A couple of years ago I came up with a “taxonomy of dice systems” which I posted on the RPGNet forums (forum.rpg.net/showthread.php?t=295085). I’ve since revised it to include some additional variants and to correct some of the examples which I’d misclassified. Here’s the updated version — if you can help to fill in the gaps in my examples, I’d be grateful.

1) Fixed Roll: Players roll either a single die (e.g. d20) or a fixed set of dice (e.g. 3d6), which are the same for all rolls. Difficulty modifiers may be added to the roll or to the target number.

1a) Vs. attribute: Target number is determined by a character’s trait or traits. Always roll-under? Examples: GURPS, BRP, Alternity, Fading Suns.

1b) Vs. difficulty: Traits are added to or subtracted from the roll and compared to a target number. May be roll-over (Examples: d20, Fudge, Unisystem) or roll-under (Example: Tri-Stat).

2) Variable Roll: Players roll a die or some combination of dice which varies according to the trait being used.

2a) Additive: Dice are added together (if more than one is rolled) and the total is compared to a target. May be roll-over (Example: Earthdawn) or roll-under (Example: ??).

2b) Independent: Each die is individually compared to the target number. May be roll-over (Examples: Ironclaw, Savage Worlds) or roll-under (Example: The Window).

2c) Inverse: Type or number of dice is determined by difficulty and target is determined by trait. May be roll-under (Example: Pokethulhu, Violence) or roll-over (Example: ??).

3) Dice Pool: Players roll several dice of the same type, the number depending on the trait being used.

3a) Additive: Dice are added together and the total is compared to a target. Always roll-over? Examples: Classic d6

3b) Independent: Each die is individually compared to the target number, and “successes” are tallied. May be roll-over (Examples: Storyteller, Shadowrun, d6 Legend) or roll-under (Example: ??). Difficulty may be adjusted by changing the target number (Example: Original ST), the number of successes required (Example: ST Revised) and/or the number of dice rolled (Example: nWoD).

3c) Select Best: The best die or dice rolled determines degree of success. May be roll-over (Examples: 7th Sea, ICON, Cartoon Action Hour) or roll-under (Example: ??), additive or independent.

4) Orthogonal Dice Pool: Attributes and skills have different effects on dice rolls.

4a) Skill vs. Attribute: Dice pool is determined by skill and target number is determined by attribute (modified by difficulty), or vice versa (Example: Iron Gauntlets). Always roll-under?

4b) Skill x Attribute: Size of dice is determined by attribute and number of dice is determined by skill (or vice versa); target number is determined by difficulty. Always roll-over? (Example: Deadlands?)

Note that I didn’t bother to include mechanics which are unique to a single game or game system, such as the One-Roll Engine.

I had a few thoughts in response to Mr. Jackson’s comments which you quoted — I would’ve posted these to your original thread, but I didn’t feel like signing up for a WordPress account just for that.

- He’s correct in pointing out that the distinction between “roll high” and “roll low” is cosmetic, but “roll low” systems don’t usually require subtraction, IME; they just require you to roll under a target number instead of over it.

- I don’t know what he means by saying that “taking the average” is a “D&Dism”, especially since you explicitly associated it with the HEX engine.

- I agree that it’s inaccurate to say that most game use the d20, although I’d add that between the various percentile-based games (BRP, WFRP, etc.) and the many permutations of the Storyteller system, I suspect that d10s are used almost as much as d6s.

Wyvern

Hm. Some reactions:

The way you’ve divided dice systems into ‘target number’ and ’success rolls’ is very odd. For example, I would call FUDGE a target number system, because you’re adding them up, it’s just that dice are labeled -1, 0, +1. In general, there seem to be a couple of variants:

1) Roll one die against a target number, which might be high or low. Skill typically gives a flat bonus, difficulty typically adjusts target number, though either one can also be implemented by adjusting the die type. Example: D&D. Often well suited to rolling multiple tasks at once, such as wargames where you roll all your units attacking at once.

2) Roll two or more dice, add them together, and compare to a target number, as (1). Skill and difficulty can work the same as 1d, or they can modify the number of dice rolled. Examples: GURPS (skill and difficulty are flat modifiers), Star Wars (skill adds dice, difficulty is a flat modifier)

3) Roll two or more dice and apply each die against a target number, as per (1); count how many of your dice succeed. Skill might modify target number, or might add dice; difficulty might modify target number, or might require extra successes. Examples: Shadowrun, Vampire.

