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Subject: The Metaphysics of Games rss

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Tuomas Korppi
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Inspired by some debate in the General Gaming forum, I took some time to translate an old text of mine, where I describe my gaming ethos. I have quite a lot of experience in Bridge and Go clubs, and it seems to me that the players there agree with me how the game should be played, even if they wouldn't present it as a theory as I do. So the document does two things: Describe game play at a club level (as opposed to tournament level, where we only scratch the surface) and show that my ethos follows from simple principles.

I challenge the proponents of different gaming ethoses to derive their ethoses similarly from simple principles.


The Metaphysics of Games, part 1
---------------------------------

In this text I study the metapysics of games. We start by making concepts exact. The word game can mean either of two things. First, it can mean a certain type of activity determined by rules. Examples of such games are Chess, Go and Pool. Second, the word game can mean an individual match. Examples of games in this sense are the game of go played by Honinbo Dosaku and Yasui Senchi 19. 11. 1693 in Shogun's palace and the game of Hex I played in in Internet (http://www.littlegolem.net/jsp/game/game.jsp?gid=902999), which started 1.7.2008 and ended 21.7.2008, and which I won. For clarity, we use the word game only in the first sense, and we call the games in the second sense matches.

In this first part I try to characterize, what is a game in the first sense. First I motivate and give a characterization, which works for a limited set of games (that are usually called board and card games). In the second part I present critique for my characterization in the case where we do not limit ourselves to that limited set.

We start by studying games such as chess, checkers and go. We see that the games are played using playing equipment (board and pieces) according to rules. So our first candidate for a characterization is that the game is determined by playing equipmant and rules.

However, we note that not all matches use physical playing equipment. For example in the match of Hex I linked above, there was no board or pieces as physical entities. They were located in the memory of a computer. If we study correspondence chess, we note that each player has his own board that have the same situation of the game. The players are not physically present, they rather mail moves to each other, and illustrate the state of the match each on his own board. It is also in principle possible, although practically cumbersome, to play without playing equipment so that the players announce the moves verbally and imagine the board in their minds.

The example of correspondence chess presented above leads us towards the characterization of a game I want to give. In correspondence chess, you use the board to illustrate an abstraction, and that abstraction is essentially the game.

What is this abstraction about? In the beginning, we noted that a game has playing equipment and rules. Then we noted that the playing equipment is irrelevant to the definition of the game. So we are left with the rules. Could it be that the rules characterize the game. Not at least in a one-to-one way, because one game can have several rule texts, which describe the same game but differ in wording. Could a game be then an abstracted collection of rules, where the details of wording have been "abstracted away?"

Now we are close to the characterization I am going to end up with. There are, however, two problems left:

* It is artificial to identify a game with rules, since game is not rules, but rather a thing described by the rules.

* The collection of rules of any game consists of two types of rules.

At this moment, we do not know what a game is, except that it is something abstract, illustrated with playing equipment and described by the rules. We continue by analyzing the two types of rules.

I give examples of the two types:

(1) In chess, the bishop moves arbitrarily many squares diagonally, but it is not allowed to jump other pieces.

(2) In chess, a move is made and you are not allowed to take it back, once the piece has touched the destination square.

The difference between these types of rules is that if you play chess so that you do not have rule (2) (but, for example, the move is judged made once you release the piece), the game is still chess. Rule (2) is also not obeyed in internet chess, where pieces are moved with mouse clicks. If you do not have rule (1) (but, for example, the bishop is allowed to move only one square diagonally), the game is not chess, but a variant of chess.

So, the rules can be divided in two categories. One class defines the game and the other does not. Next I am going to make a claim that is central to this text:

The rules of a game can be divided in two classes. The first class describes the game as an abstraction. More accurately, it describes the natural laws of a small imaginary world. (I'll explain this more later on). The second class describes how to approximate that abstraction in the real world with an adequate accuracy, or in other words, how to build a simulation of that imaginary little world into the reality.

