TURING COMPLETE SETS OF GAME COMPONENTS WITH DIVINATORY ELEMENTS

Abstract

One embodiment of a Turing complete set of game components in the form of a deck of playing cards, each card (110) having at least one divinatory element illustrated on its playing face (112). In other embodiments, the game components may take other forms, including, but not limited to components for board, dice or tile games. Additionally, the game components may be simulated in different types of non physical ways, including, but not limited to electronic games, video games, computer games, or interactive network games. The embodiments described and shown have the advantage over prior art of being able to simulate a universal Turing machine in a two player game for a finite period of time within a finite volume of space, which is sometimes referred to as a tabletop game.

Description

BACKGROUND

Prior Art

The following is a tabulation of some of the prior art that presently appears relevant:

U.S. Patents
	Patent Number	Issue Date	Patentee
	U.S. Pat. No. 2,383,081	1945 Aug. 21	Ribbe
	U.S. Pat. No. 5,662,332	1997 Sep. 08	Garfield
	U.S. Pat. No. 5,843,661	1998 Dec. 01	Rothemund

NON-PATENT LITERATURE DOCUMENTS

• CHURCHILL, ALEX. “Magic: the Gathering is Turing Complete.” Toothycat. n.d. n. pag. Version 5. Web. Archived at webcitation.org/6lyNqOClx on 18 Aug. 2013
• GOPINATH, RAHUL, et al. “Computing With Tiles.” Google Code. n.d. n. pag. Web. Archived at webcitation.org/6lyEkOfCg on 18 Aug. 2013
• GOUCHER, A. P. “3D chess is Turing-complete” Complex Projective 4-Space. 5 Apr. 2013n. pag. Web. Archived at webcitation.org/6lyDr73z6 on 18 Aug. 2013
• GRAY, JAMES W. “Magic 1513: Tarot Combat II.” Recoculous. 27 Mar. 2013 n. pag. Web. Archived at webcitation.org/6lyJoZCyj on 18 Aug. 2013
• KAISER, DAVID M. “Games are Turing Complete.” Mdc.edu. November 2003 n. pag. Web. Archived at webcitation.org/6JdU4W2H2 on 14 Sep. 2013
• KAYE, RICHARD “Infinite versions of minesweeper are Turing complete.” University of Birmingham School of Mathematics. 31 May 2007 pp. 1-15 Web. Archived at webcitation.org/6lyMn8RwL on 18 Aug. 2013
• ROBINSON, KAREN D. “Playing Card Magic.” and “Wizard's Tower.” Angelfire. n.d. n. pag. Web. Archived at webcitation.org/6lyDStacB on 18 Aug. 2013
• ROGOZHIN, YURII. “Small universal Turing machines.” Theoretical Computer Science. 20 Nov. 1996 pp. 215-40 vol. 168. issue 2. Elsevier. Amsterdam, The Netherlands

Many different games and systems have been shown to be Turing complete or, in other words, equivalent to universal Turing machines (UTMs). A few examples include:

• • an infinite variation of Minesweeper (Kaye)
  • 3 dimensional chess with one dimension extending infinitely (Goucher)
  • Wang tiles (Gopinath et al.)
  • John Conway's Game of Life (Gardner)

However, to my knowledge only one game playable on a finite playing surface or within a finite volume of space (sometimes referred to as a tabletop game) is currently claimed to be Turing complete—Magic: The Gathering—also known as MTG. (CHURCHILL, Magic: The Gathering is Turing Complete.).

‘I think it's the first demonstration of Turing completeness in the rules of any tabletop game. I don't think there are any other board games or card games whose rules accommodate the complexity required to make a Turing machine (and I've played a few hundred).’ Alex Churchill (CHURCHILL et al.)

It appears possible to discover one or more combinations of multiple MTG cards which when played in certain specific combinations by several players will lead to the implementation of a universal Turing machine within MTG. However, so far it appears as though such an implementation would require roughly 70 cards with 20 or more different names, played by 4 or more different players in a precise order. Considering that there are many thousands of MTG cards available for each individual player to choose from in constructing a MTG card deck, the odds against actually simulating a UTM during the course of a game would be astronomical.

In the past, games which have been shown to be Turing complete have had disadvantages in terms of playability in one or more of the following ways:

• • a. most (Conway's Life, Wang tiles, 3D chess, infinite Minesweeper) of the above listed games aren't tabletop games, as they require one or more infinite dimension
  • b. many (Conway's Life, Wang tiles, infinite Minesweeper) are 0 or 1 player games, which are more akin to logical puzzles than to games
  • c. implementation of a UTM within the tabletop game MTG is extremely complex, requires many players, and would be rare in actual play
  • d. no known game between only two players which can be played within a finite surface area or volume is able to approximate a UTM in the manner demonstrated with Magic: The Gathering

Therefore, described in detail below is one embodiment of a set of game components in the form of playing cards (110) which can be used to play a variety of games, including two player games. The cards (110) are designed as a set to simuate a UTM in certain game conditions for a predetermined finite length of time. By halting UTM calculations after a finite length of time, we truncate some calculations which would have halted naturally given more time and we also halt some calculations which would not have halted otherwise. In the embodiment described herein, Yurii Rogozhin's 4 state 6 color UTM (ROGOZHIN, 1996) instructions are used (FIG. 9C), but in other embodiments, different UTMs may be used. Also, in other embodiments the game components may resemble chess pieces (1018) or may take the form of other board game pieces which have round or polygonal shapes with different numbers of sides, either within the same set or different numbers of sides in different embodiments. Tiles, dominoes, or dice with various numbers of sides are other potential embodiments for the game components. Additionally, the game components may be replicated or embodied in other forms or media, for example as electronic games, video games, or computer games. The triggering of the UTM aspect as part of the play of a game can be more or less of a strategic factor to be considered during the play of the game, depending on the rules of the particular game chosen. Additionally, the game pieces may contain, be marked with, or be associated with one or more fortune telling or divinatory symbols or elements. Briefly described below is some of the history linking games and fortune telling or divination.

Both divination by casting dice (Astragalomancy) and games which involve the casting of dice like Backgammon have been practiced or played for thousands of years in countries throughout the world. In more recent times, both tarot and standard playing card decks have been used for recreational game purposes as well as for divination purposes. Wim van Binsbergen has made a comparison between the Mancala family of board games and the method of divination known as geomancy. Therefore, the complete history of recreational games and methods of divination would likely fill several books and the earliest parts of that history will likely continue to remain somewhat shrouded in mystery.

In the more modern history of divination and games, we find many patent results for a patent search of “fortune telling” AND game. Many patented fortune telling games, however, have as a primary goal or purpose of playing the game amusing or entertaining one or more players via a novel method of fortune telling or divination. As an example, in the rules for Oracle Card Game by R. Ribbe the patent states: “The player or dealer is supposed to concentrate upon the subject on which information or prediction is desired” and “The object of the invention is to provide a novel form of amusement, which may be played as solitaire or for group diversion.” (Ribbe, U.S. Pat. No. 2,383,081) While each playing card (110) or game component described herein may contain one or more fortune telling (divinatory) elements or symbols, the game components differ from the above mentioned example as follows:

• • the rules and goals for games which may be played with the game components will vary, but in general the primary goal of the game will not be divination
  • divinatory meanings of cards may change during play of the game, for example a tarot card (132, 734, 735, 946) or I Ching lines (956, 960, 962, 164) may be interpreted differently when in an upside down orientation
  • divinatory elements or symbols may alter attributes (190) of the cards they appear on, for example a card's associated star (176, 178) may add power, toughness, and/or speed (190) to that card when the turn number of the game matches that star's (176, 178) lunar mansion (180)

SUMMARY

Sets of game playing components with divinatory elements which are able to function as universal Turing machines. In one embodiment, a set of game playing cards (110) which under certain game conditions will simulate Rogozhin's (4,6) universal Turing machine (FIG. 9c).

ADVANTAGES

Accordingly, several advantages of one or more aspects are as follows: to allow the playing of tabletop Turing complete games including two player games, to make the simulation of a UTM within the framework of various games a strategic factor for consideration, to simplify the simulation of a UTM within the framework of a tabletop game, to add divinatory aspects to game components without making divination the primary object or goal of using the game components, and to allow divinatory elements to change or be changed by the play of the game. More advantages of one or more aspects will become apparent through consideration of the drawings and ensuing description.

