two faces. In this example, neither the rank nor the suit attribute values are distributed uniformly. U.S. Pat. No. 5,169,148 to Wheeler (1992) disclosed a set of thirteen four-sided poker dice with design markings comprised of thirteen rank values and four suit values. In this example, the suit attribute values are distributed uniformly, while the rank attribute values are not. U.S. Pat. No. 7,871,077 B2 disclosed a set of nine six-sided poker dice with design markings comprised of thirteen rank values and four suit values on fifty-two die faces and ‘joker’ design marking on the two remaining die faces. In this example, neither the rank nor the suit attribute values are distributed uniformly. 
         [0012]    Phase 10™ Dice (Fundex Games, 2008) is an example of a dice game based on a non-poker card game. The dice set is comprised of ten six-sided dice with design markings comprised of eleven rank attribute values, numerical values one through ten and the letter W, and four color attribute values. Neither the rank nor the color attribute values are distributed uniformly. 
         [0013]    The prior art also has examples of dice sets where the die face design markings have more than a single attribute and the dice game is not related to a conventional card game. U.S. Pat. No. 6,764,075 B2 to Nigale (2004) discloses a game that uses a six-sided die with the six face design markings formed by every combination of two colors with three numerical values. U.S. Pat. No. 4,585,232 to Sheppard and Darnell (1986) disclosed a game the uses two six-sided dice with twelve die face design markings formed by every combination of three colors and four numerical values. The color attribute values and the numerical values are not distributed uniformly between the two dice. 
         [0014]    Also prevalent in the prior art are dice sets in which the die face design markings on each die are formed from a series of attribute values, such as numerical value or shape, and a single element of a second attribute series, such as color, is applied to all the faces of a given die. Examples are conventional dice in which the dice cubes are fabricated using plastics with different pigments. Such dice comprise elements of the game disclosed in U.S. Pat. No. 6,659,868 B2 to Stern (2003). Closely related is the example of the Qwirkle™ Cubes game (Mind Ware, 2009). In this example, the body of the dice are all the same color, each die bearing design markings of six shape values in a single color selected from a series of six colors. 
         [0015]    Of relevance are examples of dice sets in which the faces of each die have design markings comprised of a single different attribute type. U.S. Pat. No. 4,930,788 and U.S. Pat. No. U.S. Pat. No. 5,249,808 disclose games that have such dice as elements. 
         [0016]    U.S. Pat. No. 4,312,508 and U.S. Pat. No. 5,364,101 both disclose examples of dice in which a second attribute, such as color, is added to a first attribute, such as numerical value or alphabetic letter, in such a way that the number of different die face design markings is not increased. The second attribute serves to either break the first attribute series into groups or to provide additional visual distinction for the first attribute. 
       Disadvantages: 
       [0017]    One of the characteristics of a set of multiple conventional dice is that the distribution of potential outcomes is the same for any subset of the dice as it is for the whole set. For example, for a set of conventional dice, the fraction of potential outcomes, that is die faces, that show three dots, is the same, one sixth, regardless of how many dice are being considered. When using the two attribute dice of the prior art, rolling one or more dice from the set results in changing the distribution of the two attributes amongst the remaining potential outcomes. It is the non-uniform distribution of the values of at least one of the attributes amongst the dice of the prior art that causes this undesirable trait. In actual game play, this undesirable aspect will cause delays as the players evaluate what outcomes are possible. This degrades the advantage of quick play that dice games have over card games. 
         [0018]    Any of dual attribute dice sets of the prior art is designed for use in a specific game and is unsuitable to be used in a range of game types. For example, the poker dice of the prior art are unsuitable for the dice game analogs of trick-taking or card-shedding card games. 
       SUMMARY 
       [0019]    In accordance with one embodiment a dual attribute dice set comprises a set of N dice, each die with N faces, for a total of N 2  die faces in the set. A group of N 2  design markings is formed by combining each of N values of one attribute type with each of N values of a second attribute type. Each die face bears a different design marking that have been distributed among the dice such that each attribute value of each attribute type appears in only one of the N design markings on each die. 