This is my answer to the question "What is a game?" asked in the beginning of this text: Small imaginary world with its own natural laws. (I do not claim that any small imaginary world with its own natural laws is a game, but the exact characterization for when a small imaginary world is a game is not interesting. I simply claim that for each game there is a small imaginary world that can be identified with the game.)

I have claimed that part of the rules of a game characterize the natural laws of an imaginary world. I motivate my claim by describing that world in the case of chess. The space in the chess world is two-dimensional and discerte. It is eight places long and eight places wide. Each place can hold one piece, and the location of the piece is uniquely deterimined by telling in which place it is. A piece can be a king, a queen, a rook, a knight, a bishop or a pawn. During a match, the pieces move on the board. The first move is made by white, the by black, then by white and so on. With one move, the bishop moves diagonally arbitrarily many places, but it is impossible for it to jump over other piences. And so on.... I hope that the reader has at this point understood what I mean with a game world.

Next we study the rule (2). In the game world, time passes in discrete units, moves. Because the real world has continuous time, we need a means to simulate a discrete moves in the real world. In particular, we need to determine the exact moment at which a move is made. So we need the rule (2), which tells it.

This view, among other virtues, explains why cheating in a game is absurd. The type (1) rules are natural laws, which cannot be broken inside the game world. When a player cheats (i.e. breaks the type (1) rules), the player breaks the corresponcence between the game world and the real world, and in effect stops playing the game. When the player breaks the type (2) rules, the correspondence is not necessarily broken. Type (2) rules, however, as a whole, illustrate a contract between players how the game world is simulated in the real world, and the correspondence is at least weakened by breaking type (2) rules.

Now we have characterized what are games such as chess, checkers and go. In the next part we show examples of situations where it is problematic to think a game as a little world with its own natural laws.


The Metaphysics of Games, part II: The Limits of Applying the Theory
-------------------------------------------------------------------

In the previous part we studied games such as chess, checkers and go, and we decided that these games are idealized little worlds approximated by real game situations. We also decided that the rules can be divided in two categories, the first category describing the natural laws of the imaginary world, and the second category describing how to approximate the imaginary world in the real world. My theory works well for a class of games, called board and card games.

In this section we study what happens when we try to apply the theory outside the class of board and card games. We concentrate on Pool and Petanque.

In board and card games, the game is an abstraction represented or illustrated with the gaming equipment. Pool is different, because in Pool the playing equipment does not represent abstractions, but Pool is played by hitting concrete balls with concrete cue sticks. The question I am interested in is that does there exist idealized Pool, approximated by real-world Pool.

The answer seems to be "yes". In idealized Pool the table is absolutely even, and the balls are absolutely round, and the mass of the balls is absolutely evenly distributed. The real-world playing equipment never reaches the ideal completely, but Pool tables are very expensive, because the players want them to be a good approximation. Also the mass distribution of the balls is wanted be a good approximation of even: Before synthetic materials, the best pool tables were made of ivory.

Petanque seems to be different. Also ideal Petanque balls are round and the mass is evenly distributed. (In tournament Petanque there are strict rules for accepted balls. Every player plays with balls he owns, and balls where the mass is not evenly distributed are forbidden. Such balls would be advantageous in certain situations.) Nevertheless, it is a part of the spirit of petanque that the playing surface is even only to a certain extent. It is the spirit of petanque to use the deviations of evenness of the playing surface in one's strategy So, such a creature as the idealized petangue field does not exist, and petanque is played on the uneven surfaces of the real world.

So far, we have decided that such games as Pool and Petanque the playing equipment and surfaces are a part of the game (unlike board and card games, where they represent abstractions). And depending on the game and the type of equpment, they can be approximations of the ideal, or the unevennesses of the real world can be a part of the game.

In the case of board and card games I mentioned that a part of the rules describe the natural laws of an imaginary game world. Next I will study whether one can think Pool as a little world with its own natural laws.

