Digital Game Knowledge Media – Invited Keynote – The 3rd International Symposium on Ubiquitous Knowledge Network Environement Meme Media Technology Approach to the R&D of Next Generation Information Technologies
Klaus P. Jantke TU Ilmenau, Institute for Media and Communication Science Am Eichicht 1 98693 Ilmenau, Germany
[email protected] [email protected] [email protected]
Keywords: game, play, digital games, game design, game state, play state, design pattern, design knowledge, knowledge media, meme media, fun, flow
Citation: Proceedings of the 3rd International Symposium on Ubiquitous Knowledge Network Environment, February 27 – March 1, 2006, Sapporo Convention Center, Sapporo, Japan, Volume of Keynote Speaker Presentations, Yuzuru Tanaka (ed.), Hokkaido University of Sapporo, Japan, p. 53–83
Digital Game Knowledge Media Klaus P. Jantke Abstract When you deal with games, in general, and with digital games, in particular, you frequently face misunderstandings. Games are rarely taken seriously. But games form, indeed, a very serious application domain which is economically prospering (in 2005, it left the world-wide film production behind) and has a growing social impact. Game research and development rely on in-depth studies in traditional fields such as mathematical optimization and in high-tech domains such as artificial intelligence (AI). Games date back to prehistoric times and offer opportunities for exciting studies of game development. But the future of digital games is even more exciting. Quite recently, ubiquitous computing has set the stage for a new generation of digital games including completely new opportunities on the market. This market is global by its very nature; its market place is the Web. There is abundant evidence for the need of interdisciplinary work on understanding games and designing future experiences of game play. This paper is interdisciplinary, but it relies on disciplinary concepts. The disciplinary focus is on patterns in game and game playing based on concepts like game state, play state, game state transition, and state classes. Memetics is chosen as the underlying key to bring technologies and informal ideas together.
1. The Application Domain of (Digital) Games Digital games are not just computerizations of conventional games such as Reversi you may play on the Web, Chess on your PC, or Tetris on your cellphone. It’s not only a new technology, it’s not only a new media integration–it’s a different world in which humans behave rather differently. Mark Wallace [62] citing Richard Bartle, the designer of MUD1, the first of all multiuser dungeons, describes what a player does when controlling an avatar in a virtual world: ‘At the persona level of immersion, according to Bartle, the virtual world is just another place you might visit, like Sydney or Rome. Your avatar is simply the clothing you wear when you go there. There is no more vehicle, no more separate character. Its just you, in the world.’ A few lines later in his article, he continues saying that, ‘when you and the character are finally unified, then it is you in there – no metaphor about it.’ And when you are shooting another persona you meet in the virtual world, isn’t it you who is the murderer?
Questions like this point to a serious issue. There are good reasons to worry about the social impact of playing digital games. Violence on TV is known already for a long time to have a rather severe impact on some humans’ behavior [55]. Nowadays, we are extending the scope of our worries to digital games. The interested reader may consult, [54], [47] and [19], e.g., for comprehensive collections of investigations. Very recent studies show clear evidences
Figure 1: Evidence of Induced Violence that violent video games have an impact on the players’ thinking and behavior as shown in figure 1 cited from [14] and (re-)published with kind permission by the authors.
Some of the results from [14] are shown in figure 1 separately for participants who played a game in which violence was rewarded (dark bars), participants who played the same game but with violence punished (grey bars), and participants who played a nonviolent version of the same game (white bars). The crux is that digital games activate the neural reward system quite effectively (see research reports from [35] to [64]). To reward violent behavior may have a highly undesirable training effect on the human player. Spitzer [56], for instance, presents a rather comprehensive study of human learning and neurophysiology.
2. Digital Game Playing in the Era of Ubiquitous Computing and Knowledge Media Before going into details, let us get a first impression of recent trends in game design. Ubiquitous computing is paving the road for ubiquitous game playing. The variety of games available on cellphones and PDAs is continuously increasing. Interesting ideas are coming up posing both new research and development problems and novel questions for those games’ social impact. The PDA game Treasure [7] (see figure 3) has been designed for a remarkably wide spectrum of investigations. The illustrations from [7] are (re-)published here by courtesy of the authors.
Evidence for the criticality of the problem is overwhelming [5, 12, 14, 24, 27, 28, 30, 38, 46, 61] –and the debate continues [65, 66]. Beyond violent and aggressive behavior, in general, there are several special areas in which an impact of video games has been diagnozed such as teen driving in the USA [1] and in Germany [40]. The key warning expressed in [40] is that measurements toward safety on the roads must fail as long as games such as Grand Theft Auto III find such a great acceptance among teens. We have to take the social impact of digital games very seriously, because of the market’s enormous potentials. In 2005, it has left behind the film production. Turnover
2004 2008
PC Games 301 255 Console Games 1191 1597 Online Games 92 784 Mobile Games 63 543 Total
1647 3161
Figure 2: Turnover (in Mill. Euro) in Game Software (Hardware excluded) in Germany extracted from Pricewaterhouse Coopers, German Entertainment and Media Outlook Under these circumstances, the author’s present work aims at a better understanding of patterns in games and game playing, especially for future game design.
Figure 3: The Game Treasure on PDA The aim of the Treasure game is to collect ‘coins’ scattered over an urban area such as a park on display in figure 3. The players’ goal is to get them in to the treasure chest (technically, a server). Two teams of two players compete against each other. A clock counts down, and the team with the most coins in their treasure chest at the end wins the game. The coins can only be seen on the map on the players PDAs.
The game playing is captured (see videos in the ‘Replayer’ tool shown in figure 5) and analyzed afterwards.
Figure 4: Players in Pursuit of Digital Coins When players come close to a treasure, they can pick it up (see the related button on the PDA screen). For savng coins to the treasure chest, they have to come into the reach of the server’s wireless network.
Among many other issues, the authors of [7] have been interested in the players’ behavior with respect to seams. A seam is a break or gap in a number of tools or media (Medienbruch, in German). Seams appear frequently when different digital systems are used in combination, or when they are used along with the other conventional media that make up our everyday environment. The Treasure game has been intentionally designed as a seamful one. Mastery of the game requires to perceive and master seams such as a missing connection to the server.
Figure 5: The system’s Analysis Tool : PDA Logdata are Visualized in the Right Upper Window There is a variety of more player interactions such as picking pockets (by using the button ‘PickPocket’ on the PDA screen), when one player comes close to another one. Playing the game needs obviously certain awareness of network connectivity issues.
The author became interested in this work, because it seems to be a rich source of knowledge about patterns in game design. However, for the present paper we will confine ourselves to much simpler patterns in game design and game playing.
Figure 6: Virtually Kicking the Virtual Ball in a Player’s Mobile Phone to Score a Goal (or not) Another impressive game for the world of ubiquitous computing named Kickreal has been developed and implemented at C-Lab Paderborn, Germany, which is a cooperation of the University of Paderborn and Siemens AG. The game has been designed for mobile phones with an integrated camera. Figure 6 gives a first impression of how the game looks like and how it might work. The picture is published here by courtesy of the authors of [26]. This football-like game is an optimal one to be played in extremely short breaks when waiting for a bus or when shopping with your friend in a department store when she just went to the changing room. Considerable efforts have been put in the algorithmics for image recognition and for processing the human player’s foot moves to calculate the resulting effect on the virtual ball. The technologies of ubiquitous computing are bringing with it new variants of digital games where the play returns to the natural environment–where it comes from.
It may be that these two games for mobile devices presented here mark starting points of new game genres (or game classes?). But what makes a genre of games? What are the common patterns determining a categorization useful both for analysis of existing games, for pondering their potential social impact and the like, and for the invention of future games being, hopefully, less harmful? As Murray pointed out when talking about ancient games which have possibly been marked in the dirt [44], so long as a people is content to mark out the board on the ground and to use any convenient object at hand for the pieces, there is very little chance of survival. Patterns of prehistoric games had no sustainable representation. But those games that have been particularly enjoyable have surely been passed from one generation to the next even before technologies for game production and external game pattern representation have been available. These considerations lead to memetics [10]. The advent of related technologies [60] makes memes of playing games explicit.
3. Game Playing Concepts For a systematic treatment of game patterns and patterns in game playing, we need clear concepts.
3.1. Game and Play Defining game is an obviously tedious task. Some authors spend dozens of pages [23] whereas others don’t even try to say what they are working about [15, 57]. The problem is that the concept of game is metaphorically heavily overloaded. For illustration, some say that love is a battlefield, whereas other people call it a game. In different languages there are varying forms of using the word game and its derivatives as metaphors. When aiming at a clarification of the game concept, we better do not try to make it general enough to cover love as well. Some conceptualization is quite appealing at a first glance such as Juul’s definition [32]: The computer game is an activity taking place on the basis of formally defined rules and containing an evaluation of the efforts of the player. When playing a game, the rest of the world is ignored. A closer look reveals that this approach misses the point completely. Every written exam in schools or universities matches these words perfectly, but students would not call it a game. Fritz’ book [23] ‘Understanding the Game’ is truly worth reading and discussing. From the characteristics of human game-playing behavior (page 24), the author has derived his own perspective illustrated in figure 7.
