Around the Compendium in 54 Aphorisms (Including Jokers)

By Keith Tyson, 26 September 2008

A The Object – Mathematically defined, the compendium contains AXIOMS and RULES OF INFERENCE, from which the players are to construct desirable THEOREMS. The axioms are the game boards and their relevant pieces set up in starting position. The theorems are any other combination of these pieces that can be formed by recursively applying the rules of inference. (For example, in the game of chess, a desirable theorem would be one in which the opponent, while under attack, could not make another legal theorem (Checkmate!), or one in which you had a material advantage thus lessening the possibility of the former happening to you.)

2 Time – The protagonists of the compendium operate in a parody of time; often the game being split into a series of recognised states or 'Turns', in which the player possesses a unit of active gametime. The intermediate movements between these states has no bearing on the game as only the theorems are recognised as existing and authentic. Even in games where physical movement is important, such as Billiards, the game is divided into these states of play and points are calculated when the movement has stopped.

3 Unknown Information – The games within the compendium offer the players differing amounts of available information. This fact can be used to form the first of many compendium taxonomies — at one end of this scale are the games which show all the pieces, such as chess or draughts, at the other are games which give incomplete information such as Poker or Battleships.

4 Skill and luck – Although some games appear to require more skill than luck, all games in the compendium utilise some form of unpredictability : either by the use of a random generator, such as dice or roulette wheel,or, they rely on the volume of possible theorems to create enough complexity to render it ostensibly unpredictable. Skill can be defined as the acquired ability to overcome the apparently unpredictable.

5 Unpredictable generators. These include: Dice, cards and lots, wheels and spinners, electronic randomisers and other devices such as human beings & bingo machines

6 Dice. The most common form of die is the cube which is used for generation of integers 1- 6 inclusive. Less known however, is that most, if not all, ranges of numbers can be generated by the use of other polyhedra. The numbers 1-4 can be generated by reading the base of a three sided pyramid, or numbers 1 - 100 by throwing two decahedra and using a base ten system. (dia a -tens : die b-units). Dice have been found that date to First Dynasty Egypt.

7 Electronic randomisation – There is no such thing as a truly random number or sequence. The prerequisites of any digital or electronic randomisation technique are that its results (in the long term) are unpredictable and have unbiased distribution. This is a difficult balance to achieve for if a system is rigidly unbiased then it becomes, to a certain extent, predictable. The possibility of sustained repetition followed by unbiased generation thereafter must be included. There are three digital techniques that are used to 'pick' random numbers. The first is a large table of numbers which is accessed at a random position (NB. The computer will utilise some temporal device such as internal clock to get around the recursive problem of randomising the entry gates). The second method is to use a mathematical algorithm that fulfils the prerequisites of randominity. The third method (and probably most effective) is to use a combination of the two former methods. Random generators are used extensively in computer games.

8 cards – Essentially an unpredictable device that, due to the economy, elegance and hierarchical nature of its subdivisions, needs no other equipment to generate hundreds of games. One only has to study the pack's structure to see why this is so : 52 cards, divided into 4 suits, two of which are black and two red, all of which contain 13 cards in a hierarchical order. There are 4 court cards per suit (including the ace) the remainder being numbered. The ace can be counted as low or high giving the hierarchy a cyclic nature. In most packs there are other subdivisions such as one—eyed jacks and suicidal kings where half the jacks are in profile and half the kings appear to be stabbing themselves. In this way , any card belongs to several categories simultaneously (eg. The jack of spades is a jack, suicidal, spade, courtcard, black card, 11th card in suit, 4th highest card in the pack). Simple to transport and randomise by shuffling, they are used extensively throughout the compendium.

9 Dialectics and binary oppositions – The vast majority of arenas are for two players/teams or forces. The multiplayer games usually employing a knockout systems which ostensibly turn the game into a series of two horse races. Also the logic of the compendium is a binary logic of true and false. False statements, black and white, left and right, winners and losers. This simplistic logical methodology may not be the most productive because the paradoxes of statistical probability and other mathematical revelations such as Godel's Incompleteness Theorem suggest this model may not be sufficient for a true understanding of the compendium. In fact, it is extremely probable that a complete description of the compendium is beyond our cognitive capabilities – the compendium tends to humble its players...

10 Tips from the top (Scrabble) – Top nine highest scoring

seven letter words in the English language at the time of writing (1995) and their scores ( if passing through a triple word and double letter scores.)