Pool has rules such that they players play in turns, where the turn ends when the player fails to pocket a ball, that are most easily thought of as natural laws of an imaginary game world. The big difference to board and card games is that the natural laws of the real world, that is, Newtonian physics when it describes the movement and collisions of objects, are a part of the natural laws of the pool world. The same is true for petanque. Pool also has type (2) rules. Abstract Pool is most easily formed so that it is impossible for the balls to fly off the table. Because this can happen in the real world, we need type (2) rules which tell what to do it the balls fly off the table.

As a conclusion, Pool and Petanque can be thought of as imaginary game worlds. However, the natural laws of the real world is mixed with the game world unlike in board and card games. In the case of Petanque, also the unevennesses of the playing surface are mixed with the game world.

Now we have ended the excursion outside board and card games, and in the continuation, we will only study board and card games.


The Metaphysics of Games, Part III: Ethics
-----------------------------------------

I do not believe that "good" and "evil" are natural properties of the real world. They are only inventions of the man. In this case some imaginary worlds differ from the real one. For example, in the world of Lord of the Rings by J.R.R. Tolkien, "good" and "evil" are natural properties.

The game worlds are similar to the Tolkien's world in that the ethical concepts describe natural properties of the game world. Those ethical properties are not "good" and "evil", but "winning" and "losing". Winning is what the player has the duty to try to achieve, and losing is what the player has the duty to avoid.

It can be easily seen that the winning and losing conditions are part of the game world: Some games can be played as Misere (http://en.wikipedia.org/wiki/Misere), and like every gamer knows, the misere version of a game is a different game from the original.

The particular kind of winning the player has a duty to pursue can depend according to the exact variant of the game. For example, in the game of Canasta, the teams get points, and the team wins that first gets 5000 points. Canasta can be played simply to win, so that the ethical duty is to be the first team to break the 5000 point limit. The other possibility is to play so that the ethical duty of the winning team is to maximize the difference of scores, and the ethical duty of the losing team is to minimize the difference of scores. Which variant is played, is a matter of agreement among the players. We play so that normally we play the former variant, and if we want to play the latter variant, we agree that the losing team pays for the winning team the difference of scores in money. This is a way to approximate the abstract ethical responsibility of the game world with a real-world monetary incentive.

While the player functions as an agent inside the game world, the player has only one duty: To try to win, and to try to avoid losing (or, according to the variant played, to maximize the victory and to minimize the loss). Some might ask if the player has a duty to, for example, not to cheat. My answer is: Yes, but not as an internal agent of the imaginary game world. We remember that the rules of the game are the natural laws of the game world, and hence cheating, breaking the rules, is impossible for the player as an internal agent of the game world. So we do not need a responsibility for the player not to cheat as an internal agent of the game world, since it is impossible.

However, playing a game happens in the real world, and it is indeed possible to cheat, that is, break the correspondence between the imaginary game world and the part of real world that simulates it. This leads us to the central ethical responsibility that each player has as a real-world player: Act so that the correspondence between the imaginary game world and the real world remains as complete as possible. This responsibility includes choosing moves so that they are the best possible in terms of victory, not cheating, and a couple of other things we will return later on.


The Metaphysics of Games, Part IV: Examples from Card Games
------------------------------------------------------------

In other parts we have decided that board and card games are abstract, imaginary little worlds approximated by real-world gaming. In this part I explain some phenomena encountered in card games using my theory.

1. Marked cards

In card game worlds, there is an universal natural law that cards cannot be distinguished by their backs. (If we are accurate, I think that the cards are symbols for something abstract, but in this example, it is enough to talk about idealized cards as objects of the card game worlds.) In the real world, the backs of the cards are only approximately identical and there are little differences.

Usually, for example at Bridge clubs, the cards used are relatively new, and the people cannot tell the cards by their backs. In this kind of situations, relatively new playing cards approximate idealized cards with a sufficient precision.