DRAWINGS

Figures

In the drawings, related figures have the same number, but different alphabetic suffixes. The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

FIGS. 1A and B illustrate various aspects of two cards from the related clubs and wands suits.

FIGS. 2 A and B illustrate aspects of two cards from the related diamond and pentacles suits.

FIGS. 3 A and B illustrate aspects of two cards from the related hearts and cups suits.

FIGS. 4 A and B illustrate various aspects of two cards from the related spades and swords suits.

FIGS. 5 A and B illustrate various aspects of two cards of the C(hevalier) rank from the tarot portion of the deck.

FIGS. 6 A and B illustrate various aspects of the black and red jokers from the poker portion of the deck.

FIGS. 7 A and B illustrate various aspects of the Tower and Judgement cards from the tarot portion of the deck.

FIGS. 8 A and B illustrate various aspects of the Death and Justice cards from the tarot portion of the deck.

FIGS. 9 A, B, and C are reference tables which indicate how different symbols and elements have been assigned to the cards in the deck.

FIG. 10 illustrates a chessboard and chess pieces and some ways in which UTM and divinatory elements can be assigned to them.

Drawings-Reference Numerals
110 playing card                 112 playing face of card
114 UTM standard RGB color indicator symbol 516 standard RGB color blue (0, 0, 255)
118 standard RGB color red (255, 0, 0) 220 standard RGB color green (0, 255, 0)
322 standard RGB color aqua (0, 255, 255) 424 standard RGB color yellow (255, 255, 0)
626 standard RGB color magenta (255, 0, 255) 928 card rank
130 poker card rank              132 Minor Arcana (GRAY, E. p. 1) card rank
734 Major Arcana (tarot trump) card rank 735 Major Arcana card name
936 suit P(oker) (4 suits)       137 rank color - B(lack)
138 poker card suit - clubs      239 rank color - R(eddish)
240 poker card suit - diamonds   342 poker card suit - hearts
444 poker card suit - spades     946 suit T(arot) (5 suits)
747 tarot card suit - trump      148 tarot card suit - wands
250 tarot card suit - pentacles  352 tarot card suit - cups
454 tarot card suit - swords     956 I Ching (4 different numbers of lines)
958 I Ching - line               960 I Ching - bigram
762 I Ching - trigram            164 I Ching - hexagram
168 alphabet letter - Greek      170 alphabet letter - Arabic
772 alphabet letter - Phoenician 174 alphabet letter (numerical value of)
176 star name                    178 Bayer designation of star
180 Arabic lunar mansion         982 card cost (3 cost types)
184 cost - rank color B          286 cost - rank color R
788 cost - either rank color     190 P(ower)/T(oughness)/S(peed) attributes
791 arrow - forces next event/symbol 192 illustration
793 planetary symbol             194 flavor text
696 UTM color/symbol instruction box 897 new moon symbol (state 1)
798 first quarter moon symbol (state 2) 699 full moon symbol (state 3)
6100 last quarter moon symbol (state 4) 7101 move L(eft)
7102 move R(ight)                6103 halt
7104 written/symbolic UTM instructions 7105 Tower symbol
7106 Judgement symbol            7107 Muster illustration and instruction
8108 Death symbol                8109 Justice symbol
7110 written text UTM related instructions 7111 Inspection - UTM read/write head
8112 written UTM halt instruction 1010 chessboard
1012 playing surface of chessboard 1014 white square
1016 black square                1018 chess pieces
1020 white rook                  1022 white knight
1024 white bishop                1026 white king
1028 white queen                 1030 white pawn
1032 black rook                  1034 black knight
1036 black bis hop               1038 black king
1040 black queen                 1042 black pawn
1044 chess piece cost/value

DETAILED DESCRIPTION

FIGS. 1A-9C-First Embodiment

One embodiment of a Turing complete set of game components is a deck of playing cards (110) as described in detail herein. However, different arrangements of divinatory elements (956, 168, 170, 772, 973, 174, 176, 178, 180) on the playing faces (112) of the cards (110) are also possible and additional divinatory elements may be included in other embodiments. Additionally, in other embodiments, sets of playing cards (110) may differ in other ways, for example in card rank (130, 132, 734), card suit (936, 138, 240, 342, 444, 946, 747, 148, 250, 352, 454), card cost (982, 184, 286, 788), standard RGB colors (114, 516, 118, 220, 322, 424, 626), flavor text (194), illustrations (192), or number of playing cards (110) in the set.

In the embodiment described herein, the deck of playing cards (110) consists of 132 cards in total, grouped as follows: a regular or standard 52 card pack or deck (HOYLE pp. 1-2) of playing cards (130, 936, 138, 240, 342, 444) modified as described below, two modified jokers designated as B (FIG. 6A) and R (FIG. 6B), and a 78 card tarot deck (GRAY, E. pp. 13-145) (132, 734, 735, 946, 747, 148, 250, 352, 454) modified as described in detail below. The tarot cards (132, 734, 735, 946, 747, 148, 250, 352, 454) generally follow the order and naming conventions used in A. E. Waite's Rider tarot deck (GRAY, E. pp. 3, 9, 18ff) with some exceptions, such as leaving the word “The” out of trump suit card names (735) and using the card ranks (132) of J and C (FIGS. 5A and 5B) instead of Page and Knight for a closer overall correspondence between the standard poker card (130) and tarot card (132) sections of the deck. All of the playing cards (110) will be manufactured to have indistinguishable but not symmetrical designs on their reverse sides (not shown) so that when any playing card (110) is in a face down position it has right side up and upside down orientations, but cannot be distinguished from other cards (110) in the deck.

The playing cards (110) are modified from their more familiar predecessors with the addition of divinatory elements (956, 168, 170, 772, 973, 174, 176, 178, 180), standard RGB colors (114, 516, 118, 220, 322, 424, 626), flavor text (194), illustrations (192), tarot card suit (946) symbols (747, 148, 250, 352, 454) and other elements as may be seen more clearly in FIGS. 1A-9C.

FIG. 1A illustrates the Ace of clubs card. In the upper left corner of the playing face (112) of the card (110) is the universal Turing machine color indicator symbol (114). With the exception of the jokers (FIGS. 6A and 6B) this will be the standard general location for the UTM color indicator symbol (114). This symbol will be found on all of the cards, but will vary in rotational orientation and colors used. In this case, the indicated color is standard RGB red (118) which FIG. 1A shares in common with FIG. 1B. Additionally, FIGS. 1A and 1B have in common the rank color B (137). This is due to the poker clubs card suit (138) corresponding to the tarot wands card suit (148). The full list of correspondences between cards of the same rank in the poker and tarot portions of the deck is illustrated in FIG. 9A.

Below the UTM standard RGB color symbol indicator (114) on FIG. 1A we have, in descending order, the poker card rank A(ce) (130), the clubs suit symbol (138), the I Ching hexagram (164) for this card, a Greek alphabet letter (168)—α and its numerical value (174)—one, followed by a star name (176)—Sheratan, its Bayer designation (178)—β Aries, and its Arabic lunar mansion (180)—1st. In the corresponding locations on FIG. 1B are the Minor Arcana card rank (132)—5, the tarot card suit symbol for wands (148), the I Ching hexagram (164) for the 5 of Wands, the numerical value (174)—ten—of the Arabic alphabet letter (170) followed by a star name (176)—Zosma—and its Bayer designation (178)—δ Leo—and the Arabic lunar mansion (180) for the star Zosma. In general, the placement of the above mentioned elements will remain consistent throughout the poker card ranks (130) and suits (936) with the exception of the B and R Joker cards (FIGS. 6A and 6B). Similarly, the elements listed above from FIG. 1B will be located in similar positions on the playing faces (112) of the Minor Arcana (132, 946, 148, 250, 352, 454) of the tarot portion of the deck. Due to illustrations (192) of varying dimensions, other elements may be located in somewhat different locations on the playing faces (112) of different cards (110).

