<?xml version="1.0"?>

<!DOCTYPE section PUBLIC "-//OASIS//DTD DocBook XML V4//EN"

        "/usr/share/sgml/docbook/dtd/xml/4.2/docbookx.dtd"

[

  <!ENTITY % struct-dtd SYSTEM "struct.dtd">

  %struct-dtd;

]>

<section id="sactgroup" revision="$Revision: 1841 $ $Name$"

  vendor="1.19" xmlns:xi="http://www.w3.org/2003/XInclude">

  <title id="stactgroup">Group Actions</title></title>

  <para>It's often interesting to see the characters cooperate

    together for a particularly difficult task, or to put at the head

    of a troup of kobolds and see how they can make them <emphasis

    role="ironic">efficient</emphasis>.  The problem meet most often

    here is that the rules that they know can only be used to rule for

    one character at once, asking for rolling dice for each character

    and each action, which is quite long.  Arpeggii uses some

    shortcuts to manage those kinds of ruling, with only one roll, and

    obtains similar results as if each character have roll for

    themself.  You can them <link linkend="scombinaisons">compute the

    total power of a group</link>, <link linkend="sjetgroupe">count

    the number of success</link> in a group with only one roll, and

    even <link linkend="sjetdist">determine the degrees of

    success</link> of each individual character of the group.</para>

  <section id="scombinaisons">

    <title id="stcombinaisons">Values Combination</title>

    <para>Some actions can be sometime impossible for one individual

      and required the cooperation of the group to be succeed.

      However, attach a young puppy to a group of 10 horses will not

      help a lot to the task.  To find the strength of the group, you

      can <emphasis>combine</emphasis> the characters' Attributes.

      The simple method is to convert all of them in Measures, add

      them and convert it back in Value.  This way can became long and

      tedious however when they are many characters.</para>

    <para>Another way is possible but required a bit of practice from

      the GM to be efficient, and can be long if the group is too much

      heterogenous.  However, as soon as the group is composed of

      individual with identical attributes, the calculation became

      very quick and make it very clear when someone will not add

      something interesting to the total strenght of the group.</para>

    <procedure id="pcombinaison">

      <title id="ptcombinaison">Calculation of Values Combination</title>

      <step id="pscombind">

        <para>Take each individual with the same Value and form a

          group.  The Value of those group will be equal to the common

          Value of each individual, plus the Value corresponding to

          the number of individuals in the group (e.g. +5 is you have

          3 individuals, or +0 if you only have one).</para>

      </step>

      <step id="pscombgrpident">

        <para>Take all groups with the same Value and combine them

          again but this time by adding the Value of the number of

          groups instead of the number of individuals.  For example,

          if you have 3 groups with +2 each, whatever the number of

          individuals in those groups, the new group will have a Value

          of +2 + 5 (the Value of 3), which is +7.</para>

      </step>

      <step id="pscombgrpdiff">

        <para>Take the two groups with the least Value.</para>

        <substeps>

          <step id="pscomb1a3">

            <para>If the difference between both is 3 points or less,

              combine them in a new group with give them the Value of

              the strongest one +2.</para>

          </step>

          <step id="pscomb4a6">

            <para>If the difference is between 4 and 6 included,

              combine them and give the Value of the strongest +1.</para>

          </step>

          <step>

            <para>If the difference is greater than 6 points, discard

              the weakest group and keep the stronger.  The weakest

              group will be ignored in the total but if a new

              individual is add at later time, you'll be able to check

              if he can be add to discard groups first to form a

              strongest group.</para>

          </step>

        </substeps>

      </step>

      <step id="scombfinal">

        <para>Redo the last two steps until you have only one group

          left, except for the discard groups.  The combined Value of

          all individuals will be the Value of this final

          group.</para>

      </step>

    </procedure>

    <para>It should be note that's not always possible (or realistic

      if you prefer) to combine Value this way, and the Game Master

      can always impose some penalities and even restrictions to the

      numbers of characters which can participate and for their

      know-how, including asking for a leadership roll to the chief of

      the group.  It's the GM responsability to create the right

      suspension of disbelief and keep the players interest.</para>

    <example id="xcombinaison">

      <title id="xtcombinaison">Group Value Combination</title>

      <para>A group is composed of 6 characters with a score in Body

        of -10, -5, -5, +3, +4 and +5.  Since they are already

        ordered, we can began to group them:</para>

      <orderedlist>

        <listitem>

          <para>First, we group the identical Values: We have two

            individuals with -5.  We can so group them by adding to

            them the Value of 2, which is +3.  The new group value

            will be -5 + 3 = -2.</para>

        </listitem>

        <listitem>

          <para>The two weakest groups can are now -10 and -2.  The

            difference is 8 points, so the -10 group (a single

          individual) can be ignored.</para>

        </listitem>

        <listitem>

          <para>We now compare the -2 and +3 group.  The difference is

            5 points and so we combine both groups and give them the

            value of the stronger (+3) augment of one point, for a

            total of +4.</para>

        </listitem>

        <listitem>

          <para>In the remaining groups, we now have a new identical

            pair, which is two +4 groups.  Again, we can combine them

            in a new group by adding +3 to the common Value, for a

            total of +7.  The group is now composed of 3 subgroups,

            one ignored (-10), a +5 and a +7 group.</para>

        </listitem>

        <listitem>

          <para>We compare again the two weakest, +5 and +7 (the -10

            is still ignored).  The difference is only 2 points.  The

            groups can so be combined in a new group with the highest

            Value (+7) augment of 2 points, for a final group with a

            <emphasis>combined</emphasis> Body Attribute of +9.

