illustrated in fig1 is the regular hexagon shaped game board , comprised of a central figure depicting a star 1 surrounded by rays 2 , which star figure &# 39 ; s center is the common center of concentric rings of contiguous hexagons -- of which 3 is the innermost -- the outermost which ring 4 contains six equiangularly positioned heptagons 5 , and which outermost ring tessellates with linearly contiguous polygons 6 which tessellate the game board &# 39 ; s six sides . the interior and two sides 7 of each said linearly contiguous polygon extend to a game board &# 39 ; s edge , which edges have no line indicia to demarcate them . this single game board is used in the unistellar game version . however , the aforementioned linearly contiguous polygons tessellating the game board &# 39 ; s sides are proportioned so that when two congruent game boards fig3 -# 15 ,# 16 are positioned adjacently ( aligning vertex to vertex any side of one to any side of the other ), the linearly contiguous polygons of one conjoin with those of the other to form a row of regular hexagons 17 . when a third game board 18 is configured with two such that each game board shares an edge with two others that share an edge with each other there is formed two additional regular hexagon rows 19 , 20 and the three rows intersect at a common hexagon 21 , which is termed a hyperspace jump location . the three regular hexagon rows are said to form the interboard region , simulating interstellar space . the region internal to each game board is termed the intraboard region , simulating the planetary region of a star &# 39 ; s gravitational field . three or more game boards configured as described are used in the multistellar game version . illustrated in fig4 is one embodiment of the invention &# 39 ; s spacecraft marker , composed of lower region 26 colored according to spacecraft class , upper region 27 colored according to spacecraft player , and numeral 28 . there are three spacecraft classes -- primary , secondary , and tertiary -- designated with black , silver , and gold coloring , respectively . the unistellar game is played by two to four players , and therefore the spacecraft markers for that game set are differentiated by four distinct player colors . in the multistellar game set there are twelve distinct player colors . in either game , each player receives spacecraft markers consisting of three spacecraft markers of each of the three classes , making nine spacecraft markers the total a player may bring into play . player spacecraft markers of the same class are distinguished by numerals 1 , 2 , and 3 . for brevity spacecraft markers will henceforth be referred to as spacecraft . illustrated in fig5 a is an easel , termed in the game rules an array , with four ledges 31a , 31b , 31c , 31d . each player is distributed an array , whose function is to display for each of that player &# 39 ; s spacecraft in play upon the game board a spacecraft identity marker fig6 a with the color 41 of that spacecraft &# 39 ; s class and the spacecraft &# 39 ; s numeral 42 , which marker is positioned on the array &# 39 ; s topmost ledge 31a . immediately below the spacecraft identity marker on the array &# 39 ; s second ledge 31b is positioned a speed marker fig6 b distinguished by numeral 43 and color 44 , immediately below the speed marker on the array &# 39 ; s third ledge 31c is positioned a fuel marker fig6 c distinguished by numeral 45 and color 46 . the array &# 39 ; s fourth ledge 31d is reserved for resource markers , designating cargo , which are described below . markers aligned vertically upon the four ledges constitute what is termed a spacecraft column , which identifies for an individual spacecraft its speed , fuel , and cargo . illustrated in fig5 b is an array configured with grace marker 33 , three knowledge category markers 37a , 37b , 37c , and arbitrary classed spacecraft identity markers with numerals 1 , 2 , and 3 32a , 32b , 32c . in the column of the spacecraft identity marker with numeral 1 32a are speed marker with numeral 1 34 , fuel marker with numeral 2 35 , and three resource markers 36 . spacecraft identity markers with numerals 2 and 3 also have columns with respective speed , fuel , and resource markers . the area in front of an array is termed a home station , which is used for the deposit of spacecraft and resource markers until they are used and which a spacecraft accesses when it lands upon the seventh ring heptagon its player has selected for that purpose at a game &# 39 ; s beginning , designating it their home station heptagon . deposited in the home station depicted 5b -# 39 are one spacecraft and two resource markers . planet markers are disks fig7 a , 7b , 7c with diameters varying according to the size of hexagons composing the ring within which each advances , the markers distinguished by their surfaces &# 39 ; color and indicia 51 , 52 , 53 . two outer planet markers advance positioned opposite one another in ring 7 fig2 a -# 4 . two middle planet markers advance positioned opposite one another in ring 5 fig2 a -# 9 , and one inner planet marker advances in ring 3 fig2 b -# 10 . associated with each planet marker is a resource marker . the two outer planet markers are sources of spacecraft fuel . the aforementioned fuel marker numeral indicates a spacecraft &# 39 ; s fuel supply . in the future scenario simulated by the game one middle planet is source of the energy resource required for the engineering development of societies , described below , and therefore one unit of that energy cargo is represented by one energic resource marker fig8 a . the second middle planet is source of life sustaining substances such as oxygen and water required for the habitation of societies , and therefore one unit of that ecological cargo is represented by one ecologic resource marker fig8 b . the inner planet is source of mineral resources such as metals and nonmetal elements required for the engineering development of societies , and therefore one unit of that mineral cargo is