When flavor text (194) is included on a card, as it is in both FIGS. 1A and 1B, it will be distinguished from other types of text like written UTM instructions (7104) by being enclosed in parentheses. The general location of flavor text (194) on the playing face (112) of a card (110) will be centered directly below the illustration (192). The illustration (192) will be located in the upper center of the playing face (112) of each card (110) and extend downward toward the bottom of the card as far as needed for each particular illustration. Examples of different sized illustrations (192) and how they affect the location of flavor text (194) on the playing face (112) of each card (110) may be seen by comparing FIGS. 1A and 1B.

Finally, on the playing faces (112) illustrated in FIGS. 1A and 1B, we see the card cost (184) and its power, toughness and speed indicator (190) located in the lower right corner of the cards (110) in these figures. Note that cards of the A(ce) rank may have either high or low costs and P/T/S attributes associated with them, depending on what the player who plays those cards chooses. The location of each card's cost (982, 184, 286, 788) and combat attributes, i.e. P/T/S (190), may vary somewhat due to space issues (see for example FIG. 5B), but will be located at the bottom of the card when it is shown on the playing face (112) of the card (110). For reasons of space and because there are many options for what combat attributes (190) or other features the Major Arcana cards (734, 735, 747) may have (described in more detail below), not all of the playing cards (110) will have a cost (184, 286, 788) shown on their playing faces (112).

FIGS. 2A and B illustrate the 2 of diamonds (FIG. 2A) and the 6 of pentacles (FIG. 2B) playing cards (110). The UTM color indicator symbols (114) found in the upper left corner of these cards' (110) playing faces (112) have the standard RGB color green (220). Below the UTM color indicator symbol (114) on these cards, we again find the poker card rank (130)—2, and the Minor Arcana card rank (132)—6, respectively. However, in FIGS. 2A and 2B, the rank color is R(eddish) (239). Rank color R(eddish) (239) should not be confused with the standard RGB color red (118) as they indicate two different things. Standard RGB colors (516, 118, 220, 322, 424, 626) indicate which one of 6 colors a card will be read as if a UTM is implemented within a game. Certain of the standard RGB colors (516, 118, 220, 322, 424) also indicate correspondences between the poker suits (936) and the tarot suits (946). On the other hand, rank color R(eddish) (239) and its complement, rank color B(lack) (137), serve as a way to divide the poker card ranks (130) and the Minor Arcana card ranks (132) into two mixed rank decks with an equal numbers of playing cards (110) in each deck. These two decks will contain cards which have different P/T/S combat attributes (190) but should nonetheless be approximately equally matched when played against each other. Rank color R (239) and rank color B (137) also serve to indicate which cards may be used when paying a playing card's (110) card cost (982,184, 286, 788) in games which require the payment of card costs (982,184, 286, 788) in order to play a card (110). Additionally, rank color R (239) and rank color B (137) carry over from standard 52 card deck suit color (936, 138, 240, 342, 444) conventions, so leaving them unchanged enables variants of games which players may already be familiar with to be created and played more easily.

Summarizing the elements introduced in FIGS. 2A and 2B which differ from those shown in FIG. 1, we have a new standard RGB color—green (220), rank color R (239), suit symbols for the poker suit diamonds (240) and the Minor Arcana suit pentacles (250), and a card cost for rank color R (286) playing cards (110). Other elements and their general locations on the playing faces (112) of the cards (110) illustrated should be somewhat familiar from a study of FIGS. 1A and 1B and the description of those illustrations above.

FIGS. 3A and 3B illustrate the 3 of hearts (FIG. 3A) and the 7 of cups (FIG. 3B). New elements introduced with these figures are as follows: standard RGB color aqua (322), the poker card suit hearts (342), and the tarot card suit cups (352). Once again, the positions of these and other previously introduced elements should be familiar from a study of prior illustrations and their descriptions.

FIGS. 4A and 4B illustrate the 4 of spades (FIG. 4A) and the 8 of swords (FIG. 4B). Newly introduced elements on these figures are: standard RGB color yellow (424), the poker card suit symbol for spades (444), and the tarot card suit symbol for swords (454). The other elements and their locations on the playing faces (112) of these cards (110) have been introduced in previous figures and paragraphs.

FIGS. 5A and 5B introduce two cards from the tarot Minor Arcana with the rank (132) C(hevalier). The chevalier or knight ranks above a jack but below a queen. Since in the English language the words knight and king both begin with the letter K, the French designation C(hevalier) for this rank is used here instead. New elements introduced with these cards are: standard RGB color blue (516) and the variable location of the P/T/S combat attributes (190) and card cost (982,184, 286, 788) indicators due to illustration (192) size and star name (176) length. Note also that the standard RGB color blue (516) is read for UTM purposes for these cards, despite the additional presence of other (322, 424) previously introduced UTM colors in the UTM color indicator symbols (114) on the playing faces (112) of these cards (110). This is because for the Rogozhin 4 state 6 color UTM we require 6 colors and only have 5 natural suit divisions within the deck (once UTM color correspondences between poker and tarot cards are assumed). Therefore, a 6th 22 card “royal” blue (516) colored division has been constructed from the K, Q and C card ranks (130, 132) and the B and R jokers (FIG. 6). For UTM purposes, these cards fall into the standard RGB blue (516) category, but in other respects such as ranking the strength of different poker hands and card costs (982,184, 286, 788) the UTM blue (516) playing cards (110) follow their suit, with the exception of the jokers, which are described in more detail below. Note the numerical values (174) of the Arabic alphabet letters (170) associated with the cards illustrated in 5A and 5B as well, since these values (3 and 9, respectively) serve as a link between these two cards and the R joker (FIG. 6B) and B joker (FIG. 6A) respectively.

FIGS. 6A and 6B illustrate the B joker and R joker cards, which introduce a few new elements not seen in previous illustrations, but perhaps more importantly are different enough in various ways from the rest of the playing cards (110) in the deck to merit full illustrations. As was mentioned previously in the description of FIG. 1A, the jokers have a different location on their playing faces (112) for their UTM standard RGB color indicator symbols (114) from the rest of the playing cards (110) in the deck. Additionally, not mentioned previously, each joker has two of the UTM color symbols (114). This is to indicate that each joker may take the suit of any card which shares its rank color (137, 239). Therefore, for purposes of a straight flush or a flush, the B joker (FIG. 6A) may be considered to be a club (138), a spade (444), a wand (148), or a sword (454) as specified by the person who plays it at the time it is put into play. Similarly, the R joker (FIG. 6B) may take on the suits of diamonds (240), hearts (342), pentacles (250) and cups (352) as specified when it is played.

The introduction of one or more wildcards into a deck of playing cards (110) creates a paradox (EMERT and UMBACH) in terms of ranking the relative value of two poker hands based on the probability of being dealt that hand from a well shuffled deck. One way to resolve this paradox is to consider the jokers in a deck to be bug cards (HOYLE p. 37) rather than full wildcards. Players should decide before any game begins how the jokers will function in the game. John Emert and Dale Umbach proposed another method of resolving the wild card paradox in an article in Chance magazine.

As mentioned in the description of FIGS. 5A and 5B, the jokers are read as standard RGB blue (516) color cards despite the presence of other colors within their UTM color symbols (114). Also mentioned in the description of FIGS. 5A and 5B was to note the numerical values (174) associated with the Arabic alphabet letters (170) on the playing faces (112) of those two cards (110). Contained within the upside down word joker (130) on the playing faces (112) of the B joker (FIG. 6A) and the R joker (FIG. 6B) are the Greek alphabet letters (168) θ and γ respectively as well as their corresponding numerical values (174)—9 and 3 respectively, although the number 3 is oriented so that it reads like the letter E when the R joker (FIG. 6B) is turned upside down. When choosing to consider the jokers in the deck as bugs, it is therefore recommended that the default value of the B joker (FIG. 6A) be equal to the C of swords (FIG. 5B) and that the default value of the R joker (FIG. 6B) be equal to the C of cups (FIG. 5A) unless the jokers are able to complete a straight or a flush.