Figure 7: Characteristcs of Game Playing Human playing begins with and is based on an activity usually called framing. Play
is explicitly separated from everyday life. Conditions and rules of playing are set up. Humans enjoy self-determination in game playing to an extent which is often remarkably different from the degree of freedom they have otherwise. On the other hand, their gaming is bound within one, two, or more opponent’s potential actions. It may be influenced by random events such as rolling dice or tossing a coin. Playing is acting under the given framing between the poles of self-determination and indetermination. It is worth to mention that even in complete information games that are mathematically well-studied [8] players may experience indetermination due to the high complexity of the game. Consider the game Tic-Tac-Toe, for illustration. Though the game is trivialized some children might still enjoy it. Notice that it is not the only question whether there is a winning strategy for a game or not, but whether you know a winning strategy (see the case study of Hex in section 4). There is not really much pleasure in game playing without a certain degree of selfdetermination. On the other hand, excitement, challenge, and surprise may come from indetermination such as rolling a dice, drawing cards, or playing with another human who behaves somehow unpredictably. When indetermination dominates, it comes close to what Caillois [13] named ‘paidia’. The right balance makes a good game [39]. To complete the discussion of the author’s approach to game playing, let us focus on control and learning. Like Csikszentmihalyi expresses, the goal of this study is to understand enjoyment, here and now–not as compensation for past desires, not as preparation for future needs, but as an ongoing process which provides rewarding experiences in the present. (see [18], p. 9) Sayings like Suits’ definition [58] that playing a game is the voluntary attempt to overcome unnecessary obstacles are wonderful, but don’t tell us anything about the question where fun comes from.
What might a game designer derive from Suits’ definition? He receives the advice to establish unnecessary obstacles, a direction which is not very likely to result in much pleasure. Nevertheless, we suppose to adopt the concept for a moment and try to go into more detail. In [31], the author has developed his own approach outgoing from Koster’s work about ‘Fun’ [37]. Here, we choose another source: Csikszentmihalyi’s concept of ‘Flow’ [17]. Csikszentmihalyi’s investigations [17, 18] into autotelic activities, i.e. those which are intrinsically rewarding, have not been particularly driven by games and play, but he calls play the flow experience par excellence. But what is flow? Varying circumscriptions have been found of which the description as the holistic sensation that people feel when they act with total involvement ([18], p. 36) will be adopted here. Looking at figure 7, that’s what we are really interested in. An key inside is that flow has no external goals and no external rewards ([18], p. 36). It is rewarding in itself. This is throwing a particular light on flow in playing games. Pleasure in game playing does not require the game to have a goal. A goal may be fine, but it is surely not mandatory. Although this insight is sound with other approaches to fun in game design [37], most authors stick to the goal concept [51]. According to this perspective, we will subsequently look for patterns that are likely to contribute to fun or even flow. The author has designed a particular game (chapter 5) and performed several series of experimental evaluations. The experiments revealed a number of actions which are preferred by human players although they do not correlate with finally winning the game (first reports in [31]). The underlying pattern concepts assume a suitable categorization of games. Adequate concepts of game classification may support the formulation of pattern concepts which, in turn, may lead to joyful game design.
3.2. Categorization Salen and Zimmerman [50] are asking themselves as game designers the crucial question: Do we really understand the medium in which we work or the field of design to which we belong? Can we articulate what it is that generates meaningful play in any game, whether a video game, a board game, a crossword puzzle, or an athletic contest? And they give an answer: The truth? Not yet. Compare game design to other forms of design, such as architecture or graphic design. Because of its status as an emerging discipline, game design hasnt yet crystallized as a field of inquiry. It doesnt have its own section in the library or bookstore. You cant (with a few exceptions) get a degree in it. The culture at large does not yet see games as a noble, or even particularly useful, endeavor. Games are one of the most ancient forms of designed human interactivity, yet from a design perspective,we still dont really know what games are. How do we attack the problem of categorizing games? Categorization is not a matter to be taken lightly. There is nothing more basic than categorization to our thought, perception, action, and speech, as Lakoff says [41]. Categorization was considered wellunderstood and unproblematic, and categories were simply seen as containers, with things either inside or outside the category. From the ancient Greeks to Wittgenstein, things were assumed to be in the same category if and only if they had certain properties in common. And the properties they had in common were taken as defining the category. This view is still nowadays adopted when talking about board games and card games, e.g., but we know that categorization is considerably more involved. Cultural categories are real and they are made real by human activities. Games are like governments (see [41], chapter 13), in existence as humans conceived of them and behaved accordingly. Categories of games reflect peculiarities of the human mind. Therefore, categorization is crucial to pattern concepts that are crucial to fun and flow.
3.3. Semi-Formal Concepts When discussing deduction in games [22] and, in particular, what they call ‘deduction games’, Faidutti and Branham use the term ‘family’ to group several games with common features. Aleknevicus takes up the term ‘deduction games’ and contributes to the systematization of games [4], but he has no terminology for categorization. Bj¨ork and Holopainen [9] provide a remarkable background of knowledge for categorization of games by listing and analyzing what they call ‘patterns in games design’. They present more than twohundred features they name patterns–they call literally everything a pattern. A slightly finer classification seems useful. For the moment, we keep it short: • Type is used to classify games according to obvious properties that are so general and clear that no confusion is possible. From the type of a game, one can hardly derive anything about the way in which that game is played and how human players act. • Class is a term for abstracting from sufficiently clear formal properties of games. Those properties may be decisive for the way in which a game is played–the human behavior between the poles of self-determination and indetermination specifies a game class. • Genre is used to group together games which have common characteristics in the arts similar to the way in which genre is used in literature, theater, and film. • Time is a features that occurs orthogonally throughout all types, classes, and genres of games. A first usage of time considerations leads to a distinction of synchronous games from those that are asynchronous. Some games are timed, i.e. certain time constraints are used to control game playing. Another time property is persistence. For illustration of the categorization terms
introduced, we will speak about the type of board games, the class of complete information games, and the genre of video games. But notice that this categorization like any other one [41] has its fussyness. We give a few more illustrations of these terms before pointing more explicitly to the unavoidable vagueness of the approach and to interferences of phenomena. Clearly, there will be type hierarchies of games, whereas it is not necessary to generalize type hierarchies to ontologies. Classes of games may be related in different ways reflecting the richness of human thought and behavior. The investigation of a game class ontology is potentially useful, whereas the endeavor of forming ontologies of game genres sounds much too ambitious and is not undertaken in the present publication. At a first glance, classification of games into types seems easy according to the assumption that only the constituents of a game shall determine to which type(s) it belongs. There are, for instance, board games. A closer look reveals types of boards [53] such that the introduction of subtypes seems appropriate. There are fixed boards in games such as Chess, Go, Nine Men’s Morris, to name a few very classics, and Clue, Monopoly, Scrabble, El Grande, and Risk Godstorm. But what about one-dimensional Peg? To speak about just one game, we need to consider an infinite board. Another approach is to assume dynamic boards as in [53] or to speak about an infinite class of finite boards of different size. When there occur applications on the board during play which block parts of the board from future use, this might be interpreted as shrinking the board. From this perspective, Risk Godstorm, e.g., has to be transferred from the type of games with a fixed board to the dynamic boards type. The type concept is not as trivial as it looks at the first glance. Digital games may be board games. This is obvious for computerized Chess, Reversi, Go, and the like. But it holds as well for a variety of PC games such as Civilization III (see figure 8).
Figure 8: Civilization III: The Board (Square Cells) of the PC Game Literally Shining Through) As the class concept refers to the activity of human game playing, there is a quite large variety of game classes which are hardly comparable to each other. The so-called complete information games [8] form a prominent game class containing so different games like Tic Tac Toe (trivialized and not worth any further consideration), at the one end, and Chess, Go, and Shogi, at the other end. The complexity of complete information games groups them into different classes, because this complexity may be decisive for the way in which a game is played. This is bringing in a perspective which is new, to the author’s best knowledge: Whether or not a particular game is assigned to a game class may depend on the target audience, because some players may be able to master a winning strategy whereas others are not. One might introduce the notion of a player-adaptive categorization. Membership of a game in a game type or a game genre does not depend on the audience.