represented by a mineral resource marker fig8 c . all three resource markers are rectangular shaped and scaled to fit on an array ledge , and each is distinguished from the other by color and indicia on a surface 57 , 58 , 59 . associated with each planet marker is an external planet marker fig9 partitioned into four areas 61 , 62 , 63 , 64 , one area for each player , and of sufficient size to contain within each player &# 39 ; s partition their accumulation of society markers , described below , and resource markers . as the name implies , external planet markers are positioned off the game board . for brevity , planet markers will henceforth be referred to as planets . in multistellar games using three game boards the centrally located interboard hyperspace jump location fig2 -# 120 is used in conjunction with hyperspace jump markers fig2 , distinguished by indicia 110 from other markers , placed upon predetermined intraboard hexagons fig2 -# 121 ,# 122 ,# 123 such that spacecraft move between any two hyperspace jump locations in one step . in multistellar games using two game boards a hyperspace jump marker fig2 is placed upon any one of the interboard regular hexagons fig2 -# 132 -- which hyperspace jump marker takes the place of the aforementioned centrally located interboard hyperspace jump location used in triple game board configurations -- and used in conjunction with hyperspace jump markers placed upon predetermined intraboard hexagons fig2 -# 133 ,# 134 . viii . home stations and home station heptagons in relation to unistellar and multistellar games in any game board configuration the home station heptagons remain fixed , being components of the game board tessellation , and in multistellar games the location of intraboard hyperspace jump markers remain fixed , which creates for multistellar games respective problems of equal player access from home station heptagons to the interboard region and intraboard hyperspace jump markers . the solution is that in multistellar games each player has a home station marker fig2 distinguished by color and indicia 112 that rotates around ring 7 fig2 -# 125 occupying heptagons in the manner of planets rotating in ring hexagons . a player &# 39 ; s spacecraft access their home station , the area in front of their array , from their home station marker wherever it may be in its rotation , entering and exiting the game board from its location . grace markers fig1 are rectangular shaped , with a numeral 65 to indicate grace level and adjacent surface 66 with some combination of color and indicia the same for every marker , and scaled to fit on an array ledge . the numeral range is 1 to 12 inclusive . grace markers are displayed on the right side of the first array ledge 31 . knowledge markers occur in three categories fig1 a , 11b , 11c , each marker being rectangular shaped , with a numeral 71 , 73 , 75 to indicate knowledge level , and scaled to fit on an array ledge . the three knowledge category markers are distinguished by some combination of color and indicia on the surface 70 , 72 , 74 adjacent to said numeral . the first category incorporates knowledge related to physical science , engineering , mathematics , medicine , biology , and agronomy , and may be abbreviated on catastrophe and entropy cards with &# 34 ; c1 &# 34 ;, for category one . the second category incorporates knowledge related to social science and management science and may be abbreviated with &# 34 ; c2 &# 34 ;. the third category incorporates knowledge related to art , literature , music , history , philosophy , and religion , and may be abbreviated with &# 34 ; c3 &# 34 ;. knowledge markers are displayed on the right side of the second 32 , third 33 , and fourth 34 array ledges . each player &# 39 ; s collection of spacecraft , society markers , resource markers , and knowledge points constitutes their capital , and players are free to exchange that capital according to their interests . the game is played with two card decks ; the cards of one deck providing a source of instruction related to catastrophe : natural phenomena uncontingent upon human action and destructive to human purpose ; and the cards of the second deck providing a source of instruction related to entropy : the failure of human systems and devices due to causes entirely within such systems and devices and destructive to human purpose . fig1 a illustrates one possible catastrophe card , and it provides the player drawing the card information concerning the type of natural catastrophe 80 , the catastrophe severity 81 , the type of playing piece impaired : spacecraft or society marker 82 , a method determining the impact area of that destruction , within which a playing piece is impaired 83 , the minimum score for each of said three knowledge categories a player must have for any playing piece in the impact area to avoid being affected 84 , the manner of the playing piece &# 39 ; s impairment 85 , a method determining the area within which the presence of a playing piece of another player necessitates a decision whether to assist the impaired playing piece , wherein a decision to not assist results in grace level loss and a decision to assist , with diversion of capital , does not change grace level 86 , a method determining the area within which the presence of a playing piece of another player bestows an opportunity to increase the player &# 39 ; s grace level if they chose to assist the aforementioned impaired playing piece , diverting capital to assist , but necessitates no loss of grace level if that player chooses to not assist 87 . in fig1 a the catastrophe is a gamma ray burst of severity 2 which impairs any one of the card drawing player &# 39 ; s spacecraft in rings 3 and 4 , the player selecting the particular spacecraft if more than one are in that target area . however , if the player has knowledge category c1 points equal to or greater than 4 , plus knowledge category c2 points equal or greater than 4 , plus knowledge category c3 points equal to or greater than 