QUARTZY (164) • BEZIQUE (161) • CAZIQUE (158) • ZINKIFY (161) • QUETZAL (158) • JAllILY (158) • QUIZZED (155) • ZEPHYRS (155) • ZINCIFY (158)

10 Chess – Kasparov v. Tukmakov (USSR 1981)






















































Q Chess stats – There are 208,089,907,200 legal ways of placing the chess pieces on the board irrespective of rules of inference. It would take forty thousand years playing twenty four hours a day to exhaust these possibilities (if you were given a minute to clear and reset the board). Yet, in the compendium's terms, the game is' but a small one.

K Garry Kasparov – "I am constantly amazed at the inexhaustability of chess and I am becoming more convinced of its unpredictability.... as with Cleopatra, so with Caissa : 'Age cannot wither her nor custom stale her infinite variety."

A Gambling and money. The application of stakes immediately intensifies the gaming experience by bringing the result to bear on the players purse. To a certain extent, the wager can be seen as an attempt to remove the symbolic nature, of the gaming risk. However, any study of gamblers quickly reveals that it is the symbolic nature of money rather than that of the game which is frequently exposed. The hardened gambler will talk of money as a way of keeping score', money quickly develops into a new, more immediate currency of 'Action'.

2 Odds – Because we are finite beings with limited game spans, playing the odds does not guarantee success in the compendium – This mortal limitation factor causes one fundamental mistake in the interpretation of probability laws – In systems of equal chance (one of which, incidentally, I have yet to find in the whole compendium) as the number of iteration approach infinity so the different( between the theoretical outcomes ant physical ones will approach zero. This, stands to reason (eg. if I have a coin and I flip it once the result, unless it lands, on its edge, will be 50% inaccurate. After 100 spins I could expect that percentage to be less but it is not guaranteed) However, if the game is truly equal and result A comes up 1000 times in a row there is not even a 10 billionth of a percent more chance that Result B will or the next spin, this is the nature of laws that work with infinities. And yet, haying said all this, games do in fact behave with amazing obedience to the odds.

3 Probability Paradox – The mathematics of probability and statistical analysis are awash with paradox, the compendium has spawned an astonishing number of diverse impossibilities. This one is taken from 'Games of Life' by Karl Sigmund.(Oxford university press). 'The numbers 1 to 18 are inscribed upon the 18 faces of three coloured dice as follows : Red Dice (10,8,7,9,18,5), Green dice (16,4,3,15,17,2), Blue Dice (13,11,6,12,14,1). Although the total amount of points are the same on every dice (57), the red dice is better than the blue: the odds are 54 % that if they are both thrown the red will show a higher value than the blue. Similarly, the blue die is better than the green die. Have you guessed the paradox ? Yes, the green die is better than the red ! Thus whichever die I choose my opponent can choose a die giving an 8% advantage. It is better to let ones adversity pick first. This provides an example of how the compendium operates in a different way to that human notion of common sense.

4 The Architecture of addiction – The architecture of addiction is one of absorption and triggers. It is used primarily in casinos and arcades and comes in two forms: the environmental architecture and the psychological architecture. They are both designed to eradicate the player's reference to the 'Real' world so as to be absorbed by the arena of the game. Physically this is achieved by the absence of clocks, windows or any other way of judging time so that the gametime can become the chronic reference, the use of chips rather than money, and many other subtle devices such as the use of escalators coming in, stairs going out.

5 Psychological architectures – The second type of architecture is the psychological architecture of the game itself to extract the maximum money from the player. An addict will spend more money on fast action, infrequent payout games. They will be attracted to certain audio-visual triggers. They will experience jealousy (not envy) on viewing adjacent Players winning money and increase their stakes and they will be attracted to games in which they believe they have some privileged esoteric knowledge.

6 The physically challenged Bandits – Originally fruit machines worked on similar principles to poker; the payouts were inversely proportional to the odds of receiving the winning hand (minus a slight % in the machines favour of say, 25%). The compendium now contains, however, a new breed of electronic secret feature machines that have been designed to create a false sense of expertise in the player. Using a loophole to get around the jackpot limit set by the gaming board (time of writing 1995) of 56.00 token jackpot 53.00 cash, they have jackpots in excess of 550.00. (Each machine is given a 50 % repeat chance after a big win, by the use of chips this % is increased by delaying the payout, so that eventually it will give a winning streak)

7 Nick the Greek – has been called the Icarus of the Compendium; in flying too high against the face of the odds, his incredible luck eventually melted away and the once multimillionaire died pen­niless. Nick Dandalos's reputation probably boils down to a single game of no limits, straight 5 card stud-poker, played in Vegas against the Texan Johnny Moss. After betting massively ( $ 250.000.) with nothing more than jack high against a medium pair, he was dealt a second jack. He won a half million dollar pot. Johnny Moss (later to become 3 times world champion) said of the game " I'd lost a mighty big pot but I knew if he's gonna bet on dreams like that, then I'd eventually have to win." and sure enough, after a 6 months protracted game Moss came out on top.