4) Roll two or more dice and select one, such as the worst, the best, or the middle value, then apply as per (1). Skill and difficulty, again, can either modify target number or dice. Examples: Heavy Gear, Deadlands.

5) Roll two or more dice and look for patterns, such as doubles. Examples: Exalted.

6) Any of the above, plus a more complex die rolling pattern, such as rerolls on certain types of dice.

*High is Good vs Low is Good*
Your distinction here is bogus; mechanically, roll high and roll low are identical, it’s just that one requires you to perform subtraction, the other requires you to perform addition. As most humans are better at addition than subtraction, roll high usually has a mild advantage.

*Taking the Average*
This is mostly a D&Dism. Common solutions include making the task so easy that the worst possible roll still succeeds, and simply declaring that you don’t roll for trivial tasks. Some dice pool systems also have ‘declaring successes’, but that usually doesn’t give you an average result, it gives you a substantially below average result.

*Most games use the d20*
While the biggest game uses the d20, most game systems do not; the d6 is the most commonly used die type.

*Conclusion*
You mention that dice systems have shortcomings, which is true, but completely fail to identify what many of the shortcomings are.

GS: Interesting read. I’ve had much the same discussion on the Pen and Paper forum. Dice, ratios and bell curves. Yea, I have a few dice old enough to drink. I think all we old farts do.

But the kind of thing you were discussing is where one of my rules of GMing comes from. “A die roll is not required even if a die roll is required.”
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JR: Thanks Garry. I think the hardest part of writing this article was making sure I could find games that represented the two types of dice rolling resolution. I was going to talk about “matching values” but the only rule set that did that was One Roll: Wushu and Godlike use One Roll as their base systems, and even then, I realized that it was a Success roll more than anything else, so I dropped that type from the article.
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GS: Method also matters. I’ve tried to identify all the dice resolution methods I could think up.

Straight target number, be that high or low, no matter the die type, single die. “Window” fixed target number low is good, die type varies. Die test: Fixed dice, high is good, target number slides. Reverse die test, Fixed target, low is good, number of dice varies. Dice pool. Fixed target roll for number of successes.

I know I’m missing some of the ones I’ve seen.

Also the changing of the dice can have a huge affect on the game. For example instead of a d20 someone suggested using 2d10. You can do it, bu the value of a single +1 goes way up as a result. It skews the result table and virtually creates a new game in the process.
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JR: That’s why I covered the types in general. I figured that dice were the low hanging fruit of game design. Next up will be task resolution and doing things, that’s a whole ‘nuther kind of fruit.

I once contemplated using 4d6-4 for the 0-20 range. That gives you a 1:1,296 chance of rolling either a 20 or a 0. That would be a definition of a critical success or failure. Of course that’s still higher than reality, but a heck of a lot better than 1:20 chance.
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GS: That is why I use confirms and roll through. I’m an old time D&D player and yes, a automatic critical success or failure at 5% each is way too high.

So, if you need a 20 to hit, you cannot get a critical unless you roll through for a second 20. If you can’t miss on a one you have to roll through on a one to see if you miss.

If the character cannot hit on a 20 and rolls a 20 they roll through to see if they can hit.

It evens out the rather crude scale of the d20 system. It still does little for the scaling problem.
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JR: Well, you may have noted that in 4th Ed. of D&D, they dropped the confirm roll for criticals. It was the most hated feature of the 3.0 and 3.5 editions.

If you go with a 4d6-4 range, you have to redefine your target numbers on probability scale. Which means you need to draw the bell curve for the range and define your target numbers based on that curve. So average difficulty rolls would have a target number of 10, but nearly impossible difficulty rolls would be 20+. Above average target numbers would be 12 or 13.

It would look like:

Average: 10
Above average: 12
Hard: 14
Difficult: 16
Very difficult: 17-18
Impossible: 20
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GS: Ayup. Changes the whole character of the game. You pretty much have to redesign from the ground up if you change the dice.
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JR: Well, maybe, and maybe not. It depends on how your rules interpret the results of the die rolls.