Finally, FIGS. 6A and 6B introduce 2 of the color/symbol instruction boxes (696) for Rogozhin's 4 state 6 color UTM. It should be noted that these UTM color/symbol instruction boxes (696) are included on the playing faces (112) of their cards (110) to facilitate the operation of one specific UTM without needing to refer to an instruction manual or other reference material outside the deck of cards itself. A more generalized embodiment of game components would likely not include the instructions for one specific UTM, but rather allow for the possibility of choosing from a selection of UTMs before the beginning of a game. However, given that there are 22 non halting UTM color/symbol instruction boxes (696) and 22 Major Arcana cards (734) as well as two halting UTM color/symbol instruction boxes (696) and two jokers (FIG. 6) assigning these specific instruction boxes (696) to the playing faces (112) of the cards (110) illustrated in this embodiment seems appropriate.

With the introduction of the UTM color/symbol instruction boxes (696) on the playing faces (112) of the cards (110) illustrated in FIG. 6 comes the introduction of some new elements and symbols associated with these UTM instruction boxes (696). The general layout of these instruction boxes (696) is to contain two boxes in a column with the upper box containing a standard RGB color (118, 220, 322, 424, 516, 626) and a moon phase (897, 798, 699, 6100). In the case of a non halting UTM instruction box (696), the lower box will contain a UTM color (118, 220, 322, 424, 516, 626) and will have a moon phase (897, 798, 699, 6100) either to its left or to its right. In the case of a halting UTM instruction box (696), both of which are illustrated in FIG. 6, there will be identical colors (118, 220, 322, 424, 516, 626) and moon phases (897, 798, 699, 6100) in both upper and lower boxes and no moon phase shown outside of one of the two boxes (6103), indicating neither a move to the right or to the left, but rather a halt.

In summary, FIG. 6 introduces and illustrates the following new elements: different and multiple locations on the playing faces (112) of the cards (110) for the UTM color indicator (114), the concepts of wild cards and bugs in poker and the ranking paradox that wild cards can create, different locations and orientations for Greek alphabet letters (168) and their numerical values (174), and UTM color/symbol instruction boxes (696) along with their associated color (626), moon phases (699, 6100), and halting instruction (6103).

FIGS. 7A and 7B introduce several new elements not seen in previous illustrations, since these figures are the first illustrations of the Major Arcana or trump tarot suit (747) in the deck. In FIG. 6, the standard RGB color magenta appeared within the illustrated UTM color/symbol instruction boxes (696), but FIG. 7A marks its first appearance in an illustration within the UTM standard RGB color indicator symbol (114). Also of note within the UTM color indicator symbol (114) is that both black and white background colors are used within the same symbol (788). This dual background color use provides a way of indicating that any predetermined Major Arcana card costs (788) may be paid with either rank color B (137) cards, rank color R (239) cards, or a combination of the two.

Mentioned in passing with the introductory description of card costs in the description of FIGS. 1A and 1B was the fact that there are many options for assigning P/T/S (190) and other potential attributes to cards in the Major Arcana suit (747). Many of these possibilities come from known prior art associations between combat or role playing games and tarot. A sampling of online search terms which yield relevant prior art includes:

• • “building a tarot deck from magic cards”
  • “Magic: the Gathering-like Tarot card game.”
  • “Tarot Combat: A Battle-Oriented Game Using A Tarot Deck”
  • “Deck of Many Things”
  • “Deck of Illusions”
  • “Are there any RPGs out there that use Tarot cards?”

Due to this large number of possible characteristics and attributes for a fairly limited number (22) of cards, selecting a reference sheet for the costs, attributes and other aspects of the Major Arcana cards (747) before a game begins seems less limiting to the game variants playable with these cards (110). The sites listed above provide examples for the construction of several sample reference sheets of this nature.

Continuing with a description of new elements introduced in FIGS. 7A and 7B, we have, in descending order below the UTM color indicator symbol (114) the following elements: the Major Arcana card rank (734), the tarot trump suit symbol (747), and the first appearance of an I Ching element (956) other than an I Ching hexagram (164)—in this case an I Ching trigram (762). Below the I Ching trigram (762) we also find the new elements of a Phoenician alphabet letter (772) and the first example of a planetary symbol (793). All of these newly introduced elements will have similar locations on the playing faces (112) of the Major Arcana (734) playing cards (110) on which they occur. All of the Major Arcana (734) will have an associated trump suit card rank (734), Phoenician alphabet letter (772), and trump card symbol (747). The table illustrated in FIG. 9B provides a list of which Major Arcana cards (734) contain the other elements mentioned above (762, 164, 793). The element introduced in FIG. 7A which will have a consistent location on the playing faces (112) of the Major Arcana cards (734) is the Major Arcana card name (735). This will be located in the upper right corner of the playing face (112) of the Major Arcana cards (734).

FIGS. 7A, 7B, 8A and 8B illustrate all of the cards in this embodiment which contain written or symbolic UTM instructions (7104, 7110) other than those contained within the previously introduced UTM color/symbol instruction boxes (696). The written and symbolic UTM instruction set (7104) located across the bottom of the playing face (112) of the card (110) illustrated in FIG. 7A consists of the following elements: the Tower symbol (7105), , which is shown in various sizes and orientations, written text UTM related instructions (7110), arrow symbols (791) which indicate that the event or symbol pointed at by the arrow is a forced next consequence of what occurred prior to the arrow, and the Judgement symbol (7106), a silhouette of an angel blowing a trumpet, which calls for the written and symbolic UTM instruction set (7104) on the playing face (112) of the Judgement card (FIG. 7B) to be followed. The only other new element introduced in FIG. 7A is the move right instruction (7102) in the UTM color/symbol instruction box (696).

The playing face (112) of the Judgement card (FIG. 7B) introduces new elements which have not already been included in FIG. 7A or previous figures: the 1st quarter moon symbol (798) and the move left instruction (7101) contained within the UTM color/symbol instruction box (696), the Muster illustration and instruction (7107) and the Inspection instruction which functions as the UTM read/write head (7111). For those who are unfamiliar with the orientation of the moon phases and may therefore confuse the first quarter moon symbol (798) with the last quarter moon symbol (6100), the following may be helpful. If the phases of the moon are visualized on the face of a clock which has a finger pointing out from its hour hand, the new moon phase, or state 1 (897), will be when the hour hand points to 12 o'clock, the first quarter moon, or state 2 (798), corresponds to 3 o'clock, the full moon, or state 3 (699), corresponds to 6 o'clock and the last quarter moon, or state 4 (6100), corresponds to 9 o'clock. The orientation and shape of the first quarter moon (798) and last quarter moon (6100) resemble the fingernail on a finger pointing towards the corresponding hour on the clock. The Muster illustration and instruction's (7107) function and purpose will be described in detail later; visually it will be a small illustration which represents a troop muster in combination with the word “Muster” to avoid any confusion about what the illustration symbolizes.

FIGS. 8A and 8B illustrate the playing faces (112) of the Major Arcana cards with the names (735) Death (FIG. 8A) and Justice (FIG. 8B) The playing face (112) of the Death card (FIG. 8A) introduces a few elements not shown in previous figures, namely: the UTM Death symbol (8108), a skull and crossbones, and the new moon symbol contained within the UTM color/symbol instruction box (696). Additionally, on the playing face (112) of the Death card (FIG. 8A) we have the UTM halt instruction (8112) below the previously shown Muster illustration and instruction (7107), in this case written out verbally rather than indicated symbolically as before within UTM color/symbol instruction boxes (696). The only new element introduced on the playing face (112) of the Justice card (FIG. 8B) is the Justice symbol (8109), which is a balance scale.

FIGS. 9A, 9B, and 9C are tables which illustrate how UTM color (516, 118, 220, 322, 424, 626), I Ching line (956, 958, 960, 762, 164), alphabetic letter (168, 170, 772), stellar (176, 178, 180) and other symbolic elements are assigned to playing cards (110) within the deck described in this embodiment. Newly illustrated in the table shown in FIG. 9A is the general category of card cost (982) under which rank color B cost (184), rank color B (137), rank color R cost (286), and rank color R (239) elements are listed. Also new with FIG. 9A is a general category of card rank (928) which includes both poker card rank (130) and Minor Arcana card rank (132) below it. Suit P and Suit T categories are also new in this illustration and include beneath their headings the four poker card suits (138, 240, 342, 444) and the four Minor Arcana card suits (148, 250, 352, 454). The last new heading illustrated in FIG. 9A is the I Ching line heading (956) under which we find only I Ching hexagrams (164), but this heading is used again in FIG. 9B where it covers not only I Ching hexagrams (164) but also I Ching lines (958), I Ching bigrams (960) and I Ching trigrams (762) as well. These varying number of I Ching lines are the only elements which are newly illustrated in FIG. 9B.