8 The Two Maxims of Risk – Like the casino, the world of finance offers high gains for high risks. New recruits to the city are taught the following two rules:

Rule 1 — Never Lose Money.

Rule 2 — Never forget rule 1!

9 Obsession, adrenaline and curiosity -

CXA• IOPN• AAASSTX • N • GO • VRTKDSBD • AAAHALAA• A • I • XN • INI • AAANANAA • G • vxr stp gg d w ss dqj gg••• END.

10 Tip from the top (Poker) – odds of improving 1 pair to .... 2 pairs(5-1), threes(7- 1), a full H (98-1), fours(359-1) or odds of roughly 2.5 to one against any improvement.

J Gambler's 'knowledge' – This particular phenomenon,well known amongst gamblers, is a moment just prior to a result when the gambler becomes completely aware of the outcome. They do not simply think they know the result nor are they 99% sure. They unequivoqually KNOW the outcome and bet accordingly. Fortunately it is an infrequent occurrence; for how horrific would be a compendium without surprise!

Q The many worlds theory – published in 'The Review of Q Modern Physics' in 1956 by Hugh Everett III. The many worlds theory states that in any given event all possible results come into existence in a separate compendium. What holds true on a quantum level also holds on a gaming one. On every spin of the wheel 37 compendiums come into existence (probably many more with compendiums where the ball span out of the wheel etc.) Your life would be an animation through these possible worlds.

K Fyodor Dostoyevsky – From 'The Gambler' written in"under 4 weeks (1866)"and there in my waistcoat pocket I found one surviving gulden. "Ah, so I shall be able to have dinner!" I thought, but when I had walked a hundred paces I changed my mind and went back. I staked that gulden on manque, and there really is something special in the feeling when, alone in a strange country, far away from homes and friends and not knowing what you will eat that day, you stake your last gulden, your very, very last ! I won, and twenty minutes later I left the station with 170 gulden in my pocket. That's a fact! You see what one's last gulden may sometimes mean ! And what if I had lost courage then, if I had not dared to decide!

Tomorrow, tomorrow it will all come to an end!”

A The Four Structural Narratives – Thematically speaking, there are really only four tales to tell from the compendium. These are : The War or Battle, The endless Struggle for Survival, The Journey and The Accumulation of Power. In this way, it could be argued that the compendium metaphorically embodies the four anxieties of life, (A premise literally pursued in computerised Artificial Life and Evolution games). The only exceptions to these narratives might be puzzles, recreational mathematics and aesthetic games for 0 players, yet it will be seen that even these embody one or more of the above categories.

2 War and battle – This is the first and most common theme running through the compendium. It would be fair to say that the engagement in competitive pursuits means that all games have a right to be included in this category, which incidentally, is not peculiar to humans, as territorial combat forms part of the play and ritual of most of the animal kingdom. Obviously, the theme of combat is more explicit in some games than others, firstly there are the games that have combat as their medium either physically or virtually: Boxing and other martial arts (one could argue that these are not games as they ARE combat, but the gloves, rules, subdivision of time, points and hierarchy of champions, turn it into largely a symbolic pursuit rather than martial) there is also a vast range of video combat games (Street Fighter, Mortal Combat, Primal Rage Etc.) and secondly the more symbolic wargames like the territorial battle of the armies in chess or in American Football, a game which originated during the American civil war.

3 Perpetual Survival – Of all the games in the compendium, Pinball probably illustrates this scenario with most clarity. The game consists of an inevitability and a method of deferment. The inevitability being that the ball is going to eventually roll between the flippers or in the side slots. The players aim is to defer this inevitability for as long as possible and score enough points to get extra balls or replays. The symbolic relationship to mortality or a mortal battle with infinities is obvious. Unlike earlier electronic games, such as Invaders, Brickles, Tetris etc, which had endless progressive difficulty, modern video games are, on the whole, completable. They have a goal other than survival and therefore belong in other categories. The new simworlds and cities simulations are an extension of perpetual survival games that are less symbolic, a trend towards realism that has become common in the compendium.

