Comparing dice mechanics and how they affect flavor and style of gameplay

[innerdude]

So here's a list of all of the dice mechanics that I'm currently aware of, from any systems I've ever studied in any detail. I'm sure there are others out there that I'm not aware of, feel free to add them to the list.

The reason I'm doing this is because I'm curious to see what people think about the effect of the actual dice mechanic/resolution mechanic on playstyle.

For example, does the D20 resolution mechanic create a different set of assumptions about the way the game world "works" versus say, a 3d6 resolution mechanic, or a D10 "roll and keep" system like Legend of Five Rings?

The "General Observations" are my own; feel free to comment/debate. I'm actually very interested in hearing what people say.


D&D "THAC0" Brands / D20 / OGL / Pathfinder / 4e:
Die type: Single d20

Probability type: flat distribution

General observations on play style: The D20 resolution mechanic of the single D20 + modifiers has a lot going for it. It's simple, it's easy to "grok," and it makes it easy for GM calculation against the target number--for every + or - to the roll/DC, the probability increases/decreases 5%.

The flat distribution, however, means that there's a definite level of "swinginess." When I hear "horror stories" of how "somebody couldn't roll high numbers to save their lives," I know they're probably playing a D&D/D20 variant. It's easy to forget that it's highly improbable to roll a lot of low numbers IN THE LONG RUN, but a "flat" distribution means we're just as likely to roll any given number on the die on any given roll. It's not at all difficult to roll 10 consecutive numbers under 8.

The simplicity of the system makes it very appealing from an adjudication standpoint, but there have been numerous times playing a D20 variant, and the D20 was betraying me, and I thought "Come on. The level of incompetence displayed by my character is totally controlled by the dice here." The fact that a lot of D20 published adventure material assumes a "scaling DC" as things get harder means this problem can rear its head almost anywhere (i.e., higher DCs negate the benefit of skill, pushing the chance of success back to probability of die).


GURPS:
Die type: 3d6, roll UNDER the target number (almost always related to a player skill or attribute)

Probability type: Normal distribution (bell curve)

General Observations: In theory, the concept of a 3d6 is appealing, particularly if you're the type of player that goes to the nth degree to optimize your character. An optimized character is nearly always going to have a relatively high chance of success with this type of mechanic, assuming average probabilities. Approximately 67% of all rolls should fall within 1 standard deviation (2.5) of the mean (10.5) - in other words, between 8 and 13. In this way, it's very enabling to a player--I can know, before I ever play a single minute with any given character, how effective they'll be for a given skill under normal circumstances.

The problem I have, at least as GURPS has implemented it, is that at a certain point it's a little TOO automatic, especially for skills that have no opposed check, like Parry. "I sit here, and parry this opponent basically forever, because it doesn't matter how awesomely he succeeds on his/her attack roll, as long as I succeed on my parry, it works."


Savage Worlds / Deadlands
Die Type: Uneven Dice Pool. Variable skill die + standard d6 "Wild die" for PCs. Skill checks can "explode" indefinitely. Take the best result from either die.

Probability type: Modified flat distribution (since we're not adding the two dice together, it's technically a "flat" distribution, each probability of success is counted independently for each die).

General Observations: The simplicity and elegance of the skill system for Savage Worlds is a big point in its favor. Think a particular NPC is "good" at a particular skill? Assign a d8 or d10 skill, and be done. With target numbers remaining relatively static, it makes it easy to get a quick "feel" for effectiveness, and doesn't require a lot of bookkeeping. Fast, Furious, Fun indeed.

The problem is that unlike D20, and to a lesser extent 3d6, the probabilities aren't as transparent. Just how "good" is going from a d6 skill to a d8 skill, really? To calculate the difference, you actually have to count the number times on each die a d8/d6 vs. a d6/d6 would NOT be successful, multiply each die's total, then subtract that number from the total number of possible combinations (d6/d6 = 36 total possible combinations; d8/d6 = 48 possible combos, d10/d6 = 60, etc.). Did you follow that? Yeah, it took me a few times to get it right in my head too.

To make matters more interesting, exploding dice get thrown into the mix, which upset the various probabilities in certain ways. Many people have noted that in some cases it's EASIER to hit certain target numbers by having a LOWER die number and hoping it explodes. Across the entire gamut of the game, these typically represent barely 2-3 percent of total rolls made over the course of a campaign, but for statistics purists, it's an annoying anomaly.

The other problem is that the baseline die types means there's a very shallow range of character development. If a d4 means "baseline capability," Savage Worlds only provides 4 "tiers" of capability over that baseline. The scale basically goes Competent-->Good-->Very Good-->Awesome-->Kicking Ass and Chewing Bubble Gum. And the way the dice mechanic works, there's very little "leeway" for representing nuances between each die level.


Legend of Five Rings
Die Type: d10 "Roll and Keep," dice pool.

Probability Type: Normal distribution

General Observations: I haven't played with this particular mechanic, but have read a number of observations about it. Many cite that this type of a system is great for representing character skill and competency--but it's very, very difficult to hit a "home run," due to the nature of the mechanics. Each die added to the pool increases the overall ability to hit a target number, but it also decreases the chance of hitting "the high end."

More dice = the results will veer ever closer to the mean for the given dice pool.

In other words, if the commentary I've read holds any merit, it can be great for making characters feel ever more "competent" at what they do, but it makes it more difficult to represent "wild success" on any given check.


RuneQuest / Top Secret S.I.:
Die Type: Percentile (d%), roll UNDER

Probability type: Flat distribution

General comments: I have not played Runequest YET (though I bought it a couple of weeks ago and am looking forward to it), but in some ways, any percentile-based system, whether roll OVER or roll UNDER, are identical to D20. It's still a flat distribution; it just has a little more nuance in the percentages rather than in static 5% increments.