The question whether or not chance is brought into play by dice rolling or other probabilistic mechanisms is a clearly formal constituent which heavily influences human game playing. Strategy and tactics possibly invoked by human players depend on those settings which establish game classes [43]. The use of the term genre is compatible with its usage in communities dealing with web design issues [42]. Thus, it fits certain needs when speaking about genres of digital games played on the Web. The term ‘adventure game genre’ [16] is sound as well. It might be further desirable to group games according to their historical development reflecting transfer and development of ideas; a further categorization term such as family may be useful. To sum up, the categorization according to type refers to the mechanics of a game, the term class refers to human behavior, and genre characterizes the artistic dimension. Those views depend on each other.
As long as First Person Shooters such as ‘Medal of Honor: Frontline’ and adventure games such as ‘Splinter Cell: Chaos Theory’ or ‘Metal Gear Solid III’ similarly depend on a narrative structure and comparable video technologies, they belong to the same genre. When it comes to human behavior, they may be separated into different classes. Thus, in the phrase stealth adventure, the term stealth addresses a game class. So-called Beat’em Up games (in German: Pr¨ugelspiele) are distinguished both by class and genre; see figure 9 for an illustration case. Last but not least, time deserves its separate attention.
The introduction of time in a formerly timefree game does not change the game type, but adds some constituent. Similarly, the genre may remain unchanged as well. But time–and this is usually the purpose of introducing time into a game–does mostly change the game class considerably, because the human player’s behavior changes under the pressure of time. Consider, for instance, Blitz Chess which is, to some extent, no longer a complete information game. Games may be (semi-)synchronous in the sense that players act in turn. Other games may be asynchronous. Further, persistence is a crucial property surely not present in multi-user role playing games, e.g.
Figure 9: Soul Calibur II: A Scene with Head-Up Information; Player Character on the Right Games may be timed, for instance, by introduction of an egg-timer or anything like that. This does not necessarily change the time very much as known from playing Chess in a tournament. But Blitz Chess (directly translated from the German word ‘Blitzschach’) is a completely different game.
The first computer game, Higinbotham’s ‘Tennis for Two’ (1958), was interestingly not a digital game and, therefore, time was perhaps not discrete in the game (see [34]). But nowadays it seems clear that time in all our games is discrete what makes reasoning about time logically more complex [29].
3.4. Formal Game Concepts Do we need concepts more formal than those introduced in the preceding section?
placement of blocks on the board (colors do not matter). S ⊂ 2{0,1,2... ,9}×{0,1,2... ,18}
We start with a case study–the Rules of Tetris as described in [50], a really great book, where the authors develop Tetris, one of the true classics, step by step until they come to the description of rotating a block by the player’s intervention: The block rotates on its center axis. [ibid., p. 143] Unfortunately, this statement is incorrect, because it is (with the exception of a square block) simply impossible (see figures 10 and 11).
Here we adopt the mathematical custom to denote assignments from elements of B to elements of A by AB and 2 stands for any set of just two elements such as ‘0’ and ‘1’, ‘no’ and ‘yes’, or ‘free’ and ‘occupied’, e.g..
Figure 10: Tetris Illustrated Tetris may be abstractly seen as a timed board game. The board is a set of cells with the standard format 10 x 19. A set of cells is becoming a board by establishing some neighborhood relation. A Tetris board may be formalized as follows:
Figure 11: Rotation according to [50] For particular considerations, the colors of blocks matter. To distinguish blocks, it is most easy to enumerate them subsequently. If this is desired, one may represent game states as
B = {0, 1, 2 . . . , 9} × {0, 1, 2 . . . , 18}
S ⊂ NI {0,1,2... ,9}×{0,1,2... ,18}
A game state in Tetris is characterized by a
with NI denoting the set of natural numbers.
For a given board B, 2B denotes the set of all placements of zeros and ones on the board. Usually, the set of possible game states is a proper subset of all imaginable assignments.
In this model, pieces are not only colored, but also ordered (according to appearance). For a particular game state s ∈ S (figure 10), s(3, 18) = 7, s(4, 18) = 7, s(4, 17) = 7, s(5, 17) = 7, the 7th piece hast just completely entered the board slightly left of the middle. The piece is occupying the four cells (3,18), (4,18), (4,17) , and (5,17) in the uppermost rows which are numbered 18 and 17. For a clockwise 90o rotation of this z-shaped piece, the following two results are possible: s (3, 16) = 7, s (3, 17) = 7, s (4, 17) = 7, s (4, 18) = 7, s (4, 16) = 7, s(4, 17) = 7, s (5, 17) = 7, s(5, 18) = 7. s and s are potential successor states of the original game state s. One usually defines s , but not s to be the state resulting from a rotation as considered–a decision point overlooked in [50]. Formally, every player’s move may be seen as an operator on the game state space S. Every move μ : S → S transforms any given state s into some successor state μs. There may be different admissible moves resulting in different successor states. The null move ν does not change anything. In other words, the null move ν serves as the identity function on the game state space or, if concatenations of moves are studied, as the neutral element on the semi-group of moves. For the moment, we drop the aspect of time. Tetris may be seen as a game for two players. The one player, usually the computer, inserts pieces row-wise into the board beginning with the uppermost row. The piece to be introduced is chosen randomly. The human player has different moves including the null move. The computer moves after insertion consist exclusively in moving pieces row-wise downward until other pieces already on the board are hit or the bottom row is reached. The computer’s standard move γ changes the game state as illustrated for a z-shaped piece as follows.
If the current shape is represented by the cells (i − 1, j + 1), (i, j + 1), (i, j), (i + 1, j) in game state s, where s(i + 1, j) = 0 and s(i+1, j +1) = 0 is assumed (no other piece is hit), the successor state γs is defined by γs(i − 1, j + 1) = 0, γs(i, j + 1) = 0, γs(i + 1, j) = 0, γs(i − 1, j) = 1, γs(i, j − 1) = 1, γs(i + 1, j − 1) = 1. The reader might wish to check the formal representation against the particular case on display in figure 10: i = 4 and j = 17. The formalisms developed so far suffice to correct the error in [50]. Thus, we may keep the remaining part short. Even if we ignore time, we have to admit that the rules of Tetris are a little bit more involved. In some cases, one of the players has permission to perform two subsequent moves without interrupt by the opponent. When the computer inserts a new piece in the top row of the board, the immediately following move is always the computer’s standard move γ. A player scores if a row is completely filled. This property of a game state may be formally represented in different ways. The two following expressions [i] and [ii] [i] [ii]
∀i ∈ {0, . . . , 9} : s(i, j) > 0
9
i=1
s(i, j) > 0
are equivalently expressing that row j is filled. A player scores by removing a completely filled row. As a consequence of such a move, all content above this row is moved downwards accordingly. For a formal treatment, let us denote the move of scoring by removing the filled row j by σ(j). In all Tetris implementations known to the author, a certain rule has been implemented which may be informally circumscribed as follows. Whenever a piece inserted and falling down has the potential of filling more than one row (which has to happen in subsequent steps), the first of the rows filled is not removed immediately. The user has to wait with scoring until the movement of the piece has stopped.
In other words, if the subsequent moves [a]
γ γ σ(j) σ(j + 1)
would be admissible, after the first of these γ moves row j + 1 were already removable. But this is excluded by implementation. The fully synchronous interaction [b] as shown here [b]
Rules of semi-synchronization are known from many other games such as the card game Bohnanza and the digital game Zookeeper.
γ σ(j + 1) γ σ(j)
is forbidden. Instead, semi-synchronization [a] is enforced. The human player is prevent from interrupting the two subsequent standard moves γ of the computer. In turn, the computer does not interrupt two subsequent scoring moves of the human player.
Figure 13: Zookeeper at the Moment of Exchanging the pieces at the Two Positions (3, 2) and (4, 2) We refrain from a detailed discussion of Zookeeper and confine ourselves to a brief comparison to Tetris. At a first glance, Zookeeper appears like a variant of Tetris. A closer look based on our formal concepts introduced reveals that they don’t have too much in common. The most intersting commonality, perhaps, is semi-synchronization. In Zookeeper the human player may exchange the pieces on two neighboring cells in the same row or the same column in case this results in three or more pieces of the same type sitting next to each other in a row or in a column afterwards. In the state on display in figure 13, the panda in cell (3, 2) is exchanged against the hippo in cell (4, 2). As a result, there are three pandas in the cells (4, 2), (4, 3), and (4, 4).
Figure 12: Semi-Synchronization in Tetris A sample case illustrating the above discussion is on display in figure 12 where cutouts of four game states are shown with j = 0. In the second and the third cutout, the human’s move σ(1) would have been possible.
The player scores because three or more neighboring pieces of the same type are removed. In a standard move such as in Tetris, pieces move downwards to occupy empty space. New pieces are inserted randomly. In the case shown in figure 13 it follows immediately a scoring move due to the giraffes then in the cells (3, 3), (4, 3), and (5, 3).