4 The journey – All games include movement, the games that are specifically categorised here however are races, expedition and platform games. The motivation for players in electronic plat­forms tends to be to discover new levels rather than increasing their score. Unlike the games of endless survival, these games have a teleology, goal or finishing post.

"....therefore I am inclined to say that a game needs not only rules but also a point." Ludwig Wittgenstein.

5 The accumulation of power – Again, most games include this element in their play in the accumulation of wealth, material, points or control.

6 From the Symbolic to the Simulation – the biggest change presently affecting compendium is the transition from the symbolic game to the simulation. This change can be traced back before the advent of microprocessors to Role Playing Games. These attempted, through extensive rule books, to set up a simulated reality in which players could engage in any pursuit rather than the limited strategies of some symbolic battle. Players could add their own complexities to a situation and the probabilities calculated accordingly. The two main drawbacks to RPGs were the slow speed of play and vast amounts of preparation required to begin. The microprocessor has allowed the digestion of vast rule books and the realtime presentation of events on screen. Thus the compendium begins to develop virtual landscapes, playing fields and protagonists. We all know these people and places (the man throttling a chicken in the background of Streetfighter or the waterfalls of Sonic are well known tourist attractions). There are games within games that allow complexities that could not have been attempted before. There is now a pinball machine (Knights of the Round Table) in which you simultaneously play a digital game of chess. As these hybrids become more common it becomes increasingly difficult (and redundant) to locate the player' s objective. The processor replaces the metaphor, the action replay replaces the after game analysis. It is now simply enough to play.

7 Game psychosis – The boy(15), who cannot be named for legal reasons, was found guilty of manslaughter on the grounds of diminished responsibility. He and a friend had been playing (in their words) 'Real life role playing games' in which they had been requested to 'Murder a woman who has betrayed her country'. Unable to fulfil the request they generated another instruction 'Kill a fat man' After stabbing the victim 50 times they calmly walked home and wrote the incident in their Game Diaries.

8 The world Record for throwing a standard playing card (indoors) — it's 52 feet!

9 Catastrophy : the science of the unpredictable — Einstein IV once said "God does not play dice!" and he probably doesn't. That about sums up my in depth opinions on Chaos Theory.

10 Tip from the top (The National Lottery) – As all sequences have an absolutely equal chance of occurring then there is no way of predicting the sequence. However, you can ensure that if you win you get a large payout. It is probably better to use the same sets of numbers each week (preferably wheeled to cover more permutations), therefore it stands to reason that you should make your numbers as unique as possible, thus decreasing the probability of sharing a prize. For instance, 10,000 people pick the sequence 1,2,3,4,5,6 each week, so even if this sequence did come up the Jackpot payout would be a massive 5649 not particularly good for odds in excess of 14,00000 to one. You've wasted your quid, mate!

J High scores – Taken from the highscore table of a machine picked at random from the Crystal Rooms Arcade, Leicester Square, London.

(Highscores usually remain until the power is turned off or until wiped with EROM scoring either way they are not permanent).

TAZ 486,470,950

MEL 295.200,050

RTW 290,000,600

VTC 267,550,050

MIK 248,001,900

AAA 200,043,000

Q Sex and pornography – Just as the pornographic movie was the natural consequence of the new voyeuristic technology of film. So too the private interactions of video games and digital porn will probably spawn masturbatory teledildonics. The technology has not been around long enough to see the results of this new breed of 'Bevis' styled interneting teenagers, whose first sexual awakenings were with electronic porn. No doubt, just as twenty years after WWII came "Gasmask Fetishist", in a few more years we could be treated to, "Hard-disk", "Keybroad monthly" and "Joy-stick for men"

K Kevin Thomson (Sega Champion 93) - :” I just want to say to Mark Halsmith, that I've been reading what he's been saying an' if he thinks he is so hard then he can come and have a go. I'll take him on any console, on any game, anytime !"

A Life and its rules – The compendium contains many theorems, both inorganic and organic. The potentially endless game 'Deoxyribonucleic Acid I ' has now been running for over 3200 million years. It has axiomatic playing pieces of just 4 nucleotide bases which can be synthesised into an almost infinite variety of theorems. The game has one single rule of inference :

Rule number one – Survive!

2 The precursor of all games? The inventive complexity of this deceptively simple game of DNA I is truly staggering. If we take the reductionist model for a moment,the rules and structures of the DNA game are the inevitable deterministic consequence of the playing pieces embodied in their environment or board, that is to say intrinsic to their structure and without design, now note that the majority of games within the compendium were invented by the primates from this game also and are therefore derived from it as well. In short this simple game and its rule ' survive' could be the founder of all the compendiums rules other than the physical axioms required for its own creation.