2 that player averts the impairment . if not , the spacecraft loses resource cargo according to the spacecraft class ; class 1 losing 1 fuel unit , 1 energic resource marker , and 1 ecologic resource marker . losses to other spacecraft classes are interpreted similarly . players with spacecraft 5 or less polygons distant -- wherein each polygon is one distance unit -- from the impaired marker on the turn of the catastrophe card &# 39 ; s drawing must divert spacecraft to a polygon adjacent to that of the impaired marker or lose 1 grace level . players who assist just assist , without resulting grace level increase . players with spacecraft 7 or more polygons distant from the impaired marker receive one grace point if they chose to assist , but are not penalized a grace level if they chose to not assist . the entropy card illustrated in fig1 b is used in conjunction with a game set using the alternative enumerated game board fig1 a , b . in that game board some polygons contain indicia consisting of a letter and number 105 . the letters range from a to f for rings two to seven respectively . within each ring the polygons are numbered 1 to 24 . using that enumeration system , fig1 b describes a spacecraft 91 propulsion entropic failure 90 in which the target area 92 is selected by first throwing one six sided die to select a number , the numbers being agreed upon beforehand to match with letters in manner 1 - a , 2 - b , 3 - c , 4 - d , 5 - e , 6 - f . thus a throw yielding 5 signifies the letter e . next four cubic die are thrown and the selected numbers summed . for example , the die faces might sum to the number 19 . the letter and number thus obtained are combined to signify polygon e19 . reading the remainder of the field , the target area includes polygons 7 or less polygons distant from polygon e19 . other methods might be use to select a particular polygon for this purpose . fig1 c illustrates another entropy card , designating a hyperinflation entropic failure 95 . the target is a collection of player societies 96 on a particular external planet playing piece , which is the target area . that external planet playing piece is selected by the method 97 of throwing one die whose numerals have been agreed upon before hand to match with planets in manner 1 , 2 - m , 3 , 4 - e , and 5 , 6 - b , where m , e , and b signify the mineral , energy , and ecology resource planets , respectively . the societies &# 39 ; impairment 99 is that all player purchases occurring at a fix price , for example one colony for four resource markers , require one extra resource marker . other player &# 39 ; s do not incur grace lose if they fail to assist the impaired society collection 100 . however , any player with no society on that external planet marker can increment their grace 1 level by assisting the impaired society 101 . that assistance &# 39 ; s method might be described in a game rules list of general grace change circumstances as a contribution without remuneration of a sufficient number of knowledge category c2 points so that the impaired society achieves the 6 points needed for impairment mitigation 98 . whether a player is required to draw either a catastrophe card or an entropy card is dependent upon chance . a random function device and the frequency ( probability ) distribution it generates implements that chance . for example , a computer random number algorithm might generate a flat frequency distribution in which there is a 4 % chance table 1______________________________________grace level integer probability greater thancatastrophe entropy selected or equal to integer______________________________________ 1 1 1001 2 2 96 3 3 922 4 88 5 843 4 6 80 7 764 8 72 5 9 685 10 64 11 606 6 12 56 13 527 14 48 7 15 448 16 40 17 369 8 18 32 19 2810 20 24 9 21 2011 22 16 23 1212 10 24 8 11 - 12 25 4______________________________________ of selecting each number from 1 to 25 inclusive . the cumulative distribution identifying for reach integer -- column 3 -- the probability -- column 4 -- that an integer equal to or greater than that integer will be selected by the random function is demonstrated in table 1 . for each player grace level , 1 - 12 inclusive , in column 1 there is a corresponding integer in its row in column 3 . if the random function device selects an integer equal to or greater than that integer the player must draw from the catastrophe deck . thus , there is a mathematical mapping between the integers of column 1 and those of table 2______________________________________grace level integer probability greater thancatastrophe entropy selected or equal to integer______________________________________ 1 100 1 - 2 2 96 3 921 4 88 3 5 842 6 80 7 763 4 8 72 9 684 10 64 5 11 605 12 56 13 52 6 14 48 15 447 16 40 7 17 368 18 32 19 289 8 20 24 21 2010 22 16 9 23 1211 24 812 10 - 12 25 4______________________________________ column 3 , and this is designated a &# 34 ; type one mapping &# 34 ; in the patent claims section . similarly , for each player grace level in column 2 there is a corresponding integer in its row in column 3 . if the random function device selects an integer equal to or greater than that integer the player must draw from the entropy deck . the mathematical mapping between the integers of column 2 and those of column 3 is designated a &# 34 ; type two mapping &# 34 ; in the claims . the table 3______________________________________grace level integer probability greater thancatastrophe entropy selected or equal to integer______________________________________1 1 - 2 1 1002 3 2 96 3 923 4 88 4 5 844 6 80 7 765 5 8 72 9 686 10 64 6 11 607 12 56 13 528 7 14 48 15 449 16 40 8 17 3610 18 32 19 2811 9 20 24 21 2012 22 16 10 23 12 11 24 8 12 25 4______________________________________ difference between the type one mapping and the type two mapping is that for the former changes of one grace level result in less change in the cumulative probability in column 4 than for the latter . this simulates a universal moral order in which moral transformation , toward