        </listitem>

      </orderedlist>

      <para>Remark that if the group at -10 was compared with the -5

        group first, you will got a group with -4, which combined with

        the other group at -5, will also give you a group with -2.

        So, it doesn't make any difference at the end and since the

        combination of identical groups is the only one which can be

        done on multiple groups at the same time, she is favored most

        of the time.</para>

    </example>

  </section>

  <section id="sjetgroupe">

    <title id="stjetgroupe">Rolling dice for a group</title>

    <para>In a game, the players are often confronted to group of NPC

      sometime numerous and often hostile.  In a combat or a pursuit,

      it will be tedious for the GM to roll dice individually for each

      members of the group.  When the group is sufficiently <anchor

      id="refjgrpcond"/>homogeneous (no more then 5 points of

      difference in their Competency Level for this particular action)

      et that the roll is a <link linkend="sactsimple">simple

      action</link>, a quick alternative can be used instead.  First,

      the Game Master make a normal roll for the whole group.  Then,

      she takes the Value of the total number of members in this

      group.  To this value, she subtracts either the degrees of

      success if this one is positive or the degrees of failure

      elsewhere, and then subtracts 3 more points to the result.  The

      result will always be at most the Value of the group minus 3.

      This Value can then be converted in a Measure and round up to

      the lower whole number.  If the roll was positive, this Measure

      represent the number of individuals that

      <emphasis>failed</emphasis> their roll.  Elsewhere, it represent

      the number of individual that succeed their roll.</para>

    <example id="xreussitegroupe">

      <title>Simple Group Roll</title>

      <para>A group of 25 guards try to catch the characters in a

        mountain road.  The characters decide to destroy a little

        bridge to slow them down.  The guards decide to jump over the

        small gap.  The difficulty is -5 under Ag+Pw, where the guards

        have a total of +3 each.  The Game Master roll the dice and

        get +4, which is a +2 degrees of success.  The group of 25

        guards correspond to a Value of +14.  If you subtract the

        degrees of success and 3, you get +9.  The <xref

        linkend="tmesures"/> indicate that it's equivalent to a

        Measure of 8.  So, 8 guards have fail their roll into a

        dramatic end.  If the roll have give a failure at -3, the

        final value will then be (+14 - 3 - 3 =) +8, and so only 6

        guards will have <emphasis>succeed</emphasis> to jump over the

        gap.  It will have take a degrees of success of +12 for every

        guards to pass the gap.</para>

    </example>

    <para>When you roll the dice for a group, it is good advice to

      only make <link

      linkend="sjetdifference"><emphasis>closed</emphasis> difference

      roll (±d10)</link>.  The great range of open rolls create must

      of the time incredible catastrophe or miraculous prowess,

      instead of normal result.</para>

  </section>

  <section id="sjetdist">

    <title id="stjetdist">Group Degrees of Success</title>

    <para>The precedent method is very exact if you apply the

      theoretical probability curve on which is based the Harmonies,

      but which are only an approximation of the real dice dispersion.

      A similar method permit not only to be nearer than the real

      value, but also to calculate the level of success of each

      individual or, to be exact, to know the number of individual for

      each level of success.  It is, however, much more longer and

      complex.  It will be to the Game Master to choose which of both

      it will used, but must stay consistent for their players.</para>

    <para>The method need the <link linkend="refjgrpcond">same

      conditions</link> then the preceding method (homogeneous group)

