Dice Mechanics: Motivation
This is the first of three articles discussing common diceusing
mechanics used in tabletop RPGs (aka "narrative" or
"pencilandpaper" RPGs). This articles covers how dice mechanics are
generally used, and in light of this what criteria they should be
judged on.
General Dice Terminology
Nearly all dice mechanics share a similar concept at the heart.
To resolve an attempted action, the character has a numerical rating
of her effectiveness: here called the "stat". There may
sometimes be two stats (generally "attribute" and
"skill"), but more often these are combined into a single
number. The action also has a numerical rating of
"difficulty", which may default to a standard. Dice are then
rolled to determine whether the action is a "success" or a "failure",
and the degree of success/failure.
Dice abbreviations are "d" followed by the number of sides.
i.e. "d6" is a sixsided die and "d10" is a tensided die. A number
before the "d" indicating to roll that many dice. Thus, "4d6" means
rolling four sixsided dice. Unless noted otherwise, assume the
numbers are all added together. The dice commonly available at hobby
stores are: d4, d6, d8, d10, d12, and d20. "Percentile dice"
(aka "d100" or "d%") refer to a special roll from 1 to 100, where you
roll one tensided die for the "tens" digit and another tensided die
for the "ones" digit.
"Openending" refers to mechanics where if a certain roll of
the dice comes up, you make another roll: reroll and add, roll extra
dice, or something similar. This can allow for a theoretically
infinite range of results. Openending can be added to any scheme
of dice mechanic.
"Variance" is a general term for how widely spread out the
results are. For example, rolling 1d6 and taking the highest roll out
of 5d6 both can produce results between 1 and 6. However, the highest
out of 5d6 has much less variance. This can be measured by the
"rootmeansquare" of the distribution, which is calculated by:
RMS= SquareRoot[
Sum over all rolls of (Result  Average Result)^{2}
]

For a single die roll, the RMS is about 29% of the number of sides.
Criteria to Investigate
There are a number of semiobjective factors which dice mechanics
can be judged on. I will outline a few of these below.
 Determining Degree of Success/Failure
 Almost any dice mechanic can yield a "degree of success" by
seeing how close your roll was to a failure. However, some
mechanics make it easier to determine and use this. Degree of
Success is sometimes a number, or it may be a category like
"partial", "normal", and "critical" (i.e. very good) success.
 Randomness vs Skill
 Some mechanics have a wider or narrower range of results for a
character with the same amount of capability. You can measure
the variance of the die roll compared to the results, or compared
to the range of average to expert skill, say.
 Granularity
 Granularity varies from finelygrained (i.e. many small steps) to
coarsegrained (i.e. a few large steps). For a dice mechanic,
there is potentially different granularity for stat, difficulty,
and degreeofsuccess. Finer granularity lets you take into
account more subtle factors, but usually makes resolution more
complicated and slow.
 Ease and Speed of Use
 Obviously, more dice, more mathematical operations, and/or larger
numbers are slower and more difficult. In general, comparison is
easier than addition, which is easier than subtraction, which is
easier than multiplication, which is easier than division. My
rule of thumb is to ask how easily rolls can be made (1) when
tired/sleepy/distracted after a long workday plus several hours
of gameplay, and/or (2) when simultaneously eating pizza around
a crowded coffee table.
 Availability
 The only commonly available dice are d6's. Among games that use
other dice, though, you can compare the number and variety of
dice that are required. The more dice required, and especially
the more types of dice required, the more difficult it is
to have all of the dice on hand for play. A few games use
particularly unusual dice, such as 30sided dice, FUDGE dice
(special sixsided dice used by FUDGE), or knucklebones (special
eightsided dice used by Fvlminata).
Next: Methods
J. Hanju Kim <hanjujkimatgmaildotcom>
Last modified: Mon Jun 16 17:51:24 2003