       Advantages 
       [0020]    Accordingly several advantages of one or more aspects are as follows: to provide two attribute dice sets that may be used in a multitude of game types, that provide a balanced distribution of attribute values, leading to easier game state evaluation and, hence, quicker play. Other advantages of one or more aspects, such as the possibility of novel dice game types, will be apparent from a consideration of the drawings and ensuing description. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0021]      FIG. 1  is a representation of an embodiment in which the number of dice is six, the number of faces on each die is six, the first attribute is the number of dots, and the second attribute is the color of dots. 
           [0022]      FIG. 2  is a representation of an embodiment in which the number of dice is six, the number of faces on each die is six, the first attribute is rank (A, K, Q, J, 10, 9), and the second attribute is suit (club, spade, heart, diamond, crown, anchor). 
           [0023]      FIG. 3  is a representation of an embodiment in which the number of dice is six, the number of faces on each die is six, the first attribute is rank (A, K, Q, J, 10, 9), and the second attribute is colored suit (club and black design marking, spade and black design marking, heart and red design marking, diamond and red design marking, crown and blue design marking, anchor and blue design marking). 
           [0024]      FIG. 4  is a representation of an embodiment in which the number of dice is six, the number of faces on each die is six, the first attribute is numeric value (1, 2, 3, 4, 5, 6), and the second attribute is expression of numeric value (number of dots, English word, Arabic numeral, Roman numeral, Chinese numeral, binary). 
           [0025]      FIG. 5  is a representation of an embodiment in which the number of dice is four, the number of faces on each die is eight, the first attribute is numeral (1, 2, 3, 4), the second attribute is color (color A, color B, color C, color D), and each different design marking appears on two faces of the die bearing the design marking. 
           [0026]      FIG. 6  is a representation of an embodiment in which the number of dice is five, the number of faces on each die is six, the first attribute is symbol, the second attribute is color (color A, color B, color C, color D, color E), and one face of each die bears a common design marking. 
           [0027]      FIG. 7  is a representation of an embodiment in which the number of dice is four, the number of faces on each die is six, the first attribute is quantity of dots, the second attribute is color of dots, one face of each die bears a first common design marking, and a second face of each die bears a second common design marking. 
       
    
    
     DETAILED DESCRIPTION 
       [0028]      FIG. 1  shows a representation of a first embodiment. In this embodiment, the dice set consists of six dice. These dice have cubic shapes with six die faces. The first design marking attribute R is number of dots and the second design marking attribute S is color of dots. The first attribute values are R={one dot, two dots, three dots, four dots, five dots, six dots}, and the second attribute values are S={color A, color B, color C, color D, color E, color F}. From the six values of the first attribute series and the six values of the second attribute series, thirty-six different die face design markings are formed by combining one of the six values of the first attribute series with one of the six values of the second attribute series. These thirty-six different die face design markings are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, one dot of color A; on the second face, two dots of color B; on the third face, three dots of color C; on the fourth face, four dots of color D; on the fifth face, five dots of color E; and, on the sixth face, six dots of color F. The second die of the dice set bears the following design markings on its die faces: on the first face, one dot of color D; on the second face, two dots of color A; on the third face, three dots of color B; on the fourth face, four dots of color E; on the fifth face, five dots of color F; and, on the sixth face, six dots of color C. The third die of the dice set bears the following design markings on its die faces: on the first face, one dot of color E; on the second face, two dots of color D; on the third face, three dots of color A; on the fourth face, four dots of color F; on the fifth face, five dots of color C; and, on the sixth face, six dots of color B. The fourth die of the dice set bears the following design markings on its die faces: on the first face, one dot of color B; on the second face, two dots of color C; on the third face, three dots of color F; on the fourth face, four dots of color A; on the fifth face, five dots of color D; and, on the sixth face, six dots of color E. The fifth die of the dice set bears the following design markings on its die faces: on the first face, one dot of color C; on the second face, two dots of color F; on the third face, three dots of color E; on the fourth face, four dots of color B; on the fifth face, five dots of color A; and, on the sixth face, six dots of color D. The sixth die of the dice set bears the following design markings on its die faces: on the first face, one dot of color F; on the second face, two dots of color E; on the third face, three dots of color D; on the fourth face, four dots of color C; on the fifth face, five dots of color B; and, on the sixth face, six dots of color A. Colors A, B, C, D, E and F may be red, orange, yellow, green, blue and purple, respectively. 