3 John Horton Conway's life -like the DNA game, Conways life game is incredibly simple yet can become extremely complex. It is not a competitive game but more a game of solitaire played on an infinite grid. Some of the squares (or cells) in the grid are shaded and called active. The 'living cells' are shaded and the other squares are 'dead space'. Any square on the grid sits adjacent to eight other squares (4 sides and four diagonals)

Then come three simple rules of inference,

Rule one— If an empty cell is connected to exactly three living neighbours, then these reproduce and the empty cell becomes active or ' living'.

Rule two — If a cell has less than two neighbours it dies of loneliness.

Rule three — If a cell is surrounded by more than three neighbours then it dies of overcrowding.

Now a wonderful world of artificial life is created with 'gliders' , 'traffic lights' and other shapes swooping across the infinite grid.

3 Gliders — This is the simplest of gliders. There are self replicating gliders but they are too complex to go into here, (Grid references on a four by four grid) Live LIFE cells at



C1 C2 C3

This shape will glide through infinity until stopped.

4 Prediction and Magik – Fortune telling, prediction and speculation are all attempts to break our temporal binds and acquire as yet unexperienced information. It has been argued that our conscious minds are the only systems in the compendium to suffer the one way gridlock of linear time; our subconscious minds not bothering too much about ordering events. It comes as no surprise then, that the tools of the fortune teller are those of the game with its more simplistic unpredictability and gametime. I can only assume that the (X)omancer (substitute X for the Latin for anything from cards to endtrails) employs these tools not under the assumption that there is a correspondence between the unpredictability of a pack of cards, runes, dice, etc, and the greater complexity of the whole compendium, but that these microcosmic devices will act as a filter on the conscious, therefore giving an insight into some type of 'transcendental truth' - That the random event and unpredictable sequence form the perfect antidote for the rational determinism of our conscious minds.

5 Binary base language – All systems have various levels of coding. In digital games for instance, first there are the machine switches, then binary, then machine code, then the operating system, then the software or application and finally the document.

6 Binary transcriptions – The face of Bison from Street Fighter II in Binary (just data)

101011001111110100000101010001010000 001010101101010101010101101010101010 101111111101000111010000110101111010 101010101000101010101010101010101010 000111010101001001010101010101010010 001010101101010101010101101010101010 1011111111010001110100001101011110100011101010100100101010101010101001000 1010101101010101010101101010101010101 1111111010001110100001101011110101010 1010100010101010101010101010101000011 1010101001001010101010101010010001010 1011010101010101011010101010101011111 1110100011101000011010111101010101010 10001010101010101010101010100001110101010010010101010101010100100010101011 01010101010101101010101010101111111101000111010000110101111010101010101000 10101010101010101010101000011101010100100101010101010101001000101010110101 01010101011010101010101011111111010001110100001101011110101010101010001010 10101010101010101010000111010101001001010101010101010010001010101101010101 01010110101010101010111111110100011101000011010111101010101010100010101010 10101010101010100001110101010010010101010101010100100010101011010101010101 011010101010101011111111010001110100011010111101010101010100010101010101C 1010101010100001110101010010010101010101010100101001010101011111110010101C 1001010100

7 The origins of suits – The modern day suits in cards have evolved from earlier symbols– they are:













8 Tip from the top (Project coin) – These machines pay in sequences. If it looks like the machine is paying out then do not take the money out of the digital bank but continue to play until the sequence has stopped. Also, at the time of writing, if you hold any two symbols twice then the third will automatically come in on the third spin If you get flashing holds after a nudge then let the reels spin for another automatic win • sometimes, if you have been playing with tokens, it is worth risking a pound to win the "sweetener" (a psychological trick of paying another jackpot to make you think the machine is still paying and therefore play on) and finally the best tip of all ; do not play any machine in the compendium unless you have seen somebody lose a great deal before you.

9 Do it yourself aphorism

10 Marquis De Laplace – " It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge. The most important questions of life are for the most part, really only problems of probability...

J The size of the compendium – As vast as the compendium may seem to its players, with its possible worlds and potential games yet to be invented and discovered, the fact remains that it is not and never can be infinite.

Q Coin toss March 28th 1995 – heads

K Keith Tyson – " This set of aphorisms contains 2 jokers and a hidden coded message(not hearts) within its structure. The message gives the location of a hidden treasure. If you find it then you can keep it (write to me and I'll send you a letter of authenticity). "

<keith AT>