FIG. 9C is a table which shows, through the inclusion of Major Arcana card ranks (734), B JO (FIG. 6A), and R JO (FIG. 6B) abbreviations, how each one of the 24 color/symbol instruction boxes (696) of Rogozhin's 6 color 4 state UTM are assigned to playing cards (110) in the deck. FIG. 9C does not add any new elements not shown in prior figures.

Operation

FIGS. 1A-9C

Hoyle's Rules of Games (Hoyle p. 1ff) makes up a subset of the operational prior art for this embodiment, since it sets forth the rules, customs, and popular variants for numerous 52 card deck card games. If some cards (110) in the deck are not used and the novel elements of this embodiment are ignored during play, it is possible to play all card games which use only a standard 52 card deck. In one operational variant, I describe how Turing complete sets of 52 or 54 cards may be constructed for playing Turing complete variations of the games found in Hoyle's book, but in the other operational variants I will focus on operations, examples, and variants which use either the entire deck of playing cards (110) or a subset of the deck made up of tarot cards (132, 734, 735, 946, 747, 148, 250, 352, 454) in order to highlight the novel elements of this embodiment.

A. Operational Variant 1—Solitaire Games Using Turing Complete Tarot Decks

Instructions for playing variants of Klondike solitaire with 9 columns using both 2 standard decks and a tarot deck (SATIN, “How to play Tarot Solitaire.”) have been published online, so creating a solitaire game or variant which uses the entire deck in this embodiment should not pose insurmountable problems. However, for simplicity we will consider known solitaire games using only a tarot deck in order to illustrate the operations of this embodiment.

As a first example of games which may be adapted to be played using a Turing complete subset of the deck of playing cards (110) described in this embodiment, we will look at solitaire games using tarot decks. “How to play Tarot Solitaire” (SATIN) and “Wizard's Tower” (ROBINSON) provide two different examples of solitaire variants which can be created and played with a tarot deck of 78 cards. All of the UTM instruction elements (696, 7104) except for those found on the jokers (FIGS. 6A and 6B) are on the Major Arcana cards (734). We can see, therefore, that if the UTM instruction elements on the jokers (FIGS. 6A and 6B) are duplicated on their corresponding tarot cards (FIGS. 5B and 5A) the tarot portion of the deck (946) of playing cards (110) described in this embodiment is Turing complete. This is the case because we may use the tarot portion (946) of the deck (if FIGS. 5B and 5A are modified to include UTM instructions) to simulate Rogozhin's 6 color 4 state UTM for any calculation requiring less than a predetermined length of time. This assumes that we have an ample supply of token markers of some type to perform the calculation. Token markers may take the form of 6 different denominations of coins (see FIG. 10), small pieces of different colored paper, or be represented with other readily available small objects which can correspond if necessary to the number of different UTM colors (516, 118, 220, 322, 424, 626) and states (897, 798, 699, 6100) required by whatever UTM is being simulated by a given embodiment. For a prior art reference to the use of tokens as a part of the simulation of a UTM, see CHURCHILL's “Magic Turing Machine v5”.

Players of solitaire games are likely familiar with end game situations in which cards can be shifted around slightly without affecting the outcome of the game. As an example, if one has a single red 3 which is played on one of two available black 4s, it is possible to move the 3 from one 4 to the other, which in some games may affect the outcome, but in other endgame situations will make no difference in a lost game situation. With the addition of UTM elements into a card game, game variants are now available which in circumstances like this could provide an additional method of winning an otherwise unwinnable game or game position with skillful play. One way this might be implemented is by assigning win/loss result outcomes to the two halt UTM color/symbol instruction boxes (696) before beginning the game. In other words, declaring before the game “if a UTM run on the final state of this game halts in a R JO state, I win” and “if a UTM run on the final state of this game halts in a B JO state, I lose”. In a Turing complete deck consisting only of tarot cards (946) as described above, we would substitute the corresponding C rank cards (FIG. 5) for the jokers (FIG. 6) in the above statements, but the principle remains the same.

Thus, in solitaire positions where card movement or rearrangement is still possible but any potential moves will not affect the outcome of the game, it becomes theoretically possible to calculate a game state which may be reached by rearranging the cards in a legal manner according to the rules of the game and then initiating a UTM on the final game position with the result of a UTM “declared” win as the outcome. This may prove of interest in particular for otherwise unwinnable initial deck conditions in popular solitaire games like Klondike and Freecell.

In terms of operation of the UTM instruction elements (696, 7104) of the playing cards (110), the tower symbol (7105) on the playing face (112) of the Tower card (FIG. 7A) is what triggers a sequence of forced steps which treat a game position as a tape to be read and adjusted as necessary by the read/write head of a UTM (7111). Raising the tower (as it applies to the phrase “ raiser” on the Tower card (FIG. 7A)) may take on a number of different meanings in the context of a solitaire game such as, for example, moving the Tower card (FIG. 7A) during the course of the game or completing a foundation pile (HOYLE p. 194). Whatever definition is taken for raising the tower will affect the likelihood that a player is able to initiate a UTM should he or she desire to do so during a game. The phrase “At the beginning of raiser's next turn” as stated on the playing face (112) of the Tower card (FIG. 7A) is more easily understood in the context of games with more than one player, but may be interpreted for solitaire purposes as meaning the following: if the chosen meaning of a raised tower () or the phrase raising the tower has been met during the course of the game, proceed to raze tower after a certain length of time when no moves have occurred in the game. The sideways oriented tower symbol (7105) is the symbol used to indicate the phrase “raze tower”. As mentioned previously, the arrow symbols (791) indicate that the event or symbol pointed at by the arrow occurs next as a forced consequence of what occurred prior to the arrow. Given the above interpretation of the phrases used in the written UTM instructions (7104) on the playing face (112) of the Tower card (FIG. 7A), raising the tower will trigger the activation of the Judgement card UTM symbol (7106). The activation of the Judgement card UTM symbol (7106) in turn triggers the Muster UTM symbol (7107) on the playing face (112) of the Judgement card (FIG. 7B) which in turn triggers the Inspection or read/write head instruction (7111).

The Muster symbol (7107) is designed to insure that all UTM instructions are known or included in the equivalent of the Inspection read/write head (7111) of the UTM being simulated. Practically, what this means in this embodiment is that all 22 Major Arcana cards (734) and other cards which have UTM instruction elements (696, 7104) on their playing faces (112) have playing faces visible or readable for whoever or whatever is manipulating the cards as the read/write head (7111) in the game. This read/write head manipulation may be incorporated as a part of a computer program running the game in some embodiments, but in other cases this will be one or more of the players. In some cases a neutral party not involved in the game may be called upon to perform this function.

The Inspection instruction (7111) is the initiation of the read/write head on the initial state of the game in which it has been triggered. Players will need to decide before the game begins the game location where the read/write head (7111) starts. For example, in the furthest away, leftmost position of one's opponent's cards (110) as viewed by the UTM initiator might be one choice. In a solitaire game, a more likely choice would be to initiate the read/write head with the nearest, leftmost card (110) in relation to the player. Once the read/write head (7111) is initiated, it follows the instructions for the UTM which is being simulated by the embodiment—in this case Rogozhin's 4 state, 6 color UTM. The UTM instructions are found on the playing faces (112) of the Major Arcana cards (734) with the exception of the 2 halting instructions, as has been described previously.

Players of the game will need to decide before the beginning of the game how an empty space in the ranks of playing cards (110) is to be interpreted. For this embodiment it is currently recommended that when moving right into a space not occupied by a card that the space be read as though it contained a standard RGB color blue card (516) in a new moon or phase 1 state (897), or in other words to follow the UTM color/symbol instruction box (696) on the playing face (112) of Major Arcana card rank (734) V, Hierophant (735). When moving left into a space not occupied by a card, it is currently recommended to consider this empty space as though it contained a standard RGB color blue card (516) in a last quarter moon or phase 4 state (6100), or in other words to follow the UTM color/symbol instruction box (696) on the playing face (112) of Major Arcana card rank (734) XXI, World (735). Other options for how the read/write head (7111) should interpret a blank space would likely work as well, however.