Sometimes, for example in home use, older cards are used. In principle, they might be recognizable by their back, if only the players bothered study which card has which wear. Usually the players won't bother, since it takes quite a lot of effort, and it would break the correspondence between the game world and the real world, in other words, it would be cheating.

In some rare cases, typically in a summer cottage, the cards can be so worn that there are some individual cards that can be recognized by their backs. Playing with such a deck offers quite bad correspondence between the abstract game world and the part of real world approximating it, but the correspondence may be good enough for a light entertaining game.

Recognizing cards by tiny differences in their backs produces problems in one situation: When playing for so big sums of money that there might be professional card cheaters participating. They can make tiny marks that are invisible for a layman on the backs of cards and recognize the cards by those marks. In his book "Scarne's Encyclopedia of Card Games" the magician and card sharp John Scarne describes the problem as follows:

/Some years ago, I invited six card-playing couples to my home and tried an experiment. I gave them a dozen decks of cards still sealed in their original wrappers. "You have been playing cards for the past twenty years", I said. "[...] One deck is marked and can be read from the back. I'll bet that [...] none of you can find it."

[...] They even examined the card cases before opening the decks, looking for signs of tampering with the government seal. [...] Then they began examining the backs of the cards. [...]

"Okay", one of them said finally. "We give up. Which one is it?". "I have confession to make", I said then, "I lied, when I told you that one deck is marked." [...] [I said:] "As a matter of fact, all twelve decks are marked."/

In situations, where it is possible that a skillful cheater participates in a game it is very difficult to get a good correspondence between the abstract card game world and the part of real world approximating it.

As a conclusion, we have seen that in how good shape the cards have to be depends on many things: The resources available, the seriousness of the game and the ability of the players to recognize cards.

It must be noted that for example Scarne thinks that activity of the professional cheaters is cheating and not a legitimate strategy. I hold this as a strong argument for my theory: One cannot give a rule that would determine when the cards are in a good enough condition, but it is situation-specific. So the best way to understand the situation is my theory: The game happens in an idealized little world. Marking cards and recognizing marks breaks the idealization and breaks the ethical responsibility of the gamers to preserve the correspondence between the real world and the idealized game world.

2. Messaging in partnership cards

Next I study the example, for which I developed the theory about fictionary game worlds.

Some card games, such as Bridge and Canasta, are played in two-player teams. Usually in these kind of games there are two teams playing against each other, so there are total four players. The team members do not see the cards of each other. They are not allowed to discuss the playing strategy. The most important thing in this example is the following: The team mates are not allowed to message to each other by using gestures, body language, secret signals or anything like that. They are also not allowed to signal with the thinking time.

The team members are, nevertheless, allowed to communicate using things internal to the game world, that is, the choice of their move.

In his book "Uusi täydellinen skruuvipelin ohjekirja" E.N. Maalari describes the situation as follows:

/Skruuvi is a game for gentlemen. Between players, it has been always a rule to kick out players who behave bad or cheat.

One must aim at acting fast, without wasting time. To describe own situation by thinking too long is bad behaviour. The face must be emotionless like a mummy. The face must not be used to show anger, joy, disappointment or acceptance as long as the game is being played.

[...]It is not appropriate to stare at the eyes of the partner. You shame yourself and insult your partner if you try to read his face.

However hot-tempered you are, you must not show emotion as long as the game is being played. After the game many players are not able to control themselves. But outbursts after the game are not against the rules of the game./

In the light of my own theory, I analyze the situation as follows: In the idealized partnership card game world the players do not see the body language or the face of their partner, and theý are not able to (for example) talk to their partner. In idealized partnership card game worlds the players also do not know the thinking time of their partner. (In idealized card game worlds the game proceeds in discrete moves, so that there is not a block of time between turns).

Partnership card games are problematic creatures, since getting a good approximation of the idealized game is difficult. People message unintentionally with their body language, likewise with the time they take to think. Usually, at home games and also at bridge clubs, the approximation is taken care of with a gentlemen's agreement: Each player does his best to keep the "poker face" as well as possible and tries not to read the body language of the partners. Of course, making gestures intentionally is cheating.

