\chapter{Dice}

\section*{Notation}

We use \dc{N} to denote an N-sided die. The dice commonly used in this game are: \dc4, \dc6, \dc8, \dc10, \dc12, \dc20 and \dc100. If we want to say, ``roll X dice and add their results together,'' we denote that with X\dc{N}. For example, to say, ``roll two eight-sided dice and add the results'', we write 2\dc{8}.

\section*{\dc{12}}

The \dc{12} is the main die that determines the fate of characters in Kingdoms and Rulers. In general, when the fate of a character hangs in the balance of chance, the player assembles a pool of dice based on the stats (\cref{ch:stats}) that are relevant to the situation. The roll of those dice determines the outcome.


\begin{multicols}{2}

    \subsection*{Difficulty Threshold}

    Whether a roll is a success or a failure depends on the Difficulty Threshold (\stat{DT}) of the task. The DT is a value between 1 and 11, which determines which rolls are successes and which are failures. For any particular task, the \stat{DT} is either set by the GR, or is computed from the opponent's stats. Rolls with results greater than the \stat{DT} are counted as successful and the remaining rolls are failures.

    % standard difficulry 8 - prof - stat?

    \subsection*{Rolling 1 or 12}

    When rolling for a test, rolls of either 1 or 12 have special meaning: they are critical failures and critical successes, respectively. Critical rolls provide double the successes/failures. Rolling 1 gives two failures and rolling 12 gives two successes. Note that the range of \stat{DT} is 1 to 11, which means that rolls of 1 are always failures and rolls of 12 are always successes.

    In the course of play, combination of stats may produce \stat{DT} greater than 11. As a rule, such a task is impossible. However, the GR may allow a player to roll anyway and interpret the result based on the number of critical successes.

    \subsection*{Margin of Success}

    The difference between the number of successes and the number of failures on a roll is the Margin of Success. For basic tests, the size of the margin does not matter, as long as it is positive. For more complex situations, the GR can use the margin to determine the degree of success. In encounters, the margin is used for further rolls to determine the details of the result, such as damage, or how hard something is to resist.

    \begin{boxnote}
        When playing with real dice, the margin can be determined by, first, splitting the dice into piles of critical successes, successes, failures and critical failures. Then, the margin can often be determined with a quick glance, or by removing the same number of dice from matching piles, i.e., from both successes and failures, or from both critical piles, and seeing what's left.

        Alternatively, dice can be directly paired and moved to the side.

        There are more ways to do it and, with practice, each player can learn their own shortcuts to computing the margin.
    \end{boxnote}

    \subsection*{Tests}

    Depending on the complexity of the task at hand, different types of tests can be used to determine the success. Broadly, the tests fall into two categories: basic and extended. Basic test are used for quick and simple obstacles, while extended tests are used for longer tasks, such as combat.

    \subsubsection*{Basic Test}

    A basic test is used for situation with a simple success/failure outcome. If it makes sense, the margin of success can be used to determine the details of the test.

    \begin{samepage}
        \begin{enumerate}
            \item GR specifies which stats are applicable.
            \item Player assembles the dice pool.
            \item GR sets or determines the DT and possibly a required margin of success.
            \item Player selects a number of dice from their pool and rolls them.
            \item Player determines the margin of success.
            \item GR interprets the result.
        \end{enumerate}
    \end{samepage}

    The player may elect to roll fewer dice than their whole pool. The statistics of dice rolls are complex, but two observations might help with picking the number of dice.

    First, even numbers of dice have a higher chance of success. This is especially pronounced at small numbers of dice.

    Second, small numbers of dice are more likely to have a positive margin when \stat{DT} is greater than 6, and vice versa. On the other hand, the number of dice places a limit on the size of the margin. Therefore, choosing to use a smaller pool, may not generate enough successes to complete the task.

    \subsubsection*{Extended Test}\label{sec:extended_test}

    An extended test occurs during more complicated tasks; a common example is combat, or a negotiation. It represents an arduous task that requires time and concentration to complete.

    It differs from the basic test in that the pool starts with the initial size, then, after every roll, failures are removed, and new dice are added based on the relevant stat -- either \stat{con} or \stat{CHA}.

    \begin{samepage}
        \begin{enumerate}
            \item GR specifies which stats are applicable.
            \item Player assembles the dice pool.
            \item GR sets or determines the DT \label{en:start}.
            \item Player selects a number of dice from their pool and rolls them.
            \item Player determines the margin of success.
            \item GR interprets the result.
            \item Player removes all dice that came up failures from the pool.
            \item Player adds \stat{CON}/\stat{CHA} dice to the pool.
            \item Repeat from \ref{en:start}.
        \end{enumerate}
    \end{samepage}

    This test is often part of an encounter where different character take turns. In that case, the pool is replenished at the end of every character's turn, for every character that rolled in that turn.

    \begin{boxnote}
        In the rest of this book I use ``margin of success'' and ``successes'' interchangeably. This may be confusing, as I refer to the number of dice that do not pass the difficulty threshold as ``failures.'' The number of dice that do pass the threshold is never relevant on its own, so for the sake of brevity, I use the term successes for the margin.
    \end{boxnote}

    \subsubsection*{Opposed Test}

    Sometimes, an action taken by a player is opposed by an action or a reaction by their enemy (or possibly another player).

    The circumstances of the test determine the \stat{DT} for both participants. Commonly, the \stat{DT}s are independent, and the winner is whoever gets more successes.

    If one participant in the test is clearly trying to achieve something, for instance, using an ability, they must attain a margin of 0 or more, or they automatically fail the test.

    If both participants are equally involved -- having an arm wrestling competition, a game of chess, etc. -- negative margins can be successful if the opponent rolls an ever lower one.
\end{multicols}

% \section*{Saving Throws}

% GR set

% 7+margin for magic