either the good or wicked polarities , has greater corresponding ramification in the realm of human act and artifice than in the natural realm , existing apart from human influence ; which is notorious for visiting disaster upon the benignant and innocent as well as the malefic and morally compromised . table 2 illustrates , for the same cumulative distribution used in table 1 , type one and two mappings in which grace levels have been shifted toward higher cumulative probabilities , whereby is simulated a universal moral order more punitive than that signified in table 1 . alternatively , table 3 illustrates for table 1 &# 39 ; s cumulative distribution , type one and two mappings in which grace levels have been shifted toward lower cumulative probabilities , whereby is simulated a universal moral order more forgiving than that signified in table 1 . thus , table 1 signifies a moral order intermediate between table 2 and table 3 in its clement - punative degree . before commencing a game , players chose which moral order clement - punative degree to structure their interaction . for subsequent discussion of the preferred game embodiment , the random function device will be four tossed cubic die whose faces are summed to obtain an integer occurring in a cumulative distribution analogous but not equivalent to that in the tables . society markers may be manufactured from sheet material in shapes selected from a group that includes fig1 a , 14b , 14c , 14d , 14e , 14f . society markers would be ordered one in relation to the others such that the greater a society &# 39 ; s complexity , the greater the number of its marker &# 39 ; s sides . for this preferred game embodiment , fig1 a is a marker for a base , fig1 b is a marker for a colony , and fig1 c is a marker for a nation . the game rules specify the interaction of a spacecraft &# 39 ; s fuel and speed parameters for every possible polygon and planet traverse . the game board &# 39 ; s tessellation is complex and every such contingency need not be explained , but the essential contingencies involve ( a ) a correspondence between a spacecraft &# 39 ; s speed marker numeral and the number of polygons that spacecraft traverses each player turn , ( b ) the necessity that a spacecraft always sustains a position with respect to the polygons it traverses or comes to rest upon fig1 , ( c ) traversal of the central star figure , illustrated in fig1 a , b , c in which the star &# 39 ; s rays and spaces between rays and ring one polygons are used to delineate specific parabolic orbits , ( d ) differentiation of circular , parabolic , and paracircular orbits and the fuel decrement required to exit each , illustrated in fig1 a , b , ( e ) velocity ( speed and direction ) changes resulting from planetary traversal , illustrated in fig1 , 21a , b , c , ( f ) permitted traversals of hexagonal and heptagonal polygons , illustrated in fig1 a , b , and ( g ) speed and fuel implications for velocity changes in the interstellar region , illustrated in fig2 a , b . fig1 - 21 are selected from the set of game rules diagrams . throughout the rules for the unistellar game board configuration it is written that a &# 34 ; player &# 34 ; commands a home station and its nine spacecraft . however , to accelerate and simplify the game it is advantageous to distribute control of groups of a player &# 39 ; s spacecraft to individuals . thus , for example , if six of a player &# 39 ; s spacecraft are active on a game board , three individuals could control three groups of two spacecraft . when groups of individuals control spacecraft in this way , the &# 34 ; player &# 34 ; becomes a &# 34 ; team &# 34 ; in game rule parlance . &# 34 ; team &# 34 ; is used exclusively in the multistellar game board rules , because the inherent complexity of simultaneous play in multiple arenas make team control over spacecraft a beneficial simplification of play . multistellar games begin with each game board hosting two or more home stations . each team begins the game competing primarily with teams sharing its home board ( although not necessarily , if an advantage to visit another game board exists ). once a team establishes strong and stable positions regarding capital , knowledge , and grace on its home board it is free to compete on non - home boards until there is established a multiple game board team that is exemplary with regard to knowledge and grace . thus , beginning with multiple teams on multiple game boards , competition advances across all game boards until there emerges one exemplary team . the multistellar game requires rules governing the synchronization of team turns that are , first , sequential in the context of one area -- intraboard region or interboard region -- and , second , simultaneous in the context of multiple areas , with rounds of play in different areas advancing independently according to different tempos ( number of rounds of play per time interval ). in some games these synchronizations of turns may become sufficiently complex to require pencil and paper to track . an alternative to that synchronization complexity is gained by synchronizing rounds of play on all game boards such that they begin and end with the simultaneous advancement of the planets on all game boards . however , the trade - off of that synchronization &# 39 ; s simplicity is that to insure uniform play pace across all game boards such that teams on some game boards do not have to wait for teams on other game boards to complete their play round before the former teams commence a new round of play ( after planet advancements on all game boards ), it may be necessary to limit the duration of team turns using a stop watch or ( 1 , 2 , or 3 minute duration ) &# 34 ; hour glass &# 34 ;, allotting , for example , two minutes for each team to complete their turn . an additional benefit resulting from synchronizing the advancements of all planets on all game boards is that it enables the plotting of complex , stable spacecraft orbits involving planet traverses on