--- /dev/null
+\documentclass[pink]{ootc-documentation}
+\usepackage{amssymb}
+
+\title{%
+ Defining the rule: What \textit{is} The Commissioner (all hail) anyway?
+}
+\id{001}
+\type{Investigation}
+\version{v1.3}
+\exerpt{%
+ Till fingers move and words be formed,\\
+ till ink doth drip and ribbon torn,\\
+ till stone is cracked and chisel blunt.\\
+ Blackjack 2 will be born.\\
+ I may be Max but I am not Value.\\
+ I am D. Value
+}
+
+\begin{document}
+
+\maketitle
+
+\section{Introduction}
+
+Across the history of Blackjack 2, and at time of writing, there have been 4 major revisions of The Rules. Each has improved it's reliability as the foundation of the collective gamespace. However, in version 4 of The Rules, there is no direct definition of what a "rule" is. This may seem circular, to define itself within itself, but a core concept of Blackjack 2 is the idea of rules as concrete, which is to say real. Both players, and Umpire, need to be able to look across the gamespace and point out each of the rules and what they mean as discrete elements.
+
+The Rules define The Rulebook as "the metaphysical space defining the actions of all elements of Blackjack 2, including itself. It is usually linked to a physical totem (a notebook)." as well as this esoteric definition, it also implies that a rule is equivalent to a "modification to the rulebook".
+
+In this investigation, I will be looking at Blackjack 2 at its very lowest level with the intention of defining the basic metaphysical elements of the game. My intention here is to lay a solid foundation upon which the rest of Blackjack 2 will sit, I am in no way trying to programmatically describe the game, nor can any of these described expressions actually be used within play. But by examining them closely, within the context of the game, I feel some further insight may be gleamed.
+
+\section{What should a rule do?}
+
+The purpose of a rule, as broadly as possible and within the context of Blackjack 2, is to apply limits to the gamespace. It does this with a transformation, acting upon the number of cards, the limit within which you are non-bust, the number of times you can pick up etc. In this way, a rule acts as a function, taking the gamespace as input and yielding a changed gamespace
+\footnote{%
+ It should be noted that, according to version 4 of The Rules, the gamespace contains "all elements of Blackjack 2." This includes all players, the rule functions themselves and, theoretically, The Commissioner (all hail) itself.
+ }
+. From this point on, think of rules purely as one-to-one functions.
+
+The following is our first definition of a rule ($R$), defined in the $\lambda$- calculus:
+
+\begin{equation}
+RG_{n}\
+\mapsto\
+( \lambda x.\texttt{<expr.>})G_{n}\
+\mapsto
+ G_{n+1}
+\end{equation}
+
+Where $G$ is the representation of the gamespace. \texttt{<expr.>} represents a black-box, within which the body of the rule sits. Its important to remember that this is not an input, for any rule it is a real and calculable expression which has been left undefined for practical purposes.
+
+This expression of $R$ raises an interesting idea though, if the definition of a rule is a function that affects the gamespace, then does that not make players almost identical to rules?
+
+\subsection{Players as rules}
+
+With this definition of a rule in our toolkit, we can effectively describe the entire workings of a game of Blackjack 2. The rule is the foundations upon which all other elements are built and therefore any element can be described by them. This includes players, cards, the deal, a "win" etc.
+
+In practice, you would struggle to formally notate any of these elements. This is because rules operate on many different levels of higher play, effecting anything from the metaphysics of the game to the real-world actions of the players
+\footnote{%
+ An exercise to the reader: attempt to define within $\lambda$-calculus the ruling "When a player picks up a King, the song We Like To Party (The Vengabus) by the Vengaboys."
+ }
+. To define anything in the real-world at such a low level is functionally impossible. So in reality, the expressions within functions $R$ are black boxes, interpreted by the umpire.
+
+In exactly the same way, the real-world actions of the players, their entire thought process and everything effecting this (in choosing their next action or devising a rule to be implemented) could be expressed within $\lambda$-calculus
+\footnote{%
+ Non-determinism is outside of the scope of this investigation.
+ }
+, but it is not only impossible to do so, but also unhelpful.
+
+This said these concepts and actions are not unknown, nor are they some kind of "input" into the gamespace. They are simply \textit{undefined}.
+
+\subsection{Rule-chaining, \textit{or play}}
+
+But how exactly could rules be implemented? How do we describe the order in which rules are evaluated? This can be done very simply by implementing recursion:
+
+\begin{equation}
+RG_{n} \mapsto\
+( \lambda x.\texttt{<expr.>}) G_n\
+\therefore\
+RG_{n+1}\
+\mapsto\
+\ldots\
+RG_{n+n_{0}}
+\end{equation}
+
+\begin{equation}
+R\
+\equiv\
+(\lambda x.Rx)\
+\rightarrow\
+RG_{0}\
+\mapsto\
+R(R(R(...)))