The reader may be interested in looking for alternative moves to the one ongoing as sketched in figure 13. Before the move the panda was sitting in cell (3, 2) and the hippo in cell (4, 2). The actual exchange is denoted by (3, 2) ⇔ (4, 2). How many alternatives to (3, 2) ⇔ (4, 2) do you see in this game state? Which moves are admissible instead? Do you see moves which, after the first scoring move, allow for a second scoring move? There is an appendix with all solutions to these questions.
After the problem has been recognized by the game’s inventors, Segundo Santos and Alberto Serrato, a first basic rule had been introduced. To further alleviate the problem, another rule very similar in spirit has been proposed. That’s what patterns in game design are about.
We complete the present investigation of synchronization and semi-synchronization by a brief reference to Canasta [45]. Canasta is considered one of the hard card games [49]. It is played with two standard decks of 52 cards each and with 4 additional jokers resulting in 108 cards in total. The standard game is played with four players split into two teams. Canasta is a card drawing and melding game which is completely synchronous up to one exception. There are conditions in which the discard pile of cards may be taken by one player. It is quite interesting that this exceptional step to semi-synchronization is essential to the game. The game flow may suffer from only one problem–a player’s reduced hand lasting for several rounds. By repeatedly drawing one card and discarding one, there is no way out. Conditions in which the discard pile may be taken has been introduced to alleviate the problem.
Figure 14: American Football Online Scene So far, we have put emphasis on game states and on moves. These concepts apply to all games including simulation games ranging from Trauma Center: Chaos Theory to the American football game ESPN NFL 2K5 (see figures 14, 15). Several modern digital games have game spaces comparable to or even exceeding in size the game spaces of classics like Chess, Go, and Shogi. Figure 15 is showing only a single character’s parameters. A large number of further parameters such as contract data are left out.
After the game has been invented in 1939, it came to North America in 1950 and almost immediately spread all over the world. Since the game appeared, only a single change to the rules has been established by its first publisher in the US: so-called ‘hot’ cards (‘caliente’ cards). Two such cards are added to the deck. Playing a caliente card allows the player to take the discard pile.
Figure 15: Parameters of a Simulated Player
The step from synchronization to controlled semi-synchronization in Canasta is a prototypical case of dealing with some problem pattern in a game.
The data sets for all players of the two teams involved and a variety of other data such as weather conditions establish a game state. There is no space for going into more detail.
Like in ESPN NFL 2K5, weather conditions are getting more and more popular in recent adventure games. The result is not only a remarkable growth of game spaces, but also a remarkable gain in beauty.
The property of persistence is defined from an agent’s perspective. For a human player, the property of persistence means that the player can rely on stability. When it is the human player’s turn to make a move, nothing changes as long as he does not move. Timed Chess as played in tournaments is mostly persistent (with the exception of a certain final phase of the game) whereas timed Tetris is not. Interesting patterns of game design show in the game tree. The following two screenshots may serve as an illustration.
Figure 16: Winter in the Age of Empires III So far, we have confined ourselves to game states and moves, only. As seen above, we need to understand sequences of moves and related game state transitions, at least. If an initial state is given, the whole space of possibly reachable game states may be seen as a tree with the initial state as its root.
Figure 17: Silent Hill – At the Cross Road
The nodes of the tree are game states reachable by moves from the states before. When in a given state several moves are possible, the corresponding node has a successor node for every move. Leaves of the game state space tree are final game states.
On display in figure 17, the player’s avatar has reached some cross road. Without any player’s move, the next moment (figure 18) shows the avatar a bit further down in the game tree–surely a non-persistent behavior of a very special type.
This tree concept is crucial to mathematical investigations [8]. In a game tree, there may be identical subtrees outgoing from different nodes. This holds also for timed games. If a game is timed, this means that a player’s moves are subject to time-outs. In contrast, when time becomes a parameter occurring in every game state, the game tree does usually no longer contain identical subtrees in different positions. There are a very few exceptions if varying chains of moves lead to identical states which, by chance may be reached at the same point in time. In games with time persistence gets lost. Persistence is a property quite well-studied in control theory. It is particularly important in complex dynamic systems.
Figure 18: Silent Hill – Around the Corner The human player is guided by the system to avoid visiting larger parts of unimportant game states. This system guidance is rarely noticed by the human player. This is another step forward to approach what we will call patterns in game design.
4. Patterns in Game and Play The concepts introduced at the end of the preceding section although only sketched provide a sufficiently firm basis for in-depth studies of patterns in game and play. Before going into more details of the present paper’s pattern approach, let us present a case study–the game named Hex. This game has been invented by Piet Hein in 1942, re-discovered by John Nash in 1948, and brought to the market by Parker Brothers in 1952. It finally gained popularity through Martin Garnder’s great book [25] in 1959. Anshelevich [6] developed the fundamentals of his Hex playing program Hexy which is apparently the strongest ever Hex playing computer program in the world.
The game is complicated because you have a large number of potential moves–about 100 on the average. This is much more than in Chess (40) or Checkers (8). When playing Hex you need to find out certain regularities, because there is no hope to rely on an overall winning strategy. During game play you may experience thousands or more of different game states, but a few substructures will repeatedly occur–patterns. The fun of playing Hex is closely related to the pleasure–perhaps unconsciously–of identifying patterns. That’s what learning is about in figure 7.
Figure 20: Black Placed a New Piece ‘n’
Figure 19: A Standard Size Hex Board
In figure 20, the black player has put another piece (named n, for clarity) on the board. For the sake of discussion, three cells are named a, b, and c, respectively.
The goal of the black player is to connect the two black boarders of the game board by a chain of his black pieces. Similarly, the white player attempts to connect the other two opposite boarders by a chain of white pieces. Both players move in turn by placing one piece on an empty space of the board.
Consider the cell with the new black piece, the two adjacent cells a and b, and the cell with the other black piece adjacent to a and b. These four cells with the black pieces on two of them form an important game pattern. There is no way at all for the white player to prevent black from connecting his pieces.
The game can never end in a draw, because a fully occupied board must have one winning connection. As a consequence, there must be a winning strategy for the first player.
A similar game pattern may be established between the piece marked n and another piece to be placed on the cell named c.
Hex may serve as a suitable case study for several reasons. The rules are very simple. There exist both a conventional board game and computer games in a large variety of implementations. It is played on boards of different size (11 x 11 is standard) Though there is provably a winning strategy for the player who moves first, no winning strategy is known for boards lager than 7 x 7.
What we have on display here (see figure 20) is the simplest relevant game pattern in playing Hex. Based on this atomic pattern, more complex composite patterns may be defined. The computer program Hexy mentioned above [6] is based on an algebra of connectivity patterns. Game AI has recently found out that AI search methods are essential to intelligent game programming [15]. Patterns guide us beyond the limits of AI search.
4.1. Patterns in Human Life No doubt, the human brain may be seen as a pattern recognition mechanism [10, 56]. Human infants enjoy recognizing faces, they enjoy even more recognizing a smiling face. Over millions of years, the human brain has developed to identify repeatedly occurring patterns fast and efficiently. This ability is surely crucial to conceptualization [41], and it may have been crucial as well to survival, in general, because it is of some importance to recognize predators such as tigers even if they differ from each other in many details. The human brain is rewarded by dopamine releases for identifying patterns [56]. To say it more simply, it is a pleasure to recognize regularities. This is deemed a starting point for fun in game design [37]. Recent research in the brain sciences reveals that patterns in human life may have related patterns of neural activation. Some of the investigations are relevant to game research.
In the Prisoners’ Dilemma, humans have to decide whether or not to cooperate. If one player cooperates, but the other defects, this is usually advantageous to the one only who defects. Both might win when cooperating– but you never know . . . Experiments1 have been set up to play the Prisoners’ Dilemma game in subsequent rounds. These experiments show that the decision to cooperate following a cooperative choice by ones partner in the previous round activated the left anterior caudate and the right post-central gyrus as shown in the figure 21. The decision to reciprocate cooperation was also associated with activation in two regions that were activated following mutual cooperation in the reaction epoch: the rostral anterior cingulate cortex and the anteroventral striatum (see [48], p. 398). This report is sound with more recent results about dopamine release related to trust in human cooperation partners [36]. It seems open, at least for the time being, what the results of the brain sciences about different perception of human and computer partners mean to digital games. The future might bring a flood of related insights, if scientists succeed in setting up a concerted interdisciplinary action of research. In the application domain of game analysis and synthesis–call it invention, creation, or design, . . . –one is highly interested in finding out what makes fun to the players [37] and what enables flow [17].
Figure 21: More Brain Activation (Player A) when Cooperating in the Prisoners’ Dilemma Altruism, in general, reciprocal altruism and cooperation in a Prisoners’ Dilemma game, in particular, are studied in [48]. Figure 21 is (re-)published here with the authors’ kind permission.