multiple game boards . there may also be plotted simpler orbits spanning multiple game boards , simulating the influences of the stellar gravities alone . fig2 depicts for the trinary game board configuration what is termed a meta - paracircular orbit 127 and what is termed a meta - parabolic orbit 129 . two varieties of analogous metaparabolic orbits fig2 -# 137 ,# 138 exist for the binary game board configuration . the game , named &# 34 ; starworlds synergy &# 34 ;, progresses according to a complex dynamic . a game winner is determined by first summing each player &# 39 ; s three knowledge category levels to obtain a collective knowledge level for each player , and then multiplying each player &# 39 ; s collective knowledge level times their grace level to obtain their duplex score ; the player with the highest duplex score being the game winner . in games using multiple game boards in a multistellar game board configuration teams on all game boards may compete individually against each other or each game board &# 39 ; s collection of teams with home stations thereon may be deemed groups working in cooperation and their group scores being the duplex score derived by multiplying the average of group member &# 39 ; s collective knowledge levels times the average of their grace levels . in either unistellar or multistellar games a criterion must be selected for cessation of play and comparison of competitor ( player , team , or group ) scores , since the absence of competitor incentive to eliminate each other &# 39 ; s playing pieces may cause protracted games . one criteria is to use an outer planet , which revolves slowest of the planet types , like the hand of a clock and cease play when the planet achieves a predetermined position . another criteria is to cease play when one competitor ( player , team , or group ) achieves a pre - stated number of societies , such as , for example , nations on all three ( nonfuel ) resource planets . maximization of the duplex score , therefore , requires maximization of both the knowledge and grace levels , which is a player &# 39 ; s or team &# 39 ; s primary objective . society markers established on external planet markers -- which are motionless surrogates of planets revolving on the game board -- cause to be distributed to players the three knowledge category points . society markers occur in three degrees of complexity , -- bases , colonies , and nations -- and each generates a different mix of the three knowledge category points . a player &# 39 ; s collective knowledge level is the sum of their three knowledge category levels , which set of three numbers is termed the player &# 39 ; s knowledge triple . society markers generate those three categories of knowledge points at regular intervals determined by the position of planets in their orbits . since each individual society marker established for a player generates knowledge points , a subsuming player strategy is to maximize the number of their society markers . society markers are purchased , either directly or indirectly , with planetary resource markers . the fundamental unit of society marker is the base , which requires for establishment upon an external planet marker one resource marker from each of the other two planet types , which resource markers are physically transported by spacecraft using the above described array mechanism . two base markers may be exchanged for one colony marker , and two colony markers may be exchanged for one nation marker . once a society marker is established upon its external planet marker , it causes to be distributed to its player from a central store resource markers of the type associated with its planet , thus multiplying that resource marker type for its player and augmenting the player &# 39 ; s inventory used to establish further society markers , using their spacecraft to transport them to their chosen external planet markers . before a player establishes their first base , however , the player obtains their initial resource markers from planets by traversing those planets , signifying rudimentary resource collection expeditions . the spacecraft themselves are available to players in three classes with varying cargo capacity and capacity to deflect catastrophe and entropy events and capacity to extend that protection to nearby spacecraft and societies . the spacecraft are purchased at a rate of two resource markers for one primary class spacecraft , four resource markers for one secondary class spacecraft , and six resource markers for one tertiary class spacecraft , the most powerful . thus the capital value of spacecraft is their purchase rate and a player may exchange their own spacecraft at that rate , for example exchanging two primary class spacecraft for one secondary class spacecraft . such exchanges occur at a player &# 39 ; s home station , the area in front of their array where they deposit resource markers and spacecraft until their use , which home station is accessed when a player &# 39 ; s spacecraft lands upon the seventh ring heptagon the player has selected for that purpose at a game &# 39 ; s beginning , designating it the player &# 39 ; s home station heptagon . since the establishment of society markers and the purchase of differentially powerful spacecraft depend upon a player &# 39 ; s use of spacecraft to transport , using the array mechanism , resource markers between varying embarkations and destinations of planets , external planet markers , and home station , skillful navigation through the stellar planetary field , represented by game board paths , is crucial . each spacecraft carries a fuel supply , which can be incremented by traversal of an outer planet , simulating an orbit used to gather energetic subatomic particles trapped in the planet &# 39 ; s magnetic field . that fuel can henceforth be exchanged for some combination of spacecraft speed change and direction change , in which maneuvers the speed marker &# 39 ; s numeral is changed and / or the spacecraft &# 39 ; s direction is