+\end{equation}
+
+As you can see, $RG_{n}$ yields $RG_{n+1}$, which yields $RG_{n+2}$ and so on. This expression is fundamental to Blackjack 2, entirely describing the mechanics through which the game is played, and is an accurate definition of what play is.
+
+In this situation, $R$ is not necessarily constant, and changes to shape play. For example, the first $R$ function might return a gamespace where a player has an extra card as well as dictating that the next function $R$ down is the rule that returns a gamespace where that same player is bust.
+
+This works because of the nature of what a rule is, that is to say, a one-to-one function. The implications of this are that only one rule can be applied at once, meaning they can be effectively chained without internal inconsistencies.
+
+Note that the second expression is an example that only applies if $R$ is a function that simply returns its input applied to itself, in reality this situation is impossible, as described below.
+
+\subsection{What is the gamespace and where does it end?}
+
+The gamespace, in this interpretation, is defined as a function with predefined inputs containing any number of nested rules (function $R$). The gamespace can have any depth, including an infinite one, so may not yield anything.
+
+Although it may look like it will nest endlessly, it will not. This is because of the property of rules to affect themselves. In reality it is possible for play to "end" with a rule that yields no further rules
+\footnote{%
+ This rule is not "introduced", it is instead yielded by another function (representing a player) and exists as the terminus to $G$.
+ }
+, such as the following:
+
+\begin{equation}
+R\
+\equiv\
+\lambda x.z\
+\rightarrow\
+(\lambda x.y )G\
+\mapsto\
+[ G/x ]y\
+\mapsto\
+y
+\end{equation}
+
+In this way, $G$ has a finite recursion depth and will always evaluate to $y$. Instead of seeing this as "ending the game" it is more useful to see it as the simplest possible evaluation of any $G$.
+
+But what is the most complex possible $G$? That is to say, what is $G_0$? This is simple, it is an evaluation of a function which takes a "game" as input (in this case, blackjack). We will call this function $C$. Where for any input, $C$ describes all possible gamespaces, $G$, and therefore the entirety of Blackjack 2.
+
+\textit{$C$ is The Commissioner (all hail)}
+
+\section{The Commissioner (all hail)}
+
+The Commissioner (all hail) is, therefore, a function that can be described within $\lambda$-calculus. There are still, however, high-level complexities that are difficult to express.
+
+Within the context of Blackjack 2, the mechanics of starting a game are as follows: Using $C$ and the rules of blackjack, an umpire creates the initial gamespace, $G_0$; a predetermined sequence of nested rules that accounts for each possible choice that the players will make; the gamespace reduces in complexity over real-time as the number of functions left to evaluate drops to zero and eventually yields $y$.
+
+Crucially, $C$ is calculable. Should you "know everything", it would be trivial to evaluate each layer of $C$ and therefore the order in which rules will "happen". Not to say that you must "know everything" to calculate $C$, simply by playing Blackjack 2 we are, step-by-step, calculating one possible version of $C$. Each time we play, we compute the Commissioner itself (all hail), knowing fully that it will not yield anything.
+
+\section{Conclusion}
+
+Within this investigation, we have adequately described not only play, the players and the concept of rules, but The Commissioner itself (all hail).
+
+To reiterate the introduction, this is not for the purposes of describing the game programmatically, or calculating $C$ (we do this through playing the game). It is purely as a foundation to build higher-level systems off of.
+With this in mind, I propose to the Office of the Commissioner (all hail) the following restructuring of the documentation concerning Blackjack 2.
+\begin{itemize}
+\item \textbf{The Game:} Describes the elements completely as shown in this document, this is Blackjack 2.
+
+\item \textbf{The Guide:} Sets out a coherent guideline for playing Blackjack 2, with emphasis that this is not a full definition of Blackjack 2. This would be done in a similar, or identical, way to the current set of "rules".
+The Game is not The Guide.
+\end{itemize}
+
+The use of the title "The Rules" in current documentation, I believe to be needlessly confusing and inaccurate. I would personally advise against titling any further documentation the "rulebook" or the "rules", risking confusion.
+
+\end{document}
\ No newline at end of file
--- /dev/null
+\documentclass[green]{ootc-documentation}
+
+\usepackage{soul}
+
+\title{%
+ The Deck
+}
+\id{002}
+\type{Data-sheet and documentation}
+\version{v1.1}
+\exerpt{%
+ A shuffle.\\
+ A deal.\\
+ We pick up.\\
+ Hold our cards close.