         [0029]      FIG. 2  shows a representation of a second embodiment. In this embodiment, the dice set consists of six dice. These dice have cubic shapes with six die faces. The first design marking attribute R is rank and the second design marking attribute S is suit. The first attribute values are R={A, K, Q, J, 10, 9}, and the second attribute values are S={club, spade, heart, diamond, crown, anchor}. From the six values of the first attribute series and the six values of the second attribute series, thirty-six different die face design markings are formed by combining one of the six values of the first attribute series with one of the six values of the second attribute series. These thirty-six different die face design markings are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, A of clubs; on the second face, K of spades; on the third face, Q of crowns; on the fourth face, J of anchors; on the fifth face, 10 of hearts; and, on the sixth face, 9 of diamonds. The second die of the dice set bears the following design markings on its die faces: on the first face, A of spades; on the second face, K of clubs; on the third face, Q of anchors; on the fourth face, J of crowns; on the fifth face, 10 of diamonds; and, on the sixth face, 9 of hearts. The third die of the dice set bears the following design markings on its die faces: on the first face, A of hearts; on the second face, K of diamonds; on the third face, Q of clubs; on the fourth face, J of spades; on the fifth face, 10 of crowns; and, on the sixth face, 9 of anchors. The fourth die of the dice set bears the following design markings on its die faces: on the first face, A of diamonds; on the second face, K of hearts; on the third face, Q of spades; on the fourth face, J of clubs; on the fifth face, 10 of anchors; and, on the sixth face, 9 of crowns. The fifth die of the dice set bears the following design markings on its die faces: on the first face, A of crowns; on the second face, K of anchors; on the third face, Q of hearts; on the fourth face, J of diamonds; on the fifth face, 10 of clubs; and, on the sixth face, 9 of spades. The sixth die of the dice set bears the following design markings on its die faces: on the first face, A of anchors; on the second face, K of crowns; on the third face, Q of diamonds; on the fourth face, J of hearts; on the fifth face, 10 of spades; and, on the sixth face, 9 of clubs. 
         [0030]      FIG. 3  shows a representation of a third embodiment. In this embodiment, the dice set consists of six dice. These dice have cubic shapes with six die faces. The first design marking attribute R is rank and the second design marking attribute S is colored suit. The first attribute values are R={A, K, Q, J, 10, 9}, and the second attribute values are S={club and black design marking, spade and black design marking, heart and red design marking, diamond and red design marking, crown and blue design marking, anchor and blue design marking}. From the six values of the first attribute series and the six values of the second attribute series, thirty-six different die face design markings are formed by combining one of the six values of the first attribute series with one of the six values of the second attribute series. These thirty-six different die face design markings are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, black A of clubs; on the second face, black K of spades; on the third face, blue Q of crowns; on the fourth face, blue J of anchors; on the fifth face, red 10 of hearts; and, on the sixth face, red 9 of diamonds. The second die of the dice set bears the following design markings on its die faces: on the first face, black A of spades; on the second face, black K of clubs; on the third face, blue Q of anchors; on the fourth face, blue J of crowns; on the fifth face, red 10 of diamonds; and, on the sixth face, red 9 of hearts. The third die of the dice set bears the following design markings on its die faces: on the first face, red A of hearts; on the second face, red K of diamonds; on the third face, black Q of clubs; on the fourth face, black J of spades; on the fifth face, blue 10 of crowns; and, on the sixth face, blue 9 of anchors. The fourth die of the dice set bears the following design markings on its die faces: on the first face, red A of diamonds; on the second face, red K of hearts; on the third face, black Q of spades; on the fourth face, black J of clubs; on the fifth face, blue 10 of anchors; and, on the sixth face, blue 9 of crowns. The fifth die of the dice set bears the following design markings on its die faces: on the first face, blue A of crowns; on the second face, blue K of anchors; on the third face, red Q of hearts; on the fourth face, red J of diamonds; on the fifth face, black 10 of clubs; and, on the sixth face, black 9 of spades. The sixth die of the dice set bears the following design markings on its die faces: on the first face, blue A of anchors; on the second face, blue K of crowns; on the third face, red Q of diamonds; on the fourth face, red J of hearts; on the fifth face, black 10 of spades; and, on the sixth face, black 9 of clubs. 