changed coordinate with decrements of the fuel marker numeral . the skillful player utilizes circular , parabolic , and paracircular orbits , which a spacecraft can maintain indefinitely without changes to its speed or fuel . exit from such stable orbits , however , usually requires fuel decrement . all planets can be used to change spacecraft direction without fuel use and with resulting speed increase . the star figure &# 39 ; s twelve rays and the twelve spaces between rays are used to guide spacecraft traces of parabolic orbits near the star figure . in multiple game board configurations , hyperspace jump locations are designated which enable spacecraft to jump between distant game board areas without having to traverse intermediate polygonal paths . as completely as is practically feasible , all player decision &# 39 ; s with direct ramification for other players are subsumed in their consequence for the deciding players by a moral dynamic . sometimes that consequence , in terms of grace level change , is dictated by a general list covering circumstances such as player bartering and deal making , but most often the player decision is forced by the mechanism of the above described catastrophe and entropy cards . at the beginning of each turn a player selects an integer using a random function device , which in this game embodiment is the sum of the faces of four tossed cubic die , and then using a table such as described above compares that integer to an integer dictated by the player &# 39 ; s grace level to determine whether the randomly selected integer is equal to or greater than the player &# 39 ; s grace level dictated integer . if that is the case the player must draw a catastrophe card . then the player repeats the random function procedure to obtain a second integer , which the player compares to another integer , in a second table column , also dictated by the player &# 39 ; s grace level to determine whether to draw an entropy card . the player drawing a card of either type risks the loss or restriction of a society marker or spacecraft , and other player &# 39 ; s may or may not , according to conditions dictated upon the card , be forced to decide between sacrificing grace level , incurring grace level decrement , for the immediate goals of a playing piece or sacrificing the immediate goals of a playing piece for grace level increment . since the crucial integers dictating whether a player risks loss subsequent a catastrophe or entropy card draw are dependent upon a player &# 39 ; s grace level , that grace level partially determines the frequency that a player risks loss ( the other determining part being random selection structured by a frequency distribution ). thereby is simulated a universal moral order subsuming player decisions regarding other players . as explained above , that moral order can be adjusted in its clement - punative degree , the frequency at which player &# 39 ; s risk loss , by the players &# 39 ; selection at a game &# 39 ; s beginning of a mapping shifted toward higher or lower cumulative probabilities . thus , in this exchange and maneuver of markers is simulated parties in a distant human future , economically engaged in single or multiple star systems , owning fleets of spacecraft which are used to initially extract and transport planetary resources to establish societies of varying complexity in order that those societies can contribute to those players &# 39 ; wealth by ( a ) further development of planetary resources , distributed by spacecraft , to further establish societies and procure additional spacecraft of varying capability and ( b ) development of players &# 39 ; knowledge stores . spacecraft navigation is fundamental to those parties &# 39 ; prospect of wealth accumulation because they are the sole means of resource distribution , and skillful navigators master orbits which harvest fuel from planets distant from their star and adjust orbit and speed while conserving fuel by encounters with planets . spacecraft and societies both are threatened by an abundance of catastrophic natural phenomena and entropic failure of human created systems and devices , and the knowledge produced by societies enable those parties to avoid or recover from such hazard which occur randomly in part as a function of each party &# 39 ; s accumulated morality achieved through their history of neglect or response to the tribulations of other parties . it is knowledge multiplied by grace that establishes the supreme competitor . a &# 34 ; starworlds synergy &# 34 ; game begins with the distribution to players of their arrays fig5 a , three spacecraft fig4 -- two of the primary class and one of the secondary class -- spacecraft identity markers fig6 a for the three spacecraft , and for each spacecraft identity marker , speed markers fig6 b of unit two and fuel markers fig6 c of unit two , and level 7 grace markers fig1 ( intermediate in the range 1 to 12 ). players &# 39 ; chose the heptagon fig2 a -# 5 upon which they will introduce and exit spacecraft ; that heptagon being the extension onto the game board of their home station area in front of their array , where they will deposit spacecraft and resource markers until their use . the planets fig7 a , 7b , 7c are positioned initially in each &# 39 ; s ring by tossing four cubic die to obtain an integer 4 - 24 inclusive . for games using the unenumerated game board fig1 players must select an arbitrary polygon 1 position in each ring from which to begin counting the number of polygons indicated by the die sum for the initial planet position . for games using the enumerated game board fig1 a , b the polygon numbers 1 - 24 are specified . the two outer planets are positioned directly opposite one another in ring 7 fig2 a -# 4 , the two middle planets are placed directly opposite one another in ring 5 fig2 a -# 9 , and the single inner planet is positioned in ring three fig2 b -# 10 . henceforth , the outer planet will be source of spacecraft fuel , the middle planets will be source of