Classifying Methods of Randomization

Previously I compared some methods of randomly generating binary outcomes with dice. But of course there are non-binary contexts where dice can be useful as well. Roughly speaking, there are three ways to transform a dice roll into a result:

1. Binary: Roll a result greater than (or less than) a given target to succeed. Usually also includes "equal to", so that the target value is the success-threshold rather than the failure-threshold.
2. Spectrum: Roll a result, then look up the outcome of that result from a tabulated list of all possible outcomes, arranged in some ordinal schema (best to worst, etc).
3. Hash: Also by reference to a table, but for outcomes that aren't (perhaps can't be) arranged in any meaningful order.

The boundary between a "spectrum" system and a "hash" system isn't always a sharp one, but roughly speaking, if the system is amenable to having a bonus or penalty applied to it (as a modifier) it probably counts as some kind of a spectrum. A true hash table result would be senseless to modify, since being adjacent to another item in a disordered hash table has no significance.

A major trend in games over the last couple decades has been the absolute decline of spectrum systems in favor of hash systems. Almost all complicated simulationist wargames still use spectrum tables (with a battle resulting in complicated combinations of losses, retreats, and other adverse effects), but most other board games and most RPGs have switched entirely to binary rolls for everything except "combat damage".

This bothers me enough that it sometimes intrudes on my ability to enjoy a game. I need a few spectrum results to make the game's theme feel "real" to me. Plus, there's something intrinsically exciting about a system that allows not just a success, but a critical success.

For example, early editions of D&D from the 70s had a ubiquitous "social roll" system that utilized a 2d6 spectrum as its common mechanic. Here are a few examples (courtesy of Brendan at Untimately):

Social Rolls

2d6	Negotiation	Reaction	Morale
2	Refused, -1 future	Attacks	Surrenders
3-5	Refused	Hostile	Flees
6-8	Will consider another offer	Uncertain	Fights, check again
9-11	Accepted	Friendly	Fights
12	Accepted, +1 future	Proactively helpful	Fights, no further check

Note that the system is intentionally open-ended. What does "hostile" mean? In an arbitrated game, that's for the judge (the DM, for D&D) to decide. A system like this is intended to encourage creativity and flexibility, adapting to the particular circumstance while retaining the thematic pattern of "bad to good outcomes, with a bell curve distribution". In effect, every time you see a table like this, the game is saying "you're making a social roll" -- as opposed to a combat roll, or an encounter table, or a skill check. Social interactions, by their nature, have lots of possible outcomes that make them much more interesting than a "can I jump across this pit?" binary system!

In the near future, I'm intended to use some spectrum mechanics for the intelligence and logistics systems in my Guadalcanal campaign hack of Naval Thunder. In the long term, I'd like to use the specific "social roll" system to build the social subsystems of my (work in progress) hex crawl game like negotiation and recruiting, helping to give it some "old school" flavor.