One approach among others may be to find patterns of activation in the human brain, such as those reported in [48] (see figure 21), which reflect certain social behavior. What about patterns of brain activation mirroring particular activities in game playing such as, for instance, secretly changing a strategy. Suppose those activation patterns are found. One might now turn the experimental setting upside down, trying the implementation of patterns in (digital) game design intended to cause similar patterns of brain activation. 1
It is highly advisible to consult the source [48] for a more comprehensive study and for more depth.
4.2. Semi-Formal Game Patterns It is the author’s strong belief that we do need as much precision as possible when dealing with patterns in game design. The study of semi-formal patterns [9] might be a first step in the right direction. Patterns in the card game Bohnanza are discussed, among others, in [3]. We seize this suggestion and discuss semi-formal patterns in some more depth based on a Bohnanza case study (the illustrations below are from the German version published by AMIGO, the English version in the USA is published by El Grande).
how many bean cards of this variety a player must sell to earn the one, two, three, or four gold coins pictured. There is a certain peculiarity distinguishing Bohnanza from almost all other card games. Players may never change the order of the cards in their hands. Thus, sorting cards by variety or any other means is not allowed. The players must plant cards in the order they received them. When a player draws new cards, he must draw them one at a time and place them behind the last card in his hand.
According to type, Bohnanza is a card game. It belongs to the class of trading games in which the goal is to maximize income in some virtual currency. The story of the game is bean growing. Each player acts as a farmer and plants beans in two or three fields and tries to sell them as profitably as possible. When selling beans, a player earns more gold for more beans of the same variety. On one bean field, a player may only grow beans of a single variety. There are a different number of cards in each variety.
Figure 23: A Player’s Hand with 5 Cards Players draw cards and trade them. At a player’s move, he must plant the first card in his hand in one of his fields. He may also plant his second card. In addition, he may trade the cards he has drawn as well as the cards of his hand. In the case of trading, the order of cards does not matter. Players may even donate cards, but donations need not to be accepted. We refrain from further details and confine ourselves to the following explanation of a few essentials. Assume some player with the hand shown in figure 23 owns the bean fields on display in figure 22.
Figure 22: Bean Growing in Two Fields At the bottom of each bean card is a display named the ‘beanometer’. It indicates how many gold coins a player earns when selling beans of this variety. The numbers indicate
This player can not easily plant his first card. In case another player has bean fields as shown in figure 24, it might be possible to exchange the first card from the player’s in trading or, if necessary, to give it as a donation to the opponent. Perhaps, even the second card can be given away.
Assume that the player with the hand shown in figure 23 would be able to get rid of his first two cards. He were able to plant his soy bean card (in German: Sojabohne) and were not forced to harvest any of his bis bean fields for only one coin or even no payment.
Before we direct the reader’s attention to more formal concepts, let us supplement an aspect obviously missing in the discussion above: modeling the human player. When playing the Bohnanza game, one quite easily experiences different attitudes and styles of playing. This is known from most card games and such games like Poker (Draw Poker or any other of its plenty variants) are famous for it. User Modeling is a discipline of Artificial Intelligence. In the particular domain of e-Learning, for instance, one speaks about learner modeling. Though player modeling is already custom in a number of digital games (see figure 25 for a player model in the American football game ESPN NFL 2K5 where statistics of the players’ previous behavior are visualized), it is not yet an established term and far from being an established research direction.
Figure 24: An Opponent’s Bean Fields The pattern we have recognized in this case study is obvious. Give cards away, even as donation when necessary, to become able to play those cards which support your own agricultural strategy. The hand of each player can be abstracted as a list of cards. The fields are pairs of sets. Each set may be empty or characterized by a bean variety and a number. With such an approach in mind, game states may be completely formalized in the style demonstrated in the preceding section. Patterns may be found in lists of cards establishing a player’s hand and related mappings to all players’ bean fields. But for the purpose of successfully playing Bohnanza, an only semi-formal expression suffices: Give cards away until the first card of your hand fits your bean fields. Furthermore, if possible, give even more cards away until the first two cards of your hand fit your current plantation. Then plant your cards. Such a pattern of game playing may lead to success and results in pleasant and peaceful, but highly competitive games.
Figure 25: Aspects of Player Modeling Naturally, the key question in user modeling is always what to model. Human behavior is so rich that every modeling must necessarily leave many important aspects out. Ultimately, the choice one has depends both on the particular game and on the view one has at human players. Whatever information you can acquire about a human player may be used as a feature reflected within a player model. A theory of player modeling goes beyond the limits of the present paper. We assume subsequently any modeling that may reflect aspects of the player’s playing history and of anything else available.
4.3. Formal Game & Play Patterns According to our thoughts about player modeling, a so-called play state is a game state extended by state information about all the players involved. In general, formal patterns may be based on • game states and classes of game states, • play states and classes of play states, • state transitions and classes of them, • set inclusions among these constituents, • frequencies of the occurrence of any of these constituents, and, in addition, • assignments of meaning to game states,
Skat is a trick game for three players with a bidding phase. After the bidding phase, the winner plays against the other two players. He has the right to choose the trump suit. The initial state of the game is determined by 10 cards in each player’s hand and two cards faced down on the table. These two cards are named the skat. The winner of the bidding takes the skat and, in turn, puts two cards from his hand faced down on the table. These two cards are added to his tricks in the end when counting cards. The total deck of cards counts for 120 points (Ace – 11, 10 – 10, King – 4, Queen – 3, Jack –2). The single player needs 61 points to win a game.
• assignments of meaning to play states, • assignments of meaning to transitions. Meaning may be something informal such as ‘being fun’. Case studies in the following section will make the approach clear. A large amount of the twohundred patterns listed in [9], which are presented in a truly informal way, may be rewritten in formal terms using such terms as above. ‘Level’ ([ibid.], pp. 60–62), for instance, may be formalized as a class of game states. There are typically only a very few or even only a single transition between different level classes. To get a very first impression of the present paper’s formal approach, consider the card game Skat which is sometimes called ‘the German national game’ [49]. Skat has been invented (as a derivative of Tarock, which is not to be confused with Tarot) in the early 19th century and went through several stages of development until a certain stabilization in 1928. The changes to the original game are telling. From the early beginning, Skat is played with a deck of 32 cards consisting of the four suits clubs, spades, hearts, and diamonds with the cards from 7 to 10, Jack, Queen, King, and Ace.
Figure 26: A Recent Skat Deck published by Courtesy of the Producer Altenburger ASS The player sitting left to the dealer leads the first trick. Players must follow suit if possible; if not they may throw any suit they wish. The trick is won by the highest card of the suit led unless a trump is played, in which case the highest trump wins. The winner of one trick leads the next. The order of cards in a suit, originally, was Ace – 10 – King – Queen – Jack – 9 – 8 – 7. In the early days of Skat (for about 20 years, at least), there were no other games than those with simply a chosen trump suit. Let us–rather informally–assign to initial game states, when it applies, the meaning ‘impossible to win for a single player’. Though this, naturally, may depend on players and their behavior, it is a sufficiently clear concept. The frequency of initial states impossible to win for a single player–however one might define that in detail–is surely above 50%.
This insight is clearly a statement about classes of game states, about their inclusion relation, and about frequency. Up to the meaning, it is a completely formal concept. The informal meaning may be replaced2 by a variety of formal criteria of card distribution; we refrain here from going into those tedious details. As an intermediate summary, we see that Skat in its early days has been suffering from the appearance of a quite unpleasant pattern: most of the games were difficult or even impossible to win for the single player. This particular pattern shows as the quotient of the cardinalities of two set of game states. As a consequence, within a few years (about 20 or less), the so-called null game has been introduced. This is a completely different game. The order of the cards is changed to Ace – King – Queen – Jack – 10 – 9 – 8 – 7. Players try to minimize the points they get in their tricks. The invention of the null game has alleviated the problem of initial states in which nobody wants to play. The critical quotient under consideration became smaller by removing the null games from the games counted.
Though the reasoning that lead to the above mentioned extensions of the rules of Skat in the 19th century was not mathematical, but simply based on the experience of playing, it may be circumscribed in formal terms. There are game patterns behind. Even the seemingly most cumbersome games make no difference. Recall the game Silent Hill II (figures 17 and 18). There are patterns galore. When your avatar moves along roads, through corridors such as the one shown in figure 27 and the like, it may happen that you find some potion 3. Those things are necessary to keep your avatar ‘alive’. There is a simple pattern invoked. Suppose you perform subsequent steps of a running action which, in fact, are player moves ρi , ρi+1 , . . . Whenever you pass some potion, the system inserts some move of turning the avatar’s head toward the object of interest. That means that the sequence of moves is modified to ρi , σ, ρi+1 , . . ., where σ means a signalizing movement of the avatar introduced by the computer system.