This is a functioning compromise between functionality and ease of implementation, even if it does not work perfectly. More drastic measures are taken only in top-level bridge. In really significant bridge tournaments they use so-called screens, i.e. boards blocking the vision are placed on the table so that team-members cannot see each other.

In club and tournament bridge they also restrict unintentional messaging with the lenght of thinking time. In certain situations a player may place a so-called stop signal on the table. After that the next player (which is an opponent), must not play his next move immediately, but must at least pretend thinking for a while. In other situations, unintentional messaging with thinking time does not carry sanctions.

To prevent messaging by speaking is usually taken care of in club bridge so that you do not speak with cards in your hand (except for expressions necessary for the game, such as asking whose turn it is, if you have forgotten it.) When I play canasta with friends, we use a less strict agreement: Everything else can be discussed except for the current situation of the game. We even allow talking about past situations of the game. Sometimes players disagree whether a past situation affects the current one. In such a case any player can prohibit speaking from a particular past situation. This is a compromise between sociality and approximating the ideal, and it has proved itself a good enough compromise.

To finish, I point out that when playing bridge in the internet you do not see the partner, so you get a better approximation of the ideal than in face-to-face play.

3. Passing cards in Skruuvi.

Sometimes there arises situations where the players agree how the game proceeds in the real world, but they disagree on the correct abstracted game world.

In Skruuvi, there is a situation where a player passes four cards simultaneously for his team-mate. The cards are stacked, so in the real world they are in a certain order. However, the question whether the cards have an order in the abstract game world has raised disagreement. (Expressed mathematically, the question is whether the player passes a /set/ or a /sequence/ of cards.)

The question affects the gameplay in practice. If you give a sequence of cards, that is, the cards have an order in the abstract game world, it is legitimate to communicate things to the partner with their order. If you give a set of cards, communicating with the order is cheating.

E.N. Maalari describes the situation as follows. He is (in my terminology) in favour of the set-idealization, but admits that he is in the minority.

/Earlier it was inappropriate to signal the voided suit by using the order of cards. If someone tried it, he was not longer accepted among gentlemen. Nowadays two signals have become so common that it is hopeless to fight against them. For this reason I adopt these two signals in my book, even if I have until now tried to do everything I can against their use./

This was from the year 1944. In a Skruuvi guide published in 2004 (ed. Hannu Taskinen) there is a system called Kallio passing, which is a two-page guide to signalling with the order of cards. Even if the guide recommends the sequence interpretation, it also presents the set interpretation as a possible one:

/The development of Skruuvi we have described and in particular Kallio passing are examples of a general tendency of increasing the amount of information in card games. This has the effect of reducing the effect of chance. If it is too demanding to use these conventions, they can be ignored./

4. Accidentally shown cards

According to my theory the rules are natural laws in abstract game worlds, so the rules cannot be broken. In particular, in partnership cards, it is impossible to show cards to the partner, except in ways allowed by the rules. However, accidents happen, and in the real world the players sometimes show cards to their partner in ways not allowed by the rules.

So in Canasta (a card game player by two two-player teams) there is quite a lot of type (2) rules that deal with accidentally shown cards and other information passed in ways not allowed by the rules. The main rule is that the accidentally shown cards must be played when the first oppoturnity arises. For certain accidentally revealed illegitimate information there is also penalties in points given to the opponents.

It is the purpose of these rules to ensure that you do not suffer when the opponents accidentally and illegitimately reveal information to each other. So it makes it not worthwhile to even accidentally break the correspondence between the game world and the approximating reality. These rules mostly fulfill their purpose, although not in absolutely all cases.

What is noteworthy is that it is unethical to strategize with the above-described type (2) rules. You are not allowed to make a "mistake" intentionally, even if the penalty is less than the benefit. So we see again the ethical maximum of players to preserve the correspondence between the game world and the real world approximating it.