+}
+
+\begin{document}
+
+\maketitle
+
+\section{Introduction}
+
+With the ratification of version 3 of \textit{The Rules} came a new age of play for Blackjack 2. To commemorate this, the Office of the Commissioner (all hail) commissioned, then sanctioned: \textbf{The Deck}. In doing so, they set a new gold-standard for Blackjack 2 related works and gifted upon the players a new and convenient way to play!
+
+\section{Features}
+
+\vspace{5mm}
+\begin{minipage}{\textwidth}
+ \begin{tabular}{ r l l }
+ \textbf{Feature} & \textbf{The Deck} & \textbf{Conventional playing cards} \\
+ \hline
+ \hline
+ Number of suits & 7 & 4 \\
+ \hline
+ Number of cards per suit & 13\footnote{The 7th suit contains 4 cards, while all other suits contain 13 cards.} & 13 \\
+ \hline
+ Number of colours & 4 & 2 \\
+ \hline
+ Number of card variables (numerical) & 2 & 1 \\
+ \hline
+ Number of card variables (qualitative) & 1 & 0 \\
+ \hline
+ Size & 44.45×63.5mm & 56mm x 88mm\footnote{Varies with manufacturer.} \\
+ \hline
+ Blood & Yes & No
+ \end{tabular}
+\end{minipage}
+
+\subsection{Extra suits and colours}
+
+Both the number of suits and the number of colours has been increased. This choice was made to attempt to reduce the meaning associated with specific cards by simply increasing the overall number of them and therefore the probability that any card will be dealt. An example of meaning would be a rule that only activates when a single card is dealt.
+
+The Rings suit (or the “unknown” suit) was introduced to increase the number of edge cases while maintaining suits consistent with conventional playing cards.
+
+\vspace{5mm}
+\begin{minipage}{\textwidth}
+ \begin{tabular}{ r l l }
+ \textbf{Suit shape} & \textbf{Suit colour} & \textbf{Number of cards} \\
+ \hline
+ \hline
+ Hexagons & \cellcolor{ootc-pink}Pink & 13 \\
+ \hline
+ Diamonds & \cellcolor{ootc-pink}Pink & 13 \\
+ \hline
+ Circles & \cellcolor{ootc-green}Green & 13 \\
+ \hline
+ Triangles & \cellcolor{ootc-green}Green & 13 \\
+ \hline
+ Squares & \cellcolor{ootc-blue}Blue & 13 \\
+ \hline
+ Stars & \cellcolor{ootc-blue}Blue & 13 \\
+ \hline
+ Rings/Unknown & Black & 4
+ \end{tabular}
+\end{minipage}
+
+\subsection{Card variables}
+
+2 additional card variables where added, with the intention of convenience for the players when creating more complex rules. At the initial gamespace, only the cards numerical value is used.
+
+The un-value of the card is also notated at the bottom of the card for player convenience. When a card is flipped metaphysically, it can also be physically flipped, allowing for quicker evaluation of total hand value.
+
+The symbol for the conventional "ace" ("A") which represents either 1 or 11 has been replaced with "1/11" to provide a verbose disconnect between Blackjack 1 and Blackjack 2.
+
+\subsubsection{Qualitative variable}
+
+A new variable called "blood-type" is added to cards, it usually ranges between $\pm$(A, B, AB and O). Its nature not only implies some interesting things regarding the nature of cards, but also, in a way, provides the players with 2. These being: 1) the polarity of the blood type and 2) the type itself. This variable is distributed proportionally.
+
+\subsubsection{Public variable}
+
+A new variable called “variant” is added to the cards, it usually ranges between 1-9 (represented in Roman numerals). It is displayed, not only on the face of the card, but also its back. This allows any player to see the variant of any other players cards at any time. This variable is distributed proportionally.
+
+\subsection{The principal of edge cases}
+
+The deck has been designed with the principal of edge cases in mind, and a major factor throughout its design was the deck's effect on rules. This is to say, for any card variable, there is a card that breaks the predictable pattern of The Deck.
+
+This has, in many games, led to both interesting emergent narrative, as well as a far more interesting gamespace.