Players will also need to decide before the beginning of a game the maximum length of time they wish for a potentially non halting UTM tape to run before it is interrupted, since otherwise it could continue to run for an indefinitely long time and a game might never be completed. When this pre established upper limit is reached or when one of the halt instructions (6103) on the playing faces (112) of the cards (110) is encountered, the Inspection instruction (7111) halts (8112). By the written/symbolic UTM instructions (7104) on the playing face (112) of the Death card (FIG. 8A), the halting (8112) of the Inspection instruction (7111) forces the UTM Death symbol (8108) to happen, which signifies the end of the game. The UTM Death symbol (8108) in turn forces the occurrence of the UTM Justice symbol, as indicated on the playing face (112) of the Justice card (FIG. 8B). The Justice symbol determines the winner of the game based on values assigned to different UTM halting results before the beginning of the game.

Summarizing the operation of the UTM elements (696, 7104) as described above, we have the following: a player or players shall predetermine the conditions for how the UTM will function before beginning the game. Such conditions include:

• • what game condition shall be required in order to “raise the Tower” (7105) to initiate the UTM sequence (FIG. 7A) and whether or not raising the Tower is mandatory if that condition is met
  • where the read/write head (7107) of the UTM simulator will begin reading the layout of the playing cards (110) as well as overall rules for the order in which the playing cards (110) are read in a game position or layout
  • how the state of a given playing card (110) is indicated or determined—for example this may be determined by the playing card's (110) rotational orientation (right side up, rotated clockwise 90 degrees from right side up, upside down and rotated counterclockwise 90 degrees from right side up) or the position of the card in the game layout (top card, 2nd card, third card, and bottom card in a column of 4)
  • how the read/write head (7111) of the UTM simulator shall interpret spaces which are not occupied by playing cards (110) within the layout
  • how long a UTM will be allowed to run before it is halted if it does not reach a halt instruction (6103) through reading the layout of the playing cards (110) in the game
  • how halting conditions (6103) including a time limit halt shall be interpreted in terms of whether the game has been won or lost and by whom
    Players will likely find preferred values for the above mentioned initial game conditions after a few games and may then use those values as default conditions. Once a game has been started and the pre established condition for raising the Tower (7105) has been met during the game, a player may choose to raise the Tower (7105) or it may be required to happen due to its game condition having been met. This depends on the initial game conditions chosen. If or when the Tower is raised (7105) during a game, that event triggers a series of forced events, as follows:
  • 1. raze the tower at the beginning of Tower raiser's next turn (orient the Tower card (FIG. 7A) sideways to indicate this)
  • 2. follow the UTM instructions (7104) on the playing face (112) of the Judgement card (FIG. 7B)
  • 3. the Muster symbol (7107) calls for all of the playing faces (112) of cards containing UTM color/symbol instruction boxes (696) to be in a visible location
  • 4. the UTM color/symbol instruction boxes (696) instruct the UTM read/write head (7111) what to do next based on the standard RGB color and state of the playing card (112) being read
  • 5. the Inspection instruction (7111) is the read/write head of the UTM, which begins reading the game position based on the initial game conditions chosen prior to the game
  • 6. when the UTM halts (6103) due to initial game conditions of time having been met or due to encountering a halt instruction (6103) in a UTM color/symbol instruction box (696), a halting (8112) of the read/write head of the UTM (7111) forces the Death symbol (8108) on the playing face (112) of the Death card (FIG. 8 A) to occur, which ends the game
  • 7. The Death symbol (8108) forces the Justice symbol (8109) on the playing face (112) of the Justice card (FIG. 8B) to occur, which determines the win/lose outcome of the game based on the initial game conditions selected and what caused the UTM read/write head (7107) to halt
    Prior art which illustrates UTMs using color/symbol instruction boxes (696) as shown in FIG. 9C may be found in A New Kind of Science by S. Wolfram (p. 706ff). Therefore, operational details for the UTM color/symbol instruction boxes (696) and the elements contained within them (516, 118, 220, 322, 424, 626, 897, 798, 699, 6100, 7101, 7102, 6103) are assumed to be explained sufficiently by prior art, since FIG. 9C alters the colors and state symbols used by Wolfram but is equivalent in terms of the illustration method.

Turing complete variations of solitaire games like Klondike (SATIN) and Wizard's Tower (ROBINSON) use tarot cards, which have divinatory meanings as well as prior art correspondences with other established divination systems such as astrology (GRAY, E. pp. 209-25) and Hebrew alphabet letters through the Kabalah (GRAY, E. pp. 193-207). Turing complete full playing card (110) deck game operations which enable novel possibilities for divinatory interpretations will be considered in detail later, but for the present we will consider divinatory interpretations in games using only tarot cards as being obvious extensions of the prior art.

Combat attributes—card power, toughness and speed (190) would be ignored in the solitaire variants being considered and card costs (184, 286, 788) would likely be ignored as well. However, some variants of Klondike solitaire such as Las Vegas solitaire can be played for a score or dollar amount associated with each card played on a foundation. Incorporating somewhat different card costs (184, 286, 788) from those used in this embodiment for gambling or scoring purposes would be a way to use card costs (184, 286, 788) in a solitaire game. See also FIG. 10 for another example of how costs may be assigned to components within a Turing complete game.

In summary, the novel operational elements of Turing complete solitaire variants which use only tarot cards are:

• • predetermined rules regarding UTM outcomes, instructions, and initiation
  • the operation of the UTM instructions (7104) on the playing faces (112) of the cards in FIGS. 7A, 7B, 8A and 8B
  • the potential for winning otherwise unwinnable solitaire games by initiating a UTM
  • novel possibilities for gambling/scoring point systems based around card cost variations (982, 184, 286, 788)

B. Operational Variant 2—Two Player Combat Games Using Turing Complete Card Decks

Prior art examples of combat style games using both tarot decks and standard card decks including “Magic 1513: Tarot Combat II” (GRAY, J.) and “Playing Card Magic” (ROBINSON) have been mentioned previously. Playing a Turing complete variant of a two player combat game like Tarot Combat II is operationally fairly similar to playing a Turing complete tarot solitaire game as described above. Elements in this embodiment not used in solitaire games will be included in Turing complete two player combat games using standard playing cards as well as those using tarot cards. Therefore, in this variant we will discuss a Turing complete standard 54 card deck modified for Turing completeness as follows:

• • 2-10 are standard RGB color red (118)
  • 2-10 are standard RGB color green (220)
  • 2-10 are standard RGB color aqua (322)
  • 2-10 are standard RGB color yellow (424)
  • A,K,Q,J of rank color R (239) suits+R JO are standard RGB color magenta (626)
  • A,K,Q,J of rank color B (137) suits+B JO are standard RGB color blue (516)
  • the UTM color/symbol instruction boxes (696) are included on the playing faces (112) of the 9-A of all four suits, with the R JO and B JO (FIG. 6) instructions assigned to the one eyed Jacks (HOYLE, p. 261), other instructions may be assigned in ascending rank and bridge suit order (HOYLE p. 2) or in other ways
  • the written/symbolic UTM instructions (7104) on the playing faces (112) of the cards illustrated in FIGS. 7 and 8 may be assigned to cards in various ways including to the four aces, the four nines or as they seem to fit the cards symbolically

The cards in this alternate embodiment may additionally have all of the associated divinatory elements (956, 168, 170, 772, 973, 174, 176, 178, 180), combat attributes (190), and card costs (184, 286) illustrated in FIG. 9A. Using a modified standard playing card deck such as described above, it is easy to construct Turing complete 2 player combat games with divinatory elements based on prior art game rules like “Combat: A Battle-Oriented Card Game” (GRAY, J.) and “Playing Card Magic” (ROBINSON). In addition to the operations described in Operational variant A above, a two player combat game adds:

• • turns and turn numbers which can correspond to lunar mansions (180) within a game; these in turn may change a playing card's (110) UTM state (897, 798, 699, 6100) or combat attributes (190)
  • a card cost (982, 184, 286) use besides the above mentioned scorekeeping or gambling uses, as described in the prior art
  • a game use for combat attributes (190) as described in the prior art

Since we are now looking at a standard playing card deck plus jokers as the basic deck in the game, it's worth highlighting something mentioned in the description of the game “Playing Card Magic” (ROBINSON). With a 52 card deck, there are 78 non pair combinations of cards if suits are ignored. This offers the potential for a game variant based around two card combinations having the potential to be melded together to create different spells, each of which could be represented by one of the 78 different cards in a tarot deck. Therefore, a 54 card deck game could use a tarot deck as a “spellbook”. Tarot cards, in particular the Major Arcana (734, 735) cards have various prior art uses, associations, and correspondences with combat game cards and role playing games, as mentioned previously. The assigning of two poker deck card combinations to a given tarot card may be done in different ways and there are many potential game uses for the resulting tarot cards which will be covered in more detail later.