The Metaphysics of Games, Part V: Conventions
----------------------------------------------

Normally, the things related to a game comprise rules and strategies. Rules describe the possible moves, and the winning condition, which gives a goal to the players. The strategies describe how to choose the moves so that they reach the winning condition as efficiently as possible.

In partnership cards (that is, in card games played by two two-man teams) there is a third element in addition to rules and strategies: Conventions.

In partnership cards, the team-mates do not see the cards of each other, and they are not allowed to message with speech, gestures, body language or other such things. However, they are allowed to message with the choice of moves. Before the game begins, the partnership may agree that certain moves are signals with a meaning. Typically the signals are of the type "If I make such-and-such move, it means that I have such-and-such cards in my hand." These kind of pre-agreed signals are called /conventions/. So conventions have /semantics/.

Partnership card games are quite often bid trick games. In bid trick games a hand begins with an auction, where the players make bids. In bids the players commit themselves to taking a certain amount of tricks or points during the actual game. The highest bidder gets typically some privileges such as determining the trump suit. In bid trick games, including Bridge and Skruuvi, there are typically quite a lot of bidding conventions that message the contents of the hand to the partner. These are of the type "If I make in a such-and-such situation such-and-such bid, it means that I have such-and-such cards in my hand."

Next I present a proposition what kind of natural laws govern conventions in partnership card game worlds. Then I study how bridge approximates my proposition in pracitce. In the end I present critique against my proposition.

My proposition is as follows:

(1) A team agrees freely among themselves what conventions they use.
(2) Everyone knows what conventions the opponents use.
(3) A team has had a chance to agree on defence conventions agains the opponents' conventions. (And when agreeing the defence conventions, they have naturally known what conventions the opponents use.)
(4) You are allowed to break your conventions, but then you mislead your partner in the same way you mislead the opponents.

Point (2) is indisputable. This is the primary rule of conventions in partnership card games. Points (1) and (3) are ideals that sometimes contradict each other. Point (4) causes some minor problems.

Point (2) is fulfilled in club bridge by using so called system cards. A partnership writes the conventions they use on a crib sheet, and before the game starts they give the crib sheet to the opponents. The opponents can read the crib sheet throughout the game. In addition, unusual conventions must be alerted. If a played makes a bid that is an unusual convention, the partner of the player must knock on the table to alert the opponents so that they know that something happens out of the ordinary. In addition, the players can, on their own turn, ask the opponents for the meanings of their bids.

The points (1) and (3) contradict each other. Usually the system card is given to the opponents just before the game starts, and if the conventions are very unusual, the opponents have not had an oppoturnity to agree on a defense against them. Hence, in clubs and usual tournaments the usual policy is to allow the choice of conventions only from relatively usual ones. It can be assumed that a competent bridge partnership has agreed on a defence against them. The reason for this restriction is the chance to agree on defence conventions.

In the very top level bridge, there is a better approximation of (1). A partnership can agree on the conventions they use freely, but they must publish their conventions at a certain time before the tournament. This way the opponents have an oppoturnity to agree on defence conventions against their conventions.

Points (2) and (4) cause certain problems. Usually conventions leave choices for the player, and different players make these choices in their personal style. Also the players break the conventions in their personal style. If a bridge partnership has played long together, they have learned each other's personal style, and this (usually non-verbal) knowledge can be seen as de facto -conventions that the opponents do not know. Because of this (2) and (4) are not fully satisfied, but there is no remedy other than a gentlemen's agreement to minimize the effect.

I promised to give critique for my proposition to the natural laws of game worlds regarding conventions. My criticism is towards (1). As we saw earlier, it is not fully satisfied in club bridge.