To further increase the fun in playing Skat, an Ace game has been invented shortly after the null game. In the Ace game, there is no trump suit. No further changes apply. The final substantial extension of the rules was to introduce the Jacks as extra trump in every suit game and in the ace game. The effect is obvious. In a game with any trump suit, the number of totally available trump cards increases from 8 to 11. The initially discussed problem is further alleviated. 2
Just for illustration, we give one list of features establishing an initial game state impossible to win for a single player. (a) No player has more than two Aces. (b) no player has more than three cards of one suit, (c) no player has less than two cards of one suit, (d) who has two Aces, has at most one 10. Such a constellation is very likely (it may be numerically described) and determines a class of initial game states formally. There are several more completely formal descriptions of comparably bad initial game states.
Figure 27: Some Dark Way in Silent Hill II There are many more patterns occurring in digital games that can be perfectly expressed in formal terms. In adventure games you frequently need keys to pass doors, use elevators, and so on. For the sake of the player’s fun and success, many keys are hidden close to the place where they are needed. In Silent Hill II (Part 2: The Appartement) in room 208 you find a key for room 202 which 3
There are drinks and in modern adventure games you frequently find first aid kits.
is needed immediately after. When you hide in a cabinet, you find a key to the court which is needed a few steps later. When you reach the fire escape, the key is used which you find shortly before in room 303. In room 108 you find the key to the blue door which has to be opened next, and so on . . . The pattern is obvious. It is by far not as boring as it appears here. In the flow of the game, the human player is usually not aware of the simplicity of the underlying patterns that allow him to succeed. The pattern relating the finding of a key and the usage of a key in an adventure game may nicely be described in terms of game states and moves in the game tree. The evolution of games and game playing takes place within the overall evolution of culture in our human society. Patterns in games are frequently occurring forms that are repeated for several reasons. One reason for the repetition of a pattern is that it works well in its area–that it contributes to fun in game playing. Another reason for the reuse of a pattern is its ease of reproduction.
5. Patterns for Understanding and Creating Games Using pattern conceptss for analyzing and for synthesizing games me be understood as memetic engineering. The perspective of memetics is becoming increasingly more important, because nowadays meme media technologies are available [60] to make the location of memes in IT systems explicit. Game playing is seen as just one application domain such as many other domains and, consequently, digital games are treated as IT application systems. The present section aims at demonstrating memetic engineering in just one case study. How to design a game such that it is fun? Where and how to locate patterns? SDI is a board game for any number of two or more players. It has been designed by the author almost 20 years ago. SDIcore is a reduced version specified with experimental explorations in mind. It has been quite intensively studied in settings of three players [31].
Patterns that do not work well and those that are not easy to communicate, to imitate, to modify and to adapt, will hardly be reused frequently.
The board is a sequence of 32 subsequent squares. The last 5 squares form the goal area. There are a few extra event squares not mentioned here for simplicity.
Although it seems that game development is a creative area such as any other artistic field, it is also subject to the laws of evolution. Only those ideas survive that are fit enough. As Dennett says, evolution–incl. evolution of games–is design out of chaos [21].
Every player has three pieces to move. A player rolls a die and chooses any piece to move forward exactly as many squares as the die shows points. After a 6 came up, the player rolls the die again and moves again, but this time just the piece that has been moved before.
Patterns may be seen as units of knowledge which assume a definite form. In the prehistoric days of game playing, patterns could only be inherited from generation to generation by means of human doing. To survive for a long time, much luck and an intense activity such a religious rites were necessary [20]. Different human inventions such as printing technology are supporting the further spread of game patterns. Paterns in games and in game playing are (carriers of) memes in the sense of Dawkins [20] and Blackmore [10].
The selection of a piece to be moved is only limited by the rule that no piece in the goal area may be moved again. The goal is to fill the goal area of the last five squares. Sitting on one of these squares at the end of the game gives 5, 4, 3, 2, and 1 score points counting backwards from the top. When the last square in the goal area has been filled, it follows exactly one more round of rolling the die and, perhaps, moving pieces before the game ends. The crucial rule of the goal determines what
happens when a piece hits another piece to the square to which it is moved: A piece hit is shifted backwards to the next empty square. From the initial part of the linear board, a piece may be pushed off the board. It may be brought back to the board at any later move of its player. In a similar way, pieces may be pushed out of the goal area. Though pieces are not allowed to move when being in the goal area, they may be moved again after being pushed out.
There, Y hits G. The piece is moved backward to the empty square k.
Lets assume to call the three game players Red (R), Green (G), and Yellow (Y). Every player has three pieces that are not distinguished within one color.
What is of interest in the game are ‘clusters where pieces are loitering’. Figure 28 shows the formation of a cluster of size 5. For three players, only clusters of size 4 or larger are of interest.
A state of the game is characterized as an assignment of up to 3 pieces of each color to exactly one of the squares. In other terms, a state of the game may be seen as a partial mapping from the set B = {1, 2, . . . , 32} into the set {R, G, Y }. If s is a game state, the cardinality of s−1 (C) for any of the three colors C ∈ {R, G, Y } is bounded by 3. Every move is a state transition. If player C (for C ∈ {R, G, Y }) in state s rolls a die which brings up a number n, the player may choose any of her/his pieces on the board. A piece on the board is characterized by s(m) = C. In case the piece is not yet on the board, one simply assumes m = 0. The successor step s of s is defined as follows. • s (m + n) = C • s(m) is removed from the graph of the mapping. • For any color C (where C = C is admissible) with s(m + n) = C a certain conflict occurs. C hits C . C is moved backwards to the next empty square. Let k = max{z | z < m + n ∧ s(z) undef.}, then one sets s (k) = C . • For all other squares x not mentioned above, it holds s (x) = s(x). This is illustrated below. Player Y has rolled a die which came up with a five. Y decided to take its second piece in the left part of the linear game to move it 5 squares forward.
Figure 28: A State Transition in SDIcore
It turns out that humans when playing SDIcore have a tendency towards building clusters–a type of patterns we are interested in. Before presenting our results, lets say more precisely what a cluster is. Formally, a cluster in a game state s is a set of squares CL = {k, k + 1, . . . , k + l} such that every s(x) for x ∈ CL is defined. l − 1 is the size of the cluster. A player C has been causing a cluster, if this cluster occurs in game state s after C’s move. In Figure 28 is illustrated how Y has caused a cluster of size 5. There is the author’s working hypothesis, that humans tend to cause clusters. Even a little bit more explicitly, human players cause clusters, although this is not correlated with winning the game. In other words, clusters in the SDIcore game are a type of pattern exhibiting what makes fun. Here, we report only three basic experimental settings: (i) Humans playing the game, (ii) computerized simple strategies playing against each other, and (iii) more advanced computerized strategies playing against each other. After reporting the experimental results, we try to find an interpretation relevant to game design. We confine ourselves to a closer investigation of clusters of size 4, 5, and 6, although also larger clusters have been observed.
When humans play, clusters have been caused with the following frequency w.r.t. the total number of played games. • 93.54% clusters of size 4 • 87.09% clusters of size 5 • 48.39% clusters of size 6 It turns out that there is neither a positive nor a negative correlation of clustering with winning the game. The following five figures demonstrate this quite well. Humans cause clusters for fun, but not as part of a certain successful strategy; it is not advantageous. • 61.3% The winner caused clusters. • 25.8% The winner caused most clusters. • 22.6% The player neither winning nor loosing caused most clusters. • 16.1% The looser caused most clusters. • 58.1% The looser caused clusters. To find out whether or not clustering necessarily takes place in the game, completely formal strategies have been tried out in comparison to the experiments of human game playing. The results are reported in [31] in much detail. For the purpose of the present paper, a short summary shall do: Computers do not like clustering as much as humans do. When humans play together with computers, the number of occurring clusters is smaller than in games among humans only, but higher than in games among computers only. So far, this is not very much surprising. The more surprising results show in games between humans and computers when analyzing who caused the clusters. Five out of seven clusters are caused by the computers. Loosely speaking, computers have more fun when playing with humans. The author’s final hypothesis is that clusters in SDIcore are just an indication for something human players like very much, perhaps even unconsciously. To have fun in playing SDIcore, it is not necessary to win. This is consistent with Csikszentmihalyi’s concept of flow [17].
This section is closed by a brief discussion of memetics. There is a simple idea of playing the game in SDIcore: the way in which a piece is treated that has been hit by another piece. it is not taken off the board as in many other board games. Instead, it is moved backward to the next empty cell. In the author’s opinion, this is worth to be named a meme. In playing SDIcore, this pattern occurs frequently. One might even say that this is the most particular idea players learn when playing this game. In addition, this pattern is quite easy to communicate and to remember. The formal term underlying this pattern in the chosen calculus is simple. If a piece is hit in game space s on the cell numbered x, one has to move it to y = max{z | z < x ∧ s(z) undef.}. The pattern has side-effects. According to the definition, the target cell y is next to another cell y + 1 which is not empty. Thus, as we have seen above, pieces which are hit and moved away keep in contact with others. In every implementation of SDIcore, these ideas are implemented. They are written down in bits and bytes. The procedural representation of the formula above to find the cell y is carrying something of the inner clustering mechanism. The same applies to the game Hex discussed above. Hexy’s strategy is sitting in representations of digital circuits describing knowledge about patterns as shown in figure 20. In complex digital simulation games such as ESPN NFL 2K5 rules are represented how a team’s performance changes in dependence on the weather conditions. Teams from the South, e.g.e, are degraded in some respect in cold weather conditions. The ideas are, so to call, sitting in certain digital media object representing rules, for instance. Many of the key ideas that establish a good game are locally represented in certain digital media objects. We are not used to ask for them–we should learn to do so.
