# Dice Mechanics: Motivation

This is the first of three articles discussing common dice-using mechanics used in tabletop RPGs (aka "narrative" or "pencil-and-paper" RPGs). This articles covers how dice mechanics are generally used, and in light of this what criteria they should be judged on.

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## 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 six-sided die and "d10" is a ten-sided die. A number before the "d" indicating to roll that many dice. Thus, "4d6" means rolling four six-sided 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 ten-sided die for the "tens" digit and another ten-sided die for the "ones" digit.

"Open-ending" refers to mechanics where if a certain roll of the dice comes up, you make another roll: re-roll and add, roll extra dice, or something similar. This can allow for a theoretically infinite range of results. Open-ending 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 "root-mean-square" 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 semi-objective 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 finely-grained (i.e. many small steps) to coarse-grained (i.e. a few large steps). For a dice mechanic, there is potentially different granularity for stat, difficulty, and degree-of-success. 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 game-play, 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 30-sided dice, FUDGE dice (special six-sided dice used by FUDGE), or knuckle-bones (special eight-sided dice used by Fvlminata).

Next: Methods

John H. Kim <jhkim-at-darkshire-dot-net>