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Die Mechanics Revisited: Summation

Some years ago I wrote an article on the basic statistical properties of common die-rolling mechanics in games. It was one of the more popular articles on my site, but also contained errors and omissions. I’ve been wanting to do an updated version but found the hurdle of completing the entire article at once too daunting. Therefore I’m publishing it in pieces, as I have time.

I’ll consider a variety of common uses of dice, from their basic statistical properties to how they might be applied in a game, including what tone or psychological impact they might bring. We start today with the simplest of mechanics: summation.

Straightforward and familiar, in summation you roll dice and sum their faces. There are two inputs: the number of dice and their size.

Summing has the advantage of simplicity. Its speed depends largely on the number of dice rolled, placing a practical cap on the that quantity, probably near 10. Another limitation is the common availability of die sizes, from 2 to 20 or a little more—though of course this applies to every rolling method.

Statistics

• Roll NdS and sum faces.
• 2-variable

Raising N or S increases the average linearly, as well as the dispersion, but the minimum roll is always equal to N.

Uses

Almost anywhere. Summation well models situations with simple, linear effects: for instance, have 50 laborers instead of 25 may logically be twice as good, and thus merit twice as many dice. Summation is also useful where you want all values to be possible no matter the main input. For instance, if a character rolls N dice based on his skill, a novice may sometimes do as well as an expert, and vice-versa.

Psychology

Summation is perhaps the most transparent of all rolling methods, with probabilities that can be intuited fairly well. Most obviously, this means strategies can be formed with some mathematical precision. It also means players will be more comfortable with mechanics employing summation. They may see such mechanics as more ordinary, and less deserving of thought, than something more elaborate.

When designing the inputs to a summation roll, more dice sensically implies superiority: a strongman rolls more dice, or larger dice, than a pipsqueak. You reverse this logic at your own risk, as it may cause moments of confusion while playing, especially if other mechanics are calibrated in the traditional manner.

Mar 24, 2010 | Filed in design | Tagged: mechanics, rolling | 0 Comments