In summary, Turing complete versions of prior art two player combat games are operationally similar to Turing complete tarot solitaire variants, but allow for additional playing card (110) elements to be incorporated, including UTM states (897, 798, 699, 6100) and lunar mansions (180) based on the current turn number in the game, combat attributes (190) which may fluctuate based on turn based timekeeping and lunar mansions (180), card costs (982, 184, 286), and spells and transformations based on combining two unpaired poker cards and assigning that combination a corresponding tarot card.

C. Operational Variant 3—Turing Complete Battle Line/Combat Tarot Hybrid Variants

Thirdly, we look at additional elements not covered in previous variants, such as planetary symbols (793) and how wildcards (FIG. 6) and poker hand rank may be added as elements in a two player combat game. For this, we turn to the prior art game example of GMT Games' “Battle Line”, its Terrain card expansion (FORSLUND) and a prior art variant (SALANDER). Comparing and contrasting Battle Line with the Turing complete tarot deck described in Operational variant 1, we have:

• • tarot deck=4 different UTM colored suits (118, 220, 322, 424) of 11 cards each+1 UTM colored suit (516) of 12 cards and one UTM colored suit (626) of 22 cards—9 of which have planetary symbols (793) on them—for a total of 78 cards
  • Battle Line with Terrain cards=6 colors of 10 cards each for troop cards+10 tactic cards+9 terrain cards (FORSLUND) for a total of 79 cards
    The terrain and tactic portions of the Battle Line terrain deck have some close and rough correspondences with some of the Major Arcana (734, 735) cards including TOWER and Tower (FIG. 7A), Alexander/Darius (Emperor/Empress or Emperor/Hierophant), but perhaps more importantly are some close name and elemental parallels between the 9 terrain cards and the 8 trigrams of the I Ching (LEE) which are associated with Major Arcana cards (734, 735) which have planetary symbols (793) on their playing faces (112).

Given that several Battle Line tactic cards have wildcard or bug card similarities, that terrain cards are captured based on poker hand ranks and coincide well with Major Arcana (734, 735) cards, the correspondences between poker card ranks (130) and the Minor Arcana (132) card ranks and the similarities of card numbers and colors between a tarot deck and a Terrain expansion Battle Line deck, creating a close variant to Battle Line using a Turing complete Tarot deck does not appear to present insurmountable challenges. However, since some type of Combat Tarot/Battle Line with terrain expansion hybrid variant appears most readily to cover all of the elements of the playing cards (110) in this embodiment, I suggest hybrid variants of this type as the currently preferred type of game variant for a Turing complete tarot deck. A Turing complete tarot deck variant similar to “Battle Line—Ancient Battles” (SALANDER), for example, could incorporate card costs (184, 286, 788) using the point system described for that variant, use the card costs (184, 286, 788) in a manner similar to that used for “Magic 1513: Tarot Combat II” (GRAY, J.) or use them in a way similar to how card costs may be used in a gambling variant of Klondike solitaire as described in operational variant A Major Arcana (734, 735) cards with planetary symbols (793) on their playing faces (112) could be adapted to function as terrain cards based on their I Ching line (958, 762) interpretations. UTM states (897, 798, 699, 6100) and lunar mansions (180) would be calculated within the game based on the number of turns which had happened in the game, with one method described as follows: turns 4-10=UTM state 2 (798), turns 11-17 state 3 (699), turns 18-24 state 4 (6100), turns 25,26,27,28,1,2,3 state 1 (897), turns above the 29th turn have multiples of 28 subtracted from them as needed in order to have a turn number between 1 and 28. If a turn number is equal to a lunar mansion (180) number on the playing face (112) of a card (110), this gives a +1 bonus to a chosen combat attribute (190) of that card (110) at any time during that turn. Other operational elements may be handled as described in operational variant A.

With the addition of the poker cards (130, 138, 240, 342, 444, FIG. 6) to the tarot cards (132, 734,735, 747, 148, 250, 352, 454), no significant operational elements are added, however this addition allows for the possibility of each player having a deck of 55 cards, all of the same rank color (137, 239) to draw cards from and thus enables the possibility of constructing 5 or 6 card poker hands to compete against each other for terrain cards in a Battle Line variant. Also, if the two jokers (FIG. 6) are only allowed to vary between one or the other of the C cards (FIG. 5) corresponding to their rank color (137, 239) the playing strength of the poker cards (130, 138, 240, 342, 444, FIG. 6) and the Minor Arcana (132, 148, 250, 352, 454, FIG. 5) cards should be similar enough to allow competitive games to be played pitting those two decks against each other.

Mentioned in passing previously was the fact that if a game variant allows the combining or melding of two poker cards of different ranks (130) in order to form a single tarot card (132, 734, 735) according to a predetermined list of which combination yields which card, then the resulting tarot card (132, 734, 735) might have a variety of interpretations, depending on the rules of the game being played. In a full deck of playing cards (110) combining a poker deck (130, 138, 240, 342, 444, FIG. 6) and a tarot deck (132, 734, 735, 946, 747, 148, 250, 352, 454) as described in this embodiment, pairing of otherwise unique playing cards (110) in the deck, such as the Major Arcana (734, 735) could be achieved through the combining of poker cards. This type of use would require some additional hand ranking charts beyond those typically used for poker style games, but this would likely just be a matter of extending the hierarchy of pairs above Aces to include the Major Arcana cards (734, 735). Duplicated Minor Arcana (132) cards could be treated simply as pairs, or in the case of ties a pair of cards of the same rank (132) which included a card duplicated by combining two poker cards (130) could beat an ordinary pair of the same rank (132). Alternative uses for tarot cards (132, 734, 735) created by melding two poker cards (130) include spells (as covered previously) and as wildcards for suit values, where a card of rank 2 created in this way could take any suit, depending on the preference of the player making the meld.

Finally, a few practical notes touching on the physical operation of the UTM read/write head (7107) during games played with physical (as opposed to virtually simulated) playing cards. Multi colored paper clips are likely to be a good choice for easily and temporarily marking changes made by the UTM read/write head (7107). Attaching a paper clip of a similar color to the UTM color (516, 118, 220, 322, 424, 626) which a playing card (110) is being changed to by the UTM read/write head (7107) on the top, right side, bottom, or left side of the card could be a way to indicate that playing card's (110) current UTM color (516, 118, 220, 322, 424, 626) and state (897, 798, 699, 6100). Also, note that the UTM read/write head when it moves left or right according to the playing card (110) it has just read may find itself reading a blank space despite the previous card having neighboring playing cards (110) to its left and right. This is due to the state change of the UTM read/write head (7107). Each playing card (110) in a game layout can be considered to be in one of 4 states in the current embodiment. If the state of a playing card (110) does not match the state of the UTM read/write head (7107) when it moves to the left or right, that card is ignored by the read/write head (7107) and a token card is placed above or below that card, depending on the state of the read/write head (7107) and the playing card (110) in relationship to each other. What the state and color of a particular token card are has been predetermined before the game begins, as discussed previously. The token card is then read and written over by the read/write head (7107) and the process continues until a halt situation is reached.