ecologic and energic resource markers respectively , and the inner planet will be source of mineral resource markers . in the unistellar game configuration , the aforesaid actions are taken by the players using one game board , and in multistellar games using two or three conjoined game boards players on each game board take these actions . in addition , for multistellar games players must decide whether to absolutely synchronize player turns on all game boards by advancing the planets on all game boards simultaneously . such an absolute synchronization may require individual player turns be limited in duration by a timing device such as a stop watch . players in their turn then embark their spacecraft from their home station heptagons , each traversing a number of polygons equal to the numeral on each &# 39 ; s speed marker ; each player advancing on every turn all of their spacecraft in play on the game board . each player &# 39 ; s goal is to use their spacecraft to transport resource markers fig8 a , 8b , 8c of two distinct types to a planet of the third resource type , whereby a base marker fig1 a may be placed upon the latter type planet &# 39 ; s external planet marker . spacecraft obtain a resource marker from a planet simply by traversing the planet ( fig1 , 21a , b , c for example of planetary traversal ). that accomplished , the resource marker is positioned on the traversing spacecraft &# 39 ; s fourth array ledge fig5 a -# 31d in its spacecraft identity marker column . when that resource marker carrying spacecraft traverses the planet chosen by its player for a society marker , the resource marker is transferred from the array to the player &# 39 ; s arbitrarily agreed upon quadrant upon the associated external planet marker fig9 . when the player has collected two such resource markers of type different from one another and different from the external planet marker &# 39 ; s resource type , the player may exchange those two resource markers for a base marker fig1 a , the resource markers then being returned to a central store of playing pieces . subsequently , on any external planet marker , two base markers may be exchanged for one colony marker fig1 b and two colony markers exchanged for one nation marker fig1 c ; the base markers and colony markers being returned to a playing piece store after their exchange . alternatively , a colony marker may be exchanged for four resource markers of stated variety or a nation marker exchanged for eight resource markers of stated variety . the rapidity with which players establish society markers upon external planet markers is governed by their navigational skill , harvesting fuel by traversing outer planets using that fuel to increase or decrease speed or adjust orbit between the circular , parabolic , and paracircular types upon which a spacecraft may advance indefinitely without change of speed or fuel . a specific example of the exchange of fuel for speed in the context of a planetary encounter is the case of a spacecraft in a parabolic orbit that must change to another parabolic orbit in a maneuver such as that depicted in fig1 a , b cases c1 - c4 , to approach a middle planet using a requisite initial position such as depicted in fig1 . an additional characteristic of the maneuver is that the spacecraft has fuel 4 and speed 2 and the planet is two polygons distant and scheduled to advance at the beginning of the next round of play . therefore , the spacecraft &# 39 ; s speed is first advanced one unit to 3 with a corresponding decrease of its fuel to 3 , designating the expenditure of fuel to accelerate the spacecraft and accomplished with corresponding changes of array markers to fuel 3 and speed 3 . now the spacecraft has sufficient speed to traverse the planet in one turn , but it still must execute the parabolic to parabolic orbit change depicted in fig1 a , b cases c1 - c4 . as indicated in the figure , that necessitates the spacecraft &# 39 ; s fuel marker being decremented 2 units from the 3 units existing after the speed increase , leaving a fuel 1 marker in the array . thus , the spacecraft with speed 3 traverses the planet to a contiguous polygon , selecting a path designated in fig1 that accelerates the spacecraft one speed unit . therefore , the maneuver &# 39 ; s last requirement is the replacement in the array of a speed 3 marker for a speed 4 marker , which new speed the spacecraft uses on the next player turn . subsequent the maneuver the spacecraft &# 39 ; s array column indicates fuel 1 and speed 4 . the player will want to visit an outer planet to increase that spacecraft &# 39 ; s fuel . spacecraft of primary , secondary , and tertiary classes have increased cargo capacity , able to transport using the device of their array column two , four , and six resource markers respectively . spacecraft also have in increasing order of their class increased immunity from some catastrophe and entropy events , designated in card instructions , and increased capacity to project that immunity to spacecraft and societies on polygons contiguous to that of their markers , which is represented in the case of protection projected over societies by using a planet marker coupled with the substitute external planet marker upon which the society marker is positioned . such spacecraft capabilities are set forth in the game rules . in multistellar games , players who seek advantage in establishing societies on game boards other than their home game board , hosting their home station , may use hyperspace jump locations to traverse in single steps extensive polygonal paths . beginning with the second round of player turns , each player as the first act of their turn selects an integer which is the sum of the faces of four tossed die and uses a table such as table 1 to determine whether to draw from the catastrophe card deck . then using card instructions fig1 a -# 80 ,# 81 ,# 82 , # 83 ,# 84 the player determines whether a playing piece has been impaired , and if so commences the impairment condition fig . 