6. Summary, Conclusions and Outlook The present closing section of this paper is intended to direct the audience’s attention to the complexity of the field of digital games. The need for interdisciplinary research and development is stressed.
6.1. Breadth and Width In the introductory section, we have seen a few figures from the game market as well as a few results illustrating the impact of game playing on aggressive thought and behavior. Naturally, we had to keep the debate short for several reasons such as space, time, and readability. Many issues briefly touched in the present paper deserve a much deeper discussion. Take, for instance, the problem of game playing and its social impact. There is, naturally, no deterministic connection between playing violent games and aggressive behavior. Further aspect such as the player’s self-esteem come into play [65]. The social impact of digital game playing has a large variety of facettes including even fiscal aspects. Linden Lab, an enterprise in the online game market, has equipped its game Second Life with a virtual currency called the Linden Dollar (L$, for short). When typing these lines, IGE.com was selling 5 000 L$ for 18.99 $. During the hype of the .com business a few years ago, leading financial institutions have been dreaming of inventing token money such as Digicash– they all failed badly. But the online game market made it happen, with currently unforeseeable economic and legal side-effects. Pondering the market perspectives and the social impact of current digital games makes the relevance of the topic obvious. Digital games are not forming a toy reserarch area. This is serious. No doubt that every serious research and development area needs disciplinary depth. But which questions to attack first? Whom to consult? With whom to cooperate? Most of the central questions in the field require a sufficiently comprehensive point of view.
6.2. Integrating and Focusing When a field is so diverse, how to focus? When there are so many different viewpoints to be taken into account, how to unify? Memetics [10, 20, 21] is the author’s favored starting point. To arrive at memetics seems very natural. The investigation of patterns in game design leads to the question what patterns are. Shall we consider more or less everything that appears frequently a pattern such as exercised in [9]? The author’s introduction of types, classes, and genres and, in addition, the separate treatment of time leads to an overall picture of finer granularity. In this picture, patterns rely on concepts like game state, play state, state transition, and classes of those concepts. Patterns are quite specific. Going this way of systematization, we arrive at the crossroads where the question arises which regularities are worth to be called a pattern. Notice that we do not ask what a pattern is, but what is worth to be called a pattern. From the memetic point of view, it makes sense to ponder about concepts that are likely to be carried over, to be reused, to be modified, adopted and adapted. Those carry knowledge of some generality and value– memes. An integration of disciplines may serve as a guideline how to proceed. We are interested in ideas that are likely to result in fun [37] or even in flow [17]. Driven by these motivations, we direct our attention to patterns small enough and clearly enough distinguished from all the many details around which, firstly, may be related to the quality of games and play in particular cases and which, secondly, are likely to be reusable. The present paper can only exemplify this approach. So, we did arrive at patterns like steps from synchronization to semisynchronization, insertion of signalizing computer moves, generosity in donating cards to other players, and many others. Those pattern carry general ideas; they are easy to imitate and may be stated formally.
6.3. Patterns Interdisciplinary We are focusing patterns in game and play, but we know also, that the brain sciences found patterns in the brain’s activation that correspond to social behavior [2, 36, 48].
games are not really fun to play–they miss the point and are no games at all. As soon as we have implemented our first digital games within an IntelligentPad framework [60], we might be able to show our patterns of game design sitting in meme media objects. They are already there, but they are still hiding in scripts and codes of varying depth. Meme media technology may pay back in the future to its application field of digital games by extraction of digital game knowledge.
Acknowledgement
Figure 29: Brain Activation in Feeling Trust Figure 29 illustrates the flow of activation in the human brain reaching first the fusiform gyrus and the superior temporal sulcus, proceeding to the amygdala and to the insula when trust is experienced in some series of experimental settings. As argued in preceding sections, we would like to relate patterns in game and play to patterns in brain activation. There might be still a long way to go. On this way, a number of exciting questions occur. Investigations as in [36] lead to the hypothesis that humans usually do not trust in computers as much as they can trust in other humans. Does this change in the world of online games where you never know who is a ‘non-player character’ (NPC, for short) and who is a human’s avatar? Does the human perception of the world change so drastically under the impression of living in a global and digitally networked world? If it is true that we construct what we consider to be the world within the steady interaction with the environment, then next player generations might develop different patterns of perception. Or not? There are more dreams around such as employing games for pedagogical purposes [52]. But most of the current pedagogical
Many thanks to Jochen F. B¨ohm for uncountably many demonstrations and hints– students always know it better, especially when it comes to practical game play and mastery of the technology.
Appendix A – Zookeeper There are the following nine alternative moves in the game state discussed by means of figure 13: (2, 1) ⇔ (2, 2) (4, 1) ⇔ (5, 1) (7, 1) ⇔ (7, 2) (8, 1) ⇔ (8, 2) (6, 3) ⇔ (6, 4) (6, 5) ⇔ (6, 6) (5, 6) ⇔ (5, 7) (5, 7) ⇔ (5, 6) (4, 7) ⇔ (4, 8)
panda and frog hippo and elephant hippo and giraffe lion and hippo lion and hippo panda and elephant frog and hippo hippo and frog frog and giraffe
In two of these cases, after the first scoring move a second one becomes possible. Consider (5, 6) ⇔ (5, 7): The first scoring move removes the content of the cells (3, 7), (4, 7), (5, 7), (6, 7) (four frogs). Next, the three giraffes in (4, 5), (4, 6), (4, 7) allow for one additional scoring move. Consider (5, 7) ⇔ (6, 7): The first scoring move removes the content of the cells (3, 7), (4, 7), (5, 7) (three frogs). Next, as in the case above, there are three giraffes in (4, 5), (4, 6), (4, 7) allowing for one additional scoring move.
Appendix B – Games The following games are mentioned within the paper. When some particular version is referred to, e.g. Soul Calibur II instead of just Soul Calibur, this is an attempt to be fairly correct, because the author has not been able to exercise all variants of all games under consideration. Age of Empires III Bohnanza Checkers Chess Civilization III Clue (originally: Cluedo) El Grande ESPN NFL 2K5 Go Grand Theft Auto III Hex
References [1] Chronic. A report on the state of teen driving 2005. Technical report, Allstate Foundation, 2005. [2] R. Adolphs. Trust in the brain. nature neuroscience, 5(3):8–9, March 2002. [3] G. Aleknevicus. Player interaction in games. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], March 2003. [4] G. Aleknevicus. Deduction games 2.0. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], September 2005. [5] C. A. Anderson. An update on the effects of playing violent video games. Journal of Adolescence, 27:113–122, 2004.
KickReal Medal of Honor: Frontline Metal Gear Solid III: Snake Eater Monopoly MUD1 Nine Men’s Morris Peg (Draw) Poker Prisoners’ Dilemma Reversi (a.k.a. Othello) Risk Godstorm Scrabble SDIcore Settlers of Catan Shogi Silent Hill II Skat Soul Calibur II Splinter Cell: Chaos Theory Tennis for Two Tetris Tic Tac Toe Trauma Center: Under the Knife Treasure Zookeeper
[6] V. V. Anshelevich. The game of hex: An automatic theorem proving approach to game programming. In Seventeenth National Conference on Artificial Intelligence (AAAI-2000), pages 189–194. AAAI Press, 2000. [7] L. Barkhuus, M. Chalmers, P. Tennent, M. Hall, M. Bell, S. Sherwood, and B. Brown. Picking pockets on the lawn: The development of tactics and strategies in a mobile game. In Proc. Ubiquitous Computing (Ubicomp), Tokyo, Japan, volume 3660 of LNCS, pages 358–374. Springer, 2005. [8] J. Bewersdorff. Luck, Logic & White Lies. The Mathematics of Games. Wellesley, MA, USA: A K Peters, 2005. [9] S. Bj¨ork and J. Holopainen. Patterns in Game Design. Hingham, MA, USA: Charles River Media, 2004. [10] S. Blackmore. The Meme Machine. Oxford University Press, 1999.