         [0031]      FIG. 4  shows a representation of a fourth embodiment. In this embodiment, the dice set consists of six dice. These dice have cubic shapes with six die faces. The first design marking attribute R is numeric value and the second design marking attribute S is expression of a numeric value. The first attribute values are R={1, 2, 3, 4, 5, 6}, and the second attribute values are S={number of dots, English word, Arabic numeral, Roman numeral, Chinese numeral, binary}. From the six values of the first attribute series and the six values of the second attribute series, thirty-six different die face design markings are formed by combining one of the six values of the first attribute series with one of the six values of the second attribute series. These thirty-six different die face design markings are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, one dot; on the second face, the word ‘two’; on the third face, the Arabic numeral for three; on the fourth face, the Roman numeral for four; on the fifth face, the Chinese numeral for five; and, on the sixth face, the value six expressed in binary. The second die of the dice set bears the following design markings on its die faces: on the first face, the value one expressed in binary; on the second face, two dots; on the third face, the word ‘three’; on the fourth face, the Arabic numeral for four; on the fifth face, the Roman numeral for five; and, on the sixth face, the Chinese numeral for six. The third die of the dice set bears the following design markings on its die faces: on the first face, the Chinese numeral for one; on the second face, the value two expressed in binary; on the third face, three dots; on the fourth face, the word ‘four’; on the fifth face, the Arabic numeral for five; and, on the sixth face, the Roman numeral for six. The fourth die of the dice set bears the following design markings on its die faces: on the first face, the Roman numeral for one; on the second face, the Chinese numeral for two; on the third face, the value three expressed in binary; on the fourth face, four dots; on the fifth face, the word ‘five’; and, on the sixth face, the Arabic numeral for six. The fifth die of the dice set bears the following design markings on its die faces: on the first face, the Arabic numeral for one; on the second face, the Roman numeral for two; on the third face, the Chinese numeral for three; on the fourth face, the value four expressed in binary; on the fifth face, five dots; and, on the sixth face, the word ‘six’. The sixth die of the dice set bears the following design markings on its die faces: on the first face, the word ‘one’; on the second face, the Arabic numeral for two; on the third face, the Roman numeral for three; on the fourth face, the Chinese numeral for four; on the fifth face, the value five expressed as binary; and, on the sixth face, six dots. 
         [0032]      FIG. 5  shows a representation of a fifth embodiment. In this embodiment, the dice set consists of four dice. These dice are regular octahedrons with eight die faces. The first design marking attribute R is numeral and the second design marking attribute S is face color. The first attribute values are R={1, 2, 3, 4}, and the second attribute values are S={color A, color B, color C, color D}. From the four values of the first attribute series and the four values of the second attribute series, sixteen different die face design markings are formed by combining one of the four values of the first attribute series with one of the four values of the second attribute series. These sixteen different die face design markings are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first and sixth faces, numeral 1 on face of color A; on the second and fifth faces, numeral 2 on face of color B; on the third and eighth faces, numeral 3 on face of color C; and, on the fourth and seventh faces, numeral 4 on face of color D. The second die of the dice set bears the following design markings on its die faces: on the first and sixth faces, numeral 1 on face of color B; on the second and fifth faces, numeral 2 on face of color C; on the third and eighth faces, numeral 3 on face of color D; and, on the fourth and seventh faces, numeral 4 on face of color A. The third die of the dice set bears the following design markings on its die faces: on the first and sixth faces, numeral 1 on face of color C; on the second and fifth faces, numeral 2 on face of color D; on the third and eighth faces, numeral 3 on face of color A; and, on the fourth and seventh faces, numeral 4 on face of color B. The fourth die of the dice set bears the following design markings on its die faces: on the first and sixth faces, numeral 1 on face of color D; on the second and fifth faces, numeral 2 on face of color A; on the third and eighth faces, numeral 3 on face of color B; and, on the fourth and seventh faces, numeral 4 on face of color C. Colors A, B, C and D may be red, yellow, green, and blue, respectively. 