I remember seeing a humorous post on a bridge discussion forum. The writer wrote what would happen if chess was played similarly to bridge. The opponent would bring a system card which would say that his horse moves three steps to one direction and then one step to the side. The system card would also say that in such-and-such situations the rook moves diagonally. The writer presented an absurd situation where the system card changed the natural laws of the game world. The obvious purpose of the writer was to present that freely choosing the conventions changes the description of the bridge world, which is wrong. Hence everyone should start using same, most usual conventions. Hence, the writer seemed to advocate that the most usual conventions should be made mandatory, and hence into a part of the abstracted bridge world. You hear similar wishes from time to time. The reason given is usually that freely agreeable conventions make the game too complex.

I ran into a similar situation when I planned a Huutopussi tournament with other math students. We played four-player partnersip Huutopussi at the student room, and it had become customary to use a certain set of conventions, which were a nice compromise between efficiency and ease of use. However, it was expected that certain players would develop new, ultra-effective convention systems for the tournament. The end result (with which I disagreed) was to forbid other conventions than those generally used in the student room. The reason given was that those that used the ultra-effective conventions would get an unfair advantage. (My personal opinion is that using efficient conventions is good playing, and it should be rewarded.)

So that collection of conventions became a part of the abstract world of math students' Huutopussi.

This world was strange, because it has natural laws, built-in ethics (winning), and certain signals had even built-in semantics.

Hence, we must conclude that the right way to deal with conventions depends on situation: Sometimes the right way to form the abstract game world is to allow freely agreed-on conventions. Sometimes, to prevent the theory from drifting too far from practice, the conventions must be taken as a part of the game world.

Also the Skruuvi -guide (ed. Hannu Taskinen) seems to identify conventions and rules, and hence make conventions as a part of the game world:

/The only important thing is that everyone uses the same rules and conventions./

In the proposition given in the beginning of this part the above does not hold, since a team may agree on different conventions than the opponents. (In this case, the important thing is that everyone knows what conventions others use.)


The Metaphysics of Games, Part VI: Time in Board Games
-------------------------------------------------------

Earlier we have determined that games are abstract, idealized small worlds with their own natural laws.

In board and card game worlds time does not pass in hours and minutes, but in discrete moves that follow each other. Because we want to approximate game worlds in the real world, we need tools to adjust the different times of the game worlds and the real world. Because we want the moves to be of more or less high quality, the players must have a chance to think about their moves. The game must end in a reasonable time, so the thinking time must be restricted in one way or another.

At homes and clubs the matter is taken care of with a gentlemen's agreement: The players try to play relatively fast, but are allowed to take themselves time to think if the situation is difficult. Usually drawing the line between appropriate and inappropriate thinking does not cause problems, the players adjust to each other's playing speed without a verbal agreement. Sometimes there is a particularly slow player in the game, and others can either tolerate his thinking or ask him play faster.

It is important in club and tournament bridge that all the tables in the club or tournament play approximately at the same speed. Usually there is a certain amount of time (a little less than 10 min) reserved for each hard. The players do their best to stay in the schedule, but can take themselves thinking time in a difficult situation. If keeping in the schedule presents problems, tournament director shouts at the table that they should play faster. The system works.

In Go and Chess tournaments the players get an enourmous advantage from taking themselves thinking time. Hence the need of formal time control. In these games, a chess clock is used. Every player has a quota of time, and if a player exceeds his quota, he loses the game.

Losing on time is not a good approximation of the abstract game, but here we see the difference between casual play and tournament play. In a tournament winning and losing mean much to some players, and hence it is important to have rules that leave no room for interpretation. Also type (2) rules have to be such, and "gentlemen's agreements" should be minimized. Hence things such as exceeding your quota of thinking game and disrupting the game by breaking a type (1) rule are punished by a loss, (or sometimes: By a fine in points.) Because in tournament "gentlemen's agreements" are a bad thing, it is usually deemed permissible to strategize with type (2) rules.

Hence,one may think tournament chess and go so that the time control is a part of the abstract game world, a part of the game. Next I present a situation where players disagreed whether time control is a part of the game world or a part of the approximation process.

