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+<?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>
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