         [0033]      FIG. 6  shows a representation of a sixth embodiment. In this embodiment, the dice set consists of five dice. These dice have cubic shapes with six die faces. The first design marking attribute R is symbol shape and the second design marking attribute S is symbol color. The first attribute values are R={first shape, second shape, third shape, fourth shape, fifth shape}, and the second attribute values are S={color A, color B, color C, color D, color E}. From the five values of the first attribute series and the five values of the second attribute series, twenty-five different primary die face design markings are formed by combining one of the five values of the first attribute series with one of the five values of the second attribute series. These twenty-five different primary die face design markings and five instances of a common secondary die face marking, shield, are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, first shape of color A; on the second face, second shape of color E; on the third face, third shape of color D; on the fourth face, fourth shape of color C; on the fifth face, fifth shape of color B; and, on the sixth face, shield. The second die of the dice set bears the following design markings on its die faces: on the first face, first shape of color B; on the second face, second shape of color A; on the third face, third shape of color E; on the fourth face, fourth shape of color D; on the fifth face, fifth shape of color C; and, on the sixth face, shield. The third die of the dice set bears the following design markings on its die faces: on the first face, first shape of color C; on the second face, second shape of color B; on the third face, third shape of color A; on the fourth face, fourth shape of color E; on the fifth face, fifth shape of color D; and, on the sixth face, shield. The fourth die of the dice set bears the following design markings on its die faces: on the first face, first shape of color D; on the second face, second shape of color C; on the third face, third shape of color B; on the fourth face, fourth shape of color A; on the fifth face, fifth shape of color E; and, on the sixth face, shield. The fifth die of the dice set bears the following design markings on its die faces: on the first face, first shape of color E; on the second face, second shape of color D; on the third face, third shape of color C; on the fourth face, fourth shape of color B; on the fifth face, fifth shape of color A; and, on the sixth face, shield. Colors A, B, C, D and E may be red, yellow, green, blue and purple, respectively. 
         [0034]      FIG. 7  shows a representation of a seventh embodiment. In this embodiment, the dice set consists of four dice. These dice have cubic shapes with six die faces. The first design marking attribute R is number of dots and the second design marking attribute S is color of dots. The first attribute values are R={one dot, two dots, three dots, four dots}, and the second attribute values are S={color A, color B, color C, color D}. From the four values of the first attribute series and the four values of the second attribute series, sixteen different primary die face design markings are formed by combining one of the four values of the first attribute series with one of the four values of the second attribute series. These sixteen different primary die face design markings, four instances of a first common secondary die face marking, dollar symbol, and four instances of a second common secondary die face marking, skull and crossbones symbol, are distributed on the faces of the dice as follows. The first die of the dice set bears the following design markings on its die faces: on the first face, one dot of color A; on the second face, two dots of color B; on the third face, three dots of color C; on the fourth face, four dots of color D; on the fifth face, dollar symbol; and, on the sixth face, skull and crossbones symbol. The second die of the dice set bears the following design markings on its die faces: on the first face, one dot of color D; on the second face, two dots of color A; on the third face, three dots of color B; on the fourth face, four dots of color C; on the fifth face, dollar symbol; and, on the sixth face, skull and crossbones symbol. The third die of the dice set bears the following design markings on its die faces: on the first face, one dot of color C; on the second face, two dots of color D; on the third face, three dots of color A; on the fourth face, four dots of color B; on the fifth face, dollar symbol; and, on the sixth face, skull and crossbones symbol. The fourth die of the dice set bears the following design markings on its die faces: on the first face, one dot of color B; on the second face, two dots of color C; on the third face, three dots of color D; on the fourth face, four dots of color A; on the fifth face, dollar symbol; and, on the sixth face, skull and crossbones symbol. Colors A, B, C and D may be red, yellow, green, and blue, respectively. 
         [0035]    The dice sets of the first, second and third embodiments have the same functionality and may be used in poker-related or Yacht-like games. The dice may be rolled according to a variety of game rules. For example, the entire set of dice may be rolled on the first roll, and then subsets of the dice are selected for subsequent second and third rolls. The goal of these type of games would be to achieve the best poker-type hand, including straight flush, flush, straight, pairs, triples, four-of-a-kind, etc. When playing variations such as seven card stud and Texas hold-em, poker hands are evaluated based on the best five cards, so these dice games may analogously use ‘best five dice’ evaluation rules. 