*The Master of Go**

The Master of Go is a novel written by Japanese Yasunari Kawabata, which is partially fictious, partially based of true events. It describes a go game played in 1938 between Otake (based on the real player Kitani Minoru) and Master (based on the real player Honinbo Shusai).

Traditionally, in the 1800s, Japanese Go did not have formal time control. Top level games could last months, consisting of very many sessions. At the end of the day, the game was stopped at the decision of the elder player. When Japan westernised, it affected also Go, and the game described in the novel is played with formal time control, which was a new thing in that day's Japan. (Nowadays top level Go games last two days, and each player has 8 hours thinking time.)

When you play games of the lenght tof several days with formal time control, the game clocks are stopped every night, at the end of the day's session. The last move of a day is so-called sealed move. It is not played on the board, but written on a paper closed in a envelope, which is opened at the beginning of next session. This way the other player does not know what the last move is, and cannot spend the night thinking of a response move. If such thinking werepossible, it would be an unfair advantage for the player who has the possibility to think. Because of the sealed move, both players have an equally blurry picture of the continuation of the game.

The game described in the novel took 14 sessions, and it used sealed moves. Also sealed moves were a new thing at that day's Japan.

Central to the novel is a sealed move that Otake, the younger of the players made. Her made such a move that it was not the best possible in the sense of the abstract game, but the opponent could reply it only in one way. This way Otake knew what the next move of the opponent would be, and he could use the night thinking of his next move. This gave him an advantageous position.

In terms of my theory, Otake thought that making a move as a sealed move was part of the abstract game world, and using it as a tactic was legitimate. His opponent, Master, was deeply offended by this "tactic", and I'd like to interpret the situation so that the Master did not think that the time control was part of the abstract game world, and using it to gain an advatage was cheating. In Master's view, Otake should have made the move that was best when one did not consider time controls, but only the game as an abstraction.

According to the novel, Master commented the move later as follows:

/The match is over. Mr. Otake ruined it with that sealed play. It was like smearing ink over the picture we had painted. The minute I saw it I felt like forfeiting the match./

The continuation of the novel describes how the Master, whose health had not been so good, continues the game but gets seriously ill, that upset as a partial reason, and finally, after a couple of years, dies.

Appendix: Two-subject theory
-----------------------------

When a player plays a game, he actually represents two subjects, which I call the game-me and the mundane-me. The game-me operates inside the abstract game world and makes the choices of game moves. Mundane-me takes care that the correspondence between the game world and the real world is preserved, and in general makes all the decisions not concerning the choice of a move. So it is a responsibility of the mundane-me to obey type (2) rules, which are typically taken care of by gentlemen's agreements. He for example makes sure that the player does not peek at other players' cards, even if it was be possible. If in the middle of a game it is found out that the players have different ideas about the rules of the game, it is up to the mundane-me's to negotiate, which rules are used in the continuation.

Game-me has only one goal: To win the game (or to win as much as possible when playing on money, or to rank as high as possible). The goals of the mundane-me are the various motives that the players have to play a game, such as enjoying the game and learning to play better. The pleasure characteristic to a game is obtained by the mundane-me by observing the game-me in his pursuit of victory.

The main purpose of the game-me - mundane-me division is to enable playing at the same time to win, and in a way fitting to a gentleman. It is essential to the enjoyment of a game that the game-me and mundane-me stay at their reserved fields (moves in the game vs. everything else.) If you try to optimise victory in things that belong to the mundane-me, the game suffers, as well as the game suffers if you start making "fun" moves instead of moves that aim at victory.
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THIAGO LADISLAU SANTOS
Brazil
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This is simply amazing and I would like to use in my academic article about videogames.

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Franz Kafka
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St. Charles
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GameTheoristBR wrote:
This is simply amazing and I would like to use in my academic article about videogames.

Is this guy still around? 0:

You could try sending a geekmail to that user by clicking on the envelope under the username. The profile says this user has logged in a few weeks ago.
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