12a -# 85 . all other players then use the card &# 39 ; s instructions fig . 12a -# 86 ,# 87 to determine whether a grace decision is incumbent upon them . then this sequence of acts and decisions is repeated with regard to the entropy deck . on the subsequent turns of each player for whom a grace decision was incumbent , that player commences the movement or exchange of playing pieces which implements their decision . when a player makes a decision causing a grace level increase , their grace marker in their array is replaced with a marker with an incremented integer . alternatively , when a player makes a decision causing a grace level decrease , their grace marker is replaced with a marker with a decremented integer . xxxiv . planet rotation synchronization and its governance of resource and knowledge distributions from societies the methods of synchronizing planet advances upon either unenumerated or enumerated game boards simulate planets whose orbital periods vary according to their distance from their star . using the unenumerated game board , beginning each round of play subsequent the first , the planets are advanced in their orbit according to the schedule : ( 1 ) the innermost planet advances one polygon on each turn , ( 2 ) the two middle planets advance one polygon every other turn , and ( 3 ) the two outer planets advance one polygon every third turn . a player must be designated to note with pencil and paper the passage of second and third turns . on every third turn the presence of society markers on external planet markers causes to be distributed to their players from a central store resource markers and knowledge points in the three knowledge categories , the increments achieved by replacing in their array positions knowledge markers for markers with higher numerals . this pattern of planet advances and resource and knowledge distributions is maintained in games using the enumerated game board , except that the middle planets are advanced every time the inner planet lands upon a polygon labeled with an integer divisible without remainder by two , and the outer planets are advanced every time the inner planet lands upon a polygon labeled with an integer divisible without remainder by three . it is the advance of the outer planets that causes , according to the presence of society markers on external planet markers , distribution of resource markers and knowledge points from a central store . xxxv . the varieties of player capital and the exchange of one form for another each player &# 39 ; s collection of spacecraft , society markers , resource markers , and knowledge points constitutes their capital , and players are free to exchange that capital according to their interests . for example , a player may exchange some number of resource markers accumulated upon an external planet marker for the use of another player &# 39 ; s spacecraft to transport some number of additional resource markers to another external planet marker , where the hiring player might need those resource markers to establish a society marker . another example would be a player who has drawn an entropy card whose instructions threaten a society marker and which player lacks the knowledge points designated on the entropy card to avoid the impairment . that player might negotiate with another player , exchanging resource markers for the latter player &# 39 ; s knowledge points to achieve the knowledge triple required by the entropy card to avoid the impairment . the purchasing player &# 39 ; s knowledge marker levels are accordingly incremented , but the selling player &# 39 ; s knowledge marker levels are not changed because knowledge is not lost when it is distributed . the grace ramifications for such deals are explicated in a list of general conditions included in the game rules . if the selling player had instead donated the knowledge without remuneration that player would benefit an increment of their grace level . xxxvi . the cyclical collective contribution of a player &# 39 ; s society markers to their three knowledge categories each society marker a player has established upon an external planet marker generates some mix of the three knowledge category points at regular intervals of play rounds ( the resulting knowledge level increments achieved by replacing in their array positions current knowledge markers for markers with higher numerals ). at that time the three categories of knowledge points generated by all of a player &# 39 ; s society markers are summed according to category and those sums for each category are used to increment the corresponding knowledge marker levels of each category ( the player &# 39 ; s knowledge triple ) in the player &# 39 ; s array . when the condition of play cessation agreed upon at a game &# 39 ; s commencement occurs , the players &# 39 ; duplex scores ( in unistellar games ) or teams &# 39 ; duplex scores ( in multistellar games ) are calculated and the game winner declared . the implementation of starworlds synergy on a computer network , whereby players at separate computer stations interact in real time using graphical representations on their monitors and information shared across the network , is readily apparent .
a tessellating board game which combined with game rules simulates the economic development of single or multiple star planetary systems in which choices made by competing parties influencing each other &# 39 ; s economic prospects have ramifications modeled by a subsuming moral dynamic , affecting player destiny as moral or karmic law analogous to natural law . also simulated is a complex gravitational field of a star and its planets , either for a single star in the unistellar game version or for multiple stars in the multistellar game version , and players must plot spacecraft trajectories within those gravitational fields , adjusting spacecraft speed and direction using planetary encounters and fuel decrement , and , in the multistellar game , using hyperspace jump locations to transcend the constraint of distance .