      and at least hundreds of individual if we want to detail each

      level of success (the precision will be lesser elsewhere).  The

      Game Master begin again with a roll for the whole group.  She

      then convert the number of individuals in Value and subtracts

      the number of points indicate in <xref linkend="tjetdist"/>, in

      function of the difference between the degrees of success of the

      roll and the one we are interested in.  The first row of the

      table represent the difference between the degrees of success of

      the roll and the one we want to know, the second row show the

      value to subtract to obtain the Value of the number of

      individuals having exactly this number of degrees of success,

      and the last one give the value to subtract to obtain the number

      of individual that have <emphasis>at least</emphasis> this

      difference in number of degrees of success.  The result can then

      be converted into a Measure and you got the number of

      individuals having this number of degrees of success plus or

      minus the difference.  For columns with fraction (like -2.5),

      you must take the average of the two adjacent values.  For

      example, at -2.5, you must take the average of the Measure of -2

      and -3.</para>

    <table frame="all" id="tjetdist">

      <title id="ttjetdist">Groups Degrees of Success</title>

      <tgroup cols="11" align="center">

        <colspec colnum="1" colwidth="1.5in" align="right"/>

        <colspec colnum="2" colwidth="0.5in"/>

        <colspec colnum="3" colwidth="0.5in"/>

        <colspec colnum="4" colwidth="0.5in"/>

        <colspec colnum="5" colwidth="0.5in"/>

        <colspec colnum="6" colwidth="0.5in"/>

        <colspec colnum="7" colwidth="0.5in"/>

        <colspec colnum="8" colwidth="0.5in"/>

        <colspec colnum="9" colwidth="0.5in"/>

        <colspec colnum="10" colwidth="0.5in"/>

        <colspec colnum="11" colwidth="0.5in"/>

        <tbody>

          <row>

            <entry>difference</entry>

            <entry>0</entry>

            <entry>1</entry>

            <entry>2</entry>

            <entry>3</entry>

            <entry>4</entry>

            <entry>5</entry>

            <entry>6</entry>

            <entry>7</entry>

            <entry>8</entry>

            <entry>9</entry>

          </row>

          <row>

            <entry>exactly this difference</entry>

            <entry>-10</entry>

            <entry>-10.5</entry>

            <entry>-11</entry>

            <entry>-11.5</entry>

            <entry>-12</entry>

            <entry>-13</entry>

            <entry>-14</entry>

            <entry>-15</entry>

            <entry>-17</entry>

            <entry>-20</entry>

          </row>

          <row>

            <entry>this difference or more</entry>

            <entry>-2.5</entry>

            <entry>-3.5</entry>

            <entry>-4.5</entry>

            <entry>-5.5</entry>

            <entry>-7</entry>

            <entry>-8</entry>

            <entry>-10</entry>

            <entry>-12</entry>

            <entry>-15</entry>

            <entry>-20</entry>

          </row>

        </tbody>

      </tgroup>

    </table>

    <example id="xjetdist">

      <title>Group Degrees of Success</title>

      <para>We have a group of 300 soldiers (Value of +25) who get a

        +2 success margin.  With +25 - 10 = +15, so 30 soldiers that

        got exactly this success margin (+2).  For the number of

        soldiers who got +1 or +3 (1 point of difference), we must

        take the Measure of -10 (which we already have: 30) and -11

        (which is the same as the column 2, which we still don't

        know).  So, for a difference of 2 points, we have +25 - 11 =

        +14, or 25 individuals with 0 degrees of success, and another

        25 with +4 degrees of success.  We can now take the sum of 30

        and 25, which is 55, that we can split in two: there will be

        28 soldiers with +1 degree of success, and 27 with +3 degrees

        of success.</para>

    </example>

    <para>The last row ask for more explanations.  If you're looking

      for the number of individuals with +3 or more degrees of

      success, and that you roll a +2, it's easy.  You just have to

      convert for a difference of +1 or more.  But if you were looking

      for those with 0 or more, you're in trouble!  You can take only

      those with 2 points of difference or more, because you will only

      get those with +4 or more!  What's you really looking for is

      those with +0 (2 points of difference exactly), +1 (1 points of

      difference exactly) and +2 and more (0 or more points of

      difference).  But a shorter way will be to looking for the

      opposite.  Find all of them that get -1 or less (3 points of

      difference and more) and subtract them from the total of

      individual in the group to find those who get +0 and

      more.</para>

    <example id="xjetdist2">

      <title>Group Degrees of Success 2</title>

      <para>With the same group as before, we are looking for the

        number of those that got +0 and more degrees of success.  This

        represent a difference of 2 points which include the result of

        the roll.  We can then find those who got less than zero

        degrees of success (a difference of 3 points or more) and

        subtract it to the Measure of the group.  The column 3 got us

        with -5.5, which mean that we must take the average of -5 and

        -6.  +25 - 6 = +19, or 80 individuals.  +25 - 5 = +20, or 100

        individuals.  The average is (100+80)/2 = 90 soldiers who has

        less than zero degree of success.  On the initial group of 300

        soldiers, that's mean that (300-90) = 210 soldiers have got +0

        or more.  Using the method view in the preceding section, we

        would get 100 individuals that have failed (+25 -2 -3 = +20),

        so 200 individual that have succeed.</para>

    </example>

    <note userlevel="adv">

      <title>Choosing between the two methods</title>

      <para>The maximum error is 6% or less on the total of

        individuals for the first method, and less than 1% for the

        second method.  You have to choose between a more precise but

        longer roll, or a quickest but less exact one.  At the same

        time, You can choose to only take the lowest Value instead of

        calculating the average when you got an .5 factor to subtract.

        Again, this is just a compromise on speed and

        exactitude.</para>

    </note>

  </section>

</section>

<!-- Keep this comment at the end of the file

Local variables:

mode: xml

sgml-omittag:nil

sgml-shorttag:t

sgml-namecase-general:t

sgml-general-insert-case:lower

sgml-minimize-attributes:nil

sgml-always-quote-attributes:t

sgml-indent-step:2

sgml-indent-data:t

sgml-exposed-tags:nil

sgml-local-catalogs:nil

sgml-local-ecat-files:nil

sgml-default-dtd-file:"section.ced"

End:

-->