+
+\vspace{5mm}
+\begin{minipage}{\textwidth}
+ \begin{tabular}{ r l }
+ \textbf{Card variable} & \textbf{Edge case}\\
+ \hline
+ \hline
+ Value & The "i" of Rings\\
+ & The "?" of Rings\\
+ & The "$\infty$" of Rings\\
+ \hline
+ Variant & The 4 of Stars (Variant: "Null")\\
+ \hline
+ Blood type & The J of Stars (Blood type: "N/A")
+
+ \end{tabular}
+\end{minipage}
+
+\subsection{Extra cards}
+
+The Deck also contains a flavour text card, as well as an umpire token. This could potentially allow the role of umpire to be dealt into a game.
+
+\section{Conclusion}
+
+Through play, we have found The Deck to enhance the game and successfully increase gamespace complexity. There a single factor that I see as problematic, this is the distribution of edge cases. For example: I could memorise the hidden values of the edge case of the public variable, variant ("Null"). In this way the edge cases may get predicable after many rounds of play.
+
+I believe this can only be avoided by introducing more, and different, edge cases. Although this risks making the game unplayable or un-fun.
+
+As well as this, I also propose making the distribution of blood-types proportional to real-world values to enhance its narrative weight.
+
+\end{document}
\ No newline at end of file
--- /dev/null
+\documentclass[pink]{ootc-documentation}
+
+\usepackage{amssymb}
+
+\title{%
+ The Game and The Guide
+}
+\id{003}
+\type{Schema version 5}
+\version{v1.2}
+\exerpt{%
+ "If the gamespace is left in a stable state with no connection to the physical world, something terrible happens (Pillar of the Physical: 2.6.2.2)"
+}
+
+\begin{document}
+
+\maketitle
+
+\section{Introduction}
+
+This is version 5 of what have been called "The Rules of Blackjack 2"
+\footnote{%
+ This is misleading, as the "rules" contained within all previous versions where not "rules" in the eyes of the rulebook itself. This created both meta-rules and rules. This document contains no rules and instead should be seen as a schema, contained within which is Blackjack 2. Poorly formed Blackjack 2 is not illegal, or "against the rules", in any way. But it is not Blackjack 2.
+}
+. With which, a new era for Blackjack 2 has started. An era of investigation! An era of new, and more complex, play.
+
+There are two parts of this document, with different uses. The Game and The Guide. The Game is the schema of Blackjack 2, ratified by the Office of the Commissioner (all hail), and will be followed. The Guide will be shown alongside The Game, existing as a practical example or lossy translation of not only what The Game means, but also what it implies. It is important, but not essential, to understand both.
+The Game will be shown in mathematical expression, while The Guide will be shown below it.
+
+\section{The concepts}
+
+\subsection{The Rules}
+
+\begin{equation}
+R\
+\mapsto\
+(\lambda x.\texttt{<expr.>})\
+\end{equation}
+
+Where "\texttt{<expr.>}" represents the body of the rule. This is not consistent across R.
+
+\begin{equation}
+RG_{n}\
+\mapsto\
+[G_{n}/x](\texttt{<expr.>})\
+\mapsto\
+RG_{n+1}
+\end{equation}
+
+The above describes a Rule as a function that takes $G$ (the gamespace) as input and returns a changed gamespace. The expression within $R$ is difficult to calculate but could represent any possible change to the gamespace. This is not usually the case in Blackjack 2 and in practical play, the umpire may decide that a Rule must only have one single effect on the gamespace, limiting the players to making gradual changes to the game only.
+
+Under this schema, players are rules by definition. Due to the recent advancements during version 4, this fact is not widely known and has not yet been exploited. The impact on the game still has yet to be investigated.
+
+\subsection{The Gamespace}
+
+\begin{equation}
+G\
+\mapsto\
+R(R(R(\dots)))\
+\mapsto\
+y
+\end{equation}
+
+The above describes how the gamespace is nothing more than the order in which rules are applied, with $G_n$ being one rule "deeper" than $G_{n+1}$. It also describes that games always evaluate to nothing. In this way, the gamespace encodes the entire state of the game, from which you can calculate the course it will take.
+
+\subsection{Play}
+
+\begin{equation}
+RG_{ n }
+\leadsto\
+RG_{ n+1 }
+\end{equation}
+
+The above describes how play is the process of getting closer to yielding $y$ (nothing). If the game is deemed currently unplayable by the umpire (meaning "play", in this definition, has stopped), they can act to revert changes. This fits within the schema, however, as the function $R$ in which they act was already encoded within $G$. This action of the umpire should not be seen as a change to $G$, instead as an inevitable consequence of the game which could not be avoided.
+
+The umpire fills the gap between the play and the players, bringing the gamespace back to a stable state where needed. The answer, then, to "when should the umpire step in to fix the gamespace" is: "when they do".