DETAILED DESCRIPTION

FIG. 10-Second Embodiment

FIG. 10 illustrates two dimensional symbolic representations of chess pieces (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040) on the playing surface (1012) of a chessboard (1010) in their starting positions for a chess game (HOYLE p. 214). A standard RGB color (516, 118, 220, 323, 424, 626) has been assigned to all of the pawns (1030, 1042), knights (1022, 1034), bishops (1024, 1036), rooks (1020, 1032), kings (1026, 1038) and queens (1028, 1040) disregarding which side of the game they are playing on. In two dimensional symbolic form, each piece has a distinguishable right side up and upside down orientation and may also be rotated 90 or 270 degrees clockwise to indicate that it is in one of four possible states or phases, in a similar manner to the previously described first embodiment. We may envision these symbolic chess pieces (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040) as having been drawn on square pieces of transparent film, along with elements from the first embodiment (130, 734, 168, 170, 180, 696, 897, 798, 699, 6100, 7101, 7102, 6103). In this way, the transparent film squares can be seen as a 32 card deck of cards which contain many of the elements from the first embodiment. An I Ching hexagram (164) may easily be assigned to each square (1014, 1016) of the chessboard (1010) in an obvious way, since I Ching hexagrams are frequently illustrated in an 8 by 8 square grid pattern. Two different I Ching hexagrams (164) may be assigned to each chess piece (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040). The first I Ching hexagram (164) would be written on the obverse side of the square piece of film and would be determined by the I Ching hexagram (164) which corresponds to that chess piece's (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040) initial position. The second hexagram (164) would be written on the reverse side of the film and would correspond to the hexagram (164) of the chessboard (1010) square (1014, 1016) two rows closer to the center of the chessboard (1010) than that chess piece's (1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040) initial position. If pre game UTM conditions for a Turing complete chess game are established in a similar way to that described in the Operational variant 1 section of the first embodiment, Turing complete variants of chess may be played within a finite surface area or volume of space. One or more UTM initiating conditions like the one (7105) described in the first embodiment may be selected before the game begins from rare or common events within a typical chess game, for example:

• • if a player promotes a pawn to a rook (HOYLE, p. 217), initiate a UTM reading of the game
  • if a player captures en passant (HOYLE, p. 216), initiate a UTM reading of the game
  • if a player castles (HOYLE, p. 217) queenside (or kingside), initiate a UTM reading of the game
  • if the threefold repetition rule (HOYLE, p. 218) can be invoked in a game, a player may instead initiate a UTM reading of the game

One final note about this embodiment is that different denominations of coins or currency may also be used to represent the chess pieces described in this embodiment. Money may also be used for token pieces put on the board as required by a UTM reading of the game. This offers the potential for gambling within a Turing complete variant of chess in a manner which could theoretically be skill based. For example, if I can see that a high percentage of my opponent's legal next moves would result in a UTM win for me if a Turing machine reading of the game is initiated, and we are playing a Turing complete chess variant in which the winner of the game keeps any money put onto the board during the game, then I could gamble that my opponent would not be able to find a winning next move and that therefore the odds would be in my favor if I initiated a UTM.

Additional Embodiments

Many other Turing complete game embodiments are possible, but I will give just two more brief descriptive examples to illustrate some other possibilities for adapting games to be played as Turing complete variants and then discuss ramifications. Games like Gomoku (SCARNE, p. 537) and Go (SCARNE, pp. 533-7) which are played on a 19×19 grid with two different colors of pieces are also candidates for Turing complete variants with divinatory elements. In the case of these games, Rogozhin's (2,18) UTM is used. This is also the UTM used by Churchill (2012) as cited in the prior art references. In order to create a game variant of this type, we will use coins for our game pieces. Prepare to play the chosen game variant by sorting large quantities of two different coins—pennies and dimes for example—into piles based on the date on their obverse sides. In this case, dates on the coins will be used as a substitute for colors in the context of the UTM instructions. Colors have been used for UTM instructions in the previously described embodiments, but this embodiment illustrates that another attribute of the game components, in this case a number, may be used. In the most general case, I will refer to this potential for substituting another attribute of the game components in place of colors as a use of a subset of the set of game components. Each player should start with 19 stacks of 19 of their chosen coin. Each stack of pennies and dimes should contain only coins with the same date—let's say, for example, 19 pennies dated 1991, 19 dimes dated 1991, 19 pennies dated 1992, etc. through 19 dimes dated 2009. A coin may only be played in the leftmost column of the board if it has a 1991 date, the next column to the right requires a coin with the 1992 date, etc. through to 2009 in the rightmost column. Play a game of Go or Gomoku as normal except for this rule regarding which pieces may be played where. When the (2,18) UTM is initiated based on pre selected game criteria (in a similar manner to that described in other embodiments) the UTM read/write head will read a heads up coin as being in state 1 and a heads down coin as being in state 2. A coin with the date 1991 will be considered an A coin by the UTM, 1992=B, 1993=C, etc. skipping over the year 2000. Coins are replaced by others with different dates according to the UTM instructions. As far as divinatory elements are concerned, there are 360 degrees in the zodiac and 360 intersections surrounding the central intersection on a Go board, so Sabian symbols (ROCHE) are an obvious fit. For more divinatory aspects of a Go board and game, see “The Religious Dimensions of Go” (SCHNEIDER).

As a final example of an additional form an embodiment could take, I refer readers to the illustration for U.S. Pat. No. 214,048, which shows 36 equilateral triangles arranged to form 6 hexagrams which surround a 6 pointed star. Each of the 36 equilateral triangles in the illustration is divided into three smaller triangles and has a number of dots placed along each of its sides. The number of dots range between 1 and 6. If the dots are taken to indicate one of the 6 UTM colors (516, 118, 220, 322, 424, 626), then each small triangle may be colored according to the number of dots within it. If these three colored triangles within an equilateral triangle are interpreted as being three visible faces of a tetrahedron as viewed from above, then we have a pattern for a variant of the game described in U.S. Pat. No. 214,048 which would use a number of tetrahedral dice, which could have one of 6 different UTM colors (516, 118, 220, 322, 424, 626) on each face and 4 faces which could correspond to states in the UTM illustrated in FIG. 9C.

CONCLUSIONS, RAMIFICATIONS, AND SCOPE

Accordingly, the reader will see that designed sets of Turing complete game components in various embodiments allow for the playing of Turing complete two player tabletop games, afford a simpler way to simulate a Turing machine in a tabletop game than has been demonstrated in the prior art, and the ability to initiate a Turing machine calculation on a game state adds an additional strategic factor to games.

The first embodiment in particular has ramifications for cryptography, since it includes three complete alphabets on the playing faces (112) of the cards (110) and an encryption method using a standard 52 card deck plus jokers exists in the prior art. See “The Solitaire Encryption Algorithm” by Bruce Schneier as featured in Neal Stephenson's book Cryptonomicon for further details on using a deck of cards for encryption purposes. The potential for ramifications involving gambling on deterministic rather than chance outcomes has been mentioned for the different embodiments covered, and it can be used for games with either perfect information or imperfect information. Having the option to implement a Turing machine during a game can also provide a method for winning otherwise unwinnable game as was mentioned in the case of solitaire. This could also have ramifications for game which have positions considered as draws in their non Turing complete forms, for example checkers, chess, and shogi. Many other games in the prior art are good candidates for Turing complete variations with divinatory elements, including but not limited to: Checkers, Chinese Checkers, Bridge (including 5 and 6 suit prior art variants of Bridge), Pinochle, and Dominoes. In some cases, it may be preferable to simulate a universal Turing machine for a finite maximum number of steps rather than a finite period of time.

Claims

1. Manufactured sets of game components comprising:

a. a plurality of game components with a plurality of attributes associated with each of said game components, including a plurality of distinct colors or subsets within each set of game components; and

b. said game components shall additionally have a plurality of distinct states or orientations which they may take during a game; and

c. the distinct colors and states of each set of game components shall be at least equal in number to the number of colors and states in a Turing machine which has been proven to be universal; and

d. a set of instructions whereby, when the instructions are applied to the colors and states of said game components as they are arrayed within a finite playing area during a game, said set of instructions will cause the reader of said set of instructions to simulate the operation of a universal Turing machine for a finite period of time, the maximum length of said period of time being predetermined before the game begins.

2. The manufactured sets of game components of claim 1 wherein a plurality of said game components have at least one divinatory element written upon, inscribed on, affixed to, or otherwise associated with each of said game components; and

a. some of said divinatory elements may temporarily alter at least one of the attributes of its associated game component during a game; and

b. a change in the state or orientation of said game components may change how some of said divinatory elements are interpreted.