[11] A. Blass, Yu. Gurevich, L. Nachmanson, and M. Veanes. Play to test. Technical Report MSR-TR-2005-04, Microsoft Research, April 2005. [12] B. J. Bushman and C. A. Anderson. Violent video games and hostile expectations: A test of the general aggression model. Personality and Social Psychology Bulletin, 28(6/7):1679–1686, June/July 2002. [13] R. Caillois. Man, Play and Games. Free Press of Glencoe, Inc., 1961. [14] N. L. Carnagey and C. A. Anderson. The effects of reward and punishment in violent video games on aggressive affect, cognition, and behavior. Psychological Science, 16(11):882–889, 2005. [15] A. J. Champandard. AI Game Design. Synthetic Creatures with Learning and Reactive Behaviors. Indianapolis, IN, USA: New Riders, 2003. [16] C. Crawford. The Art of Computer Game Design. 1982. [17] M. Csikszentmihalyi. Flow: The Psychology of Optimal Experience. Harper Perennial, 1991. [18] M. Csikszentmihalyi. Beyond Boredom and Anxiety. Experiencing Flow in Work and Play. Jossey-Bass Inc. Publishers, 2000. [19] G. Cumberbatch. Video violence. Villain or victim? Technical report, The Video Srandards Council, 2004. [20] R. Dawkins. The Selfish Gene. Oxford University Press, 1976.
[23] J. Fritz. Das Spiel verstehen. Eine Einf¨uhrung in Theorie und Bedeutung. Weinheim & M¨unchen: Juventa, 2004. [24] J. B. Funk, H. Bechtoldt Baldacci, T. Pasold, and J. Baumgardner. Violence exposure in real-life, video games, television, movies, and the internet: is there desensitization? Journal of Adolescence, 27:23–39, 2004. [25] M. Gardner. The Scientific American Book of Mathematical Puzzles and Diversions. New York, USA: Simon and Schuster, 1959. [26] C. Geiger, V. Paelke, and C. Reimann. Mobile entertainment computing. In S. G¨ober et al., editor, TIDSE 2004, volume 3105 of LNCS, pages 142–147. Springer, 2004. [27] D. A. Gentile, P. J. Lynch, J. R. Linder, and D. A. Walsh. The effects of violent video game habits on adolescent hostility, aggressive behaviors, and school performance. Journal of Adolescence, 27:5–22, 2004. [28] M. D. Griffiths, M. N. O. Davies, and D. Chappell. Online computer gaming: a comparison of adolescent and adult gamers. Journal of Adolescence, 27:87–96, 2004. [29] Yu. Gurevich. Zero-one laws. In G. Rozenberg and A. Salomaa, editors, Current Trends in Theoretical Computer Science, volume 40 of Series in Computer Science. World Scientific, 1993.
[21] D. C. Dennett. Darwin’s Dangerous Idea: Evolution and the Meanings of Life. New York: Simon & Schuster, 1995.
[30] S. H´ebert, R. B´eland, O. DionneFournelle, M. Crˆete, and S. J. Lupien. Physiological stress response to videogame playing: the contribution to builtin music. Life Sciences, 76:2371–2380, 2005.
[22] P. Faidutti and Branham. Deduction games. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], December 2000.
[31] K. P. Jantke. Knowledge evolution in game design – just for fun. In CSIT 2006, Amman, Jordan, April 5-7, 2006, 2006.
[32] J. Juul. A Clash between Game and Narrative. PhD thesis, University of Copenhagen, 1999. [33] R. W. Kaye. Minesweeper is NPcomplete. Mathematical Intelligencer, 22(2):9–15, 2000. [34] S. L. Kent. The Ultimate History of Video Games. New York, USA: Three Rivers Press, 2001. [35] M. J. Koepp, R. N. Gunn, A.D. Lawrence, V. J. Cunningham, A. Dagher, T. Jones, D. J. Brooks, C. J. Bench, and P. M. Grasby. Evidence for stratial dopamine release during a video game. Nature, 393:266–268, 1998. [36] M. Kosfeld, M.AND Heinrichs, P. J. Zak, U. Fischbacher, and E. Fehr. Oxytocin increases trust in humans. nature, 435:673–676, 2005. [37] R. Koster. A Theory of Fun for Game Design. Scottsdale, AZ, USA: Paraglyph Press, Inc., 2005. [38] B. Krah´e and I. M¨oller. Playing violent electronic games, hostile attributional style, and aggression-related norms in german adolescents. Journal of Adolescence, 27:53–69, 2004. [39] W. Kramer. What makes a game good? The Games Journal, http://www.thegamesjournal.com, [02/01/2006], July 2000. [40] J. Kubitzki. Auto- und MotorsportVideospiele sowie Reparatur- und Tuningverhalten bei 13- bis 17j¨ahrigen m¨annlichen Jugendlichen. Technical report, Allianz Zentrum f¨ur Technik GmbH, 2004. [41] G. Lakoff. Women, Fire and Dangerous Things. What Categories Reveal about the Mind. The University of Chicago Press, 1987.
[42] T. Lavie and N. Tractinsky. Assessing dimensions of perceived visual aesthetics of web sites. Int. J. HumanComputer Studies, 60:269–298, 2004. [43] L. Levy. The genesis of a game. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], February 2002. [44] H. J. R. Murray. History of Board Games other than Chess. Clarendon Press, 1952. [45] P. E. Orbanes. The Canasta story. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], August 2000. [46] S. Pappata, S. Dehaenne, J. B. Poline, M. C. Gregoire, A. Jobert, J. Delforge, V. Frouin, M. Bottlaender, F. Dolle, L. Di Giamberardino, and A. Syrota. In vivo detection of stratial dopamine release during reward: A PET study with [11 C]raclopride and a single dynamic scan approach. neuroimage, 16:1015– 1027, 2002. [47] D. Ravitch and J. P. Viteritti, editors. kid Stuff. Marketing Sex and Violence to America’s Children. The Johns Hopkins University Press, 2003. [48] J. K. Rilling, D. A. Gutman, T. R. Zeh, G. Pagnoni, G. S. Berns, and D. K. Clinton. A neural basis for social cooperation. Neuron, 35:395–405, July 2002. [49] S. Sackson. Card Games around the World. New York, USA: Dover Publications, 1981. [50] K. Salen and E. Zimmerman. Rules of Game. Game Design Fundamentals. MIT Press, 2003. [51] K. Salen and E. Zimmerman, editors. The Game Design Reader. A Rules of Play Anthology. The MIT Press, 2005.
[52] L. Sch¨afer, A. Stauber, and B. Bokan. StoryNet: An educational game for social skills. In S. G¨ober et al., editor, TIDSE 2004, volume 3105 of LNCS, pages 148–157. Springer, 2004. [53] D. Shapiro. Boards. The Games Journal, http://www.thegamesjournal.com, [02/01/2006], February 2005. [54] J. L. Sherry. The effects of violent video games on agression. a metaanalysis. Human Communication Research, 27(3):409–431, July 2001. [55] M. Spitzer. Lernen. Gehirnforschung und die Schule des Lebens. Spektrum Akademischer Verlag, 2002. [56] M. Spitzer. Vorsicht Bildschirm! Elektronische Medien, Gehirnentwicklung, Gesundheit und Gesellschaft. Klett, 2005. [57] P. Spronck. Adaptive Game AI. Maastricht: Universitaire Pers, 2005. [58] B. Suits. The Grashopper: Games, Life and Utopia. Godine Press, 1978. [59] B. Suits. Construction of a definition. In K. Salen and E. Zimmerman, editors, The Game Design Reader. A Rules of Play Anthology, pages 172–191. The MIT Press, 2005. [60] Y. Tanaka. Meme Media and Meme Market Architectures. IEEE Press and Wiley-Interscience, 2003. [61] E. Uhlmann and J. Swanson. Exposure to violent video games increases automatic aggressiveness. Journal of Adolescence, 27:41–52, 2004. [62] M. Wallace. In celebration of the inner Rouge. the escapist, http://www.escapistmagazine.com/issue/8/3 [03/02/2006], February 2006. [63] P. Watzlawick, J. H. Beavin, and Jackson D. D. Menschliche Kommunikation. Formen, Sto¨ rungen, Paradoxien. Verlag Hans Huber, 1969.
[64] R. Weber, U. Ritterfeld, and K. Mathiak. Does playing violent video games induce aggression? Empirical evidence of a functional magnetic resonance imaging study. Media Psychology, 8:39–60, 2006. [65] G. D. Webster and L. A. Kirkpatrick. Behavioral and self-reported aggression as a function of domain-specific self-esteem. Aggressive Behavior, 32:17–27, 2006. [66] D. Williams and M. Skoric. Internet fantasy violence: A test of aggression in an online game. Communication Monographs, 72(2):217–233, June 2005. [67] J. P. Zagal, M. Mateas, C. Fern´andezVara, B. Hochhalter, and N. Lichti. Towards ab ontological language for game analysis. In DIGRA 2005 Conference: Changing Views – Worlds in Play. Digital Games Research Association, 2005.