         [0036]    These embodiments may also be used in dice games that mimic card-shedding games, such as crazy eights and Uno™ (Mattel). In such games, the dice would be rolled to form sequences in which adjacent dice share an attribute element, such as a color or numeric value. The goal of such games would be to assemble the longest possible sequences. 
         [0037]    Multiple sets of dice of the first, second and third embodiments may also be used in dice games that mimic trick-taking card games, such as Euchre or hearts. In such games, each player would have a set of dice. These dice sets may have another attribute, such as body color, so as to easily distinguish each players&#39; dice. These games may involve picking a trump suit and following suit during a trick. The highest ranking die, determined by the rules, would take each trick. The goal of such games is to take or avoid tricks or points. 
         [0038]    The fifth embodiment, with a smaller number of dice, may be used in simpler versions of the same games as the first, second and third embodiments. 
         [0039]    The dice set of the sixth embodiment may be combined with an additional two dice for a novel type of dice game. Each of the two additional six-sided dice would have face design markings formed from the values of each of the two attribute series. The first additional die would have the first attribute series, symbol shape, expressed in a neutral color, as the design markings. The second additional die would have simple face design markings to indicate the color values of the second attribute series. Both of the additional dice may have the same common face design marking, namely the shield. Rolling the two attribute series dice determines which face design markings of the dice set of the sixth embodiment represent positive points, and which represent negative points. The shield design markings may represent a neutral outcome, resulting in zero points. The goal of such a game would be to maximize the outcome point value of the rolled dice of the sixth embodiment in a certain number of rolls. 
         [0040]    The dice set of the seventh embodiment may be used for another novel type of dice game. Each player would have a dice set of this embodiment. These dice sets may have another attribute, such as body color, so as to easily distinguish each players&#39; dice. In turn, the players roll their dice one or more times to achieve the best result. The skull and crossbones may require players to add chips to a common bank, while the money symbol would allow players to take chips from this bank. The player with the best ‘hand’ formed by the colored dots would receive a bonus, such as chips equivalent to all players&#39; money symbols. The goal of such a game would be to have the most chips at the game&#39;s end. 
       RAMIFICATIONS AND SCOPE 
       [0041]    Accordingly, the reader will see that the dual attribute dice of the various embodiments may be used to provide balanced outcome statistics for a variety of dice games, including games that are analogs to best-hand or poker-like, card-shedding and trick-taking card games as well as novel types of dice games. 
         [0042]    Attribute types that may be used include, but are not limited to: playing card rank, color, playing card suit, numerical value, quantity, numeral, roman numeral, font, expression form, shape, symbol, language, and pattern. In addition to visual attribute types, an attribute series may be composed of any group of attribute values that the users recognize as having a logical connection. The dice set of the fourth embodiment is comprised of an attribute series for which the values are different means of expressing numerical values. 
         [0043]    The design markings incorporated into the several embodiments may be trademarked or copyrighted and the embodiments may be used as material for commercial promotion. A couple of examples serve to illustrate the range of possible attribute types as well as use in commercial promotion. The first example is a set of five six-sided dice similar to the sixth embodiment with a first attribute type ‘city with a team from each of five professional sports leagues’ and a second attribute type ‘professional sports team logo’ with the values: football team logo, baseball team logo, basketball team logo, hockey team logo, and soccer team logo. The common design marking is the logo of a sports equipment company. Such an embodiment would have the same game functionality as the sixth embodiment, but it would also serve a commercial promotional purpose as well. Similarly, such a dice set could have a first attribute set of university and a second attribute set of university identifier with values: university name, football helmet graphic, sports team logo, sports team nickname, sports team motto. The common design marking may be the logo of a college football conference. 
         [0044]    Anyone familiar with the art will recognize that all of the several embodiments may be implemented as machine equivalents in digital gaming devices, including, but not limited to electronic video game devices, computers, and hand-held video devices. Any of the several embodiments may be used as elements in games that include elements such as cards, chips, game tokens, game boards, tiles as well as other game elements. 
         [0045]    Although the description above contains many specificities, these should not be construed as limiting the scope of the embodiments but as merely providing illustrations of some of several embodiments. 
         [0046]    Thus the scope of the embodiments should be determined by the appended claims and their legal equivalents, rather than by the examples given.