+
+\subsection{The Commissioner (all hail)}
+
+\begin{equation}
+C\
+=\
+(\lambda x.G_{0})\
+\rightarrow\
+[\texttt{The Universe}/x](G_{0})
+\mapsto
+RG_{1}
+\mapsto
+\ldots
+\mapsto
+y
+\end{equation}
+
+The Commissioner (all hail) can therefore be defined as a function taking the universe as input and evaluating though nested rules of finite depth before yielding $y$, or, nothing.
+In this way, by playing Blackjack 2, we evaluate each layer of $C$, calculating the Commissioner (all hail) each time we play. This is an emergent feature of the game, not being primarily focused on during play.
+
+\section{Conclusion}
+
+Within this document, the core concepts of Blackjack 2: Rules, The Gamespace, Play and the Commissioner (all hail), have been fully described mathematically and elaborated upon. The purpose of this document is to clear up any ambiguity around the difficult question "what even is a rule?" or "is the Commissioner (all hail) even real?". Providing a clear and succinct answer: "$(\lambda x.\texttt{<expr.>})$" and "no".
+
+\end{document}
\ No newline at end of file
--- /dev/null
+\documentclass{ootc-memo}
+
+\begin{document}
+
+\maketitle
+
+\begin{enumerate}
+\item Across the history of Blackjack 2, and at time of writing, there have been 4 major revisions of The Rules. Each has improved it's reliability as the foundation of the collective gamespace. However, in version 4 of The Rules, there is no direct definition of what a "rule" is. This may seem circular, to define itself within itself, but a core concept of Blackjack 2 is the idea of rules as concrete, which is to say real. Both players, and Umpire, need to be able to look across the gamespace and point out each of the rules and what they mean as discrete elements.
+\begin{enumerate}
+\item second test
+\item and another
+\begin{enumerate}
+\item this is a stupid amount of levels of list to be honest
+\begin{enumerate}
+\item toooo many
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+\end{enumerate}
+
+
+\end{document}
\ No newline at end of file
--- /dev/null
+% ---------------------------------------------------------
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+%
+% This file is licenced under the Blackjack 2 Esoteric
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+ The Office of the Commissioner (all hail)}
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+% ---------------------------------------------------------
+\AtEndDocument{%
+ \newpage
+ \section*{Inprint}
+ \noindent Published by The Office of the Commissioner (all hail).\par
+ \noindent Designed by Goodnight Publishing.\par
+ \vspace{5mm}
+ \noindent For more information, see: \texttt{https:// blackjack2.neocities.org}\par
+ \noindent Address inquiries to: \texttt{commissionerallhail@gmail.com}\par
+
+ \section*{Licence}
+
+ All works related to Blackjack 2, including those published by the Office of the Commissioner (all hail) are licenced under the \texttt{Blackjack 2 Esoteric Licence}.
+ For the latest version, see: \texttt{https://blackjack2.neocities.org/licence.txt }\par
+ \vspace*{\fill}
+ \includegraphics[height=3cm]{ootcgray}
+ \hspace{5mm}
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+\endinput
\ No newline at end of file
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+
+\renewcommand{\maketitle}{%
+ Office of the Commissioner (all hail)\includegraphics[width=3cm]{ootccolour}
+ \vspace{5mm}\\
+ MEMORANDUM
+ \rule{\textwidth}{0.4pt}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent ID:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \noindent\@id
+ \end{minipage}
+ \vspace{5mm}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent From:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \noindent\@from
+ \end{minipage}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent To:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \noindent\@to
+ \end{minipage}
+ \vspace{5mm}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent Subj:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \noindent\@title
+ \end{minipage}
+ \vspace{5mm}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent Ref:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \renewcommand{\labelenumi}{(\alph{enumi})}
+ \begin{enumerate}[wide, labelwidth=1cm, labelindent=0pt]
+ \@refs
+ \end{enumerate}
+ \end{minipage}
+ \vspace{5mm}\\
+ \begin{minipage}[t]{2cm}
+ \vspace{0pt}
+ \noindent Encl:
+ \end{minipage}
+ \begin{minipage}[t]{10cm}
+ \vspace{0pt}
+ \renewcommand{\labelenumi}{(\arabic{enumi})}
+ \begin{enumerate}[wide, labelwidth=1cm, labelindent=0pt]
+ \@encl
+ \end{enumerate}
+ \end{minipage}
+ \vspace{5mm}\\
+ \rule{\textwidth}{0.4pt}
+ \thispagestyle{empty}
+ \raggedright
+ }
+\endinput
\ No newline at end of file
projects / ootc-docs / commitdiff