I would suspect that systems that use a mechanic like this would "feel" at least somewhat similar to D20/OGL--can feel "swingy," but also allows for more "Woot woo!" moments than a normal distribution mechanic.


FATE / FATE-based systems:
Have no experience with this yet.


Burning Wheel / Mouseguard:
No experience


Warhammer Fantasy RPG:
No experience

 

[the Jester]

Here's an interesting one for you (I use it in my homebrew; it's based on the most interesting stretch on ability checks in 2e).

Roll dice to get your attribute or lower. The difficulty is determined by the dice you roll. As long as you succeed, higher is better, and some tasks have a minimum DC to succeed. Also, sometimes you can add a die to the difficulty in order to do more/harder work on it (e.g. climbing this wall is a 3d6 check to move at half your speed, or 4d6 to move at full speed).

The dice are determined by the circumstances and affect how one looks at the task in many ways; for instance, if that same wall was crumbly and falling apart, the dice might be 3d8 instead (4d8 to move at full speed) to indicate the increased element of chance in the attempt (due to the possibility of the wall crumbling away beneath you).

For example, moving a boulder that blocks a tunnel might be a strength check on 3d10, DC 16 (so nobody with a Str < 16 can possibly succeed).

 

[Dalamar]

I read this on another thread about various rolling mechanics, so I can't remember the details (but I'm certain somebody'll come along to provide those).

The system was an RPG based on some Korean (I think) comic, where you had a varying pool of d10s based on ability and skill. When you rolled, you chose all dice that showed the same face, and the number of dice you had was the tens digit, while the face was the ones digit.
For example, if you had a die pool of 5 and rolled 1, 4, 6, 4, and 9, your possible results would be 11 (one die with a 1), 16 (one die with a 6), 19 (one die with a 9) and 24 (two dice with a 4).

I think there was also the option of "storing" the unused matches from a roll and use it later, but I might be misremembering on that.

 

[Asmor]

I read this on another thread about various rolling mechanics, so I can't remember the details (but I'm certain somebody'll come along to provide those).

The system was an RPG based on some Korean (I think) comic, where you had a varying pool of d10s based on ability and skill. When you rolled, you chose all dice that showed the same face, and the number of dice you had was the tens digit, while the face was the ones digit.
For example, if you had a die pool of 5 and rolled 1, 4, 6, 4, and 9, your possible results would be 11 (one die with a 1), 16 (one die with a 6), 19 (one die with a 9) and 24 (two dice with a 4).

I think there was also the option of "storing" the unused matches from a roll and use it later, but I might be misremembering on that.

I think that may be Feng Shui's system. Someone who's played the system care to comment?

Cthulhutech has a neat system. You roll a number of d10s, and you get to choose a set of dice from your roll to add up. The set of dice can either be all dice showing the same number (so three 7s would count as a 21), or it can be a consecutive run of 3 or more dice (e.g. 4,5,6 = 15).

Also, surprised you don't have a White Wolf-style "success" system, where you roll a number of dice and any dice that meet a target number are considered a success, but the actual value of the die doesn't matter much (a 9 isn't any better than an 8, as long as both are higher than the target number).

 

[dagger]

I also like the Rolemaster/MERP/Harp method which is (d%) roll high and it includes the open ended on stuff as well.

 

[Vyvyan Basterd]

I read this on another thread about various rolling mechanics, so I can't remember the details (but I'm certain somebody'll come along to provide those).

The system was an RPG based on some Korean (I think) comic, where you had a varying pool of d10s based on ability and skill. When you rolled, you chose all dice that showed the same face, and the number of dice you had was the tens digit, while the face was the ones digit.
For example, if you had a die pool of 5 and rolled 1, 4, 6, 4, and 9, your possible results would be 11 (one die with a 1), 16 (one die with a 6), 19 (one die with a 9) and 24 (two dice with a 4).

I think there was also the option of "storing" the unused matches from a roll and use it later, but I might be misremembering on that.

I think that may be Feng Shui's system. Someone who's played the system care to comment?

I can't speak for Feng Shui, but the mechanic described is used in Weapons of the Gods (which is based on a Hong Kong comic book series). You can choose to save rolled dice in your "River" in hopes of achieving greater results on future rolls. Starting characters have two slots intheir River to store dice.

Edit: One distinction from the usual use of d10s is that the "0" face is an actual zero. A single "0" results in 10, while two "0"s are 20, etc.

 

[OnlineDM]

I think this is an interesting topic for a thread, and I love learning about the various dice mechanics that are out there. But the stats nerd in me had to speak up on this one...

It's easy to forget that it's highly improbable to roll a lot of low numbers IN THE LONG RUN, but a "flat" distribution means we're just as likely to roll any given number on the die on any given roll. It's not at all difficult to roll 10 consecutive numbers under 8.

Actually, it's really difficult to roll 10 consecutive numbers under 8. Yes, it will happen if you play long enough, but it's exceedingly rare.

How rare? Well, it's (7/20)^10 = 0.0028% of the time. So, every 100,000 times you roll a series of 10 d20s, you'll have them all be under 8 only about 3 of those 100,000 times. That's pretty freaking difficult.

And if you meant "8 or lower" that's still only (8/20)^10 = 0.0105%, which is once in every 10,000 times. Still very, very uncommon.

But the spirit of your points stands: With a flat distribution, you'll randomly get some streaks here and there, more often than you might expect. You'll roll below an 8 three times in a row about 4% of the time, so that's something we've all experienced.

 

[innerdude]

I think this is an interesting topic for a thread, and I love learning about the various dice mechanics that are out there. But the stats nerd in me had to speak up on this one...

Actually, it's really difficult to roll 10 consecutive numbers under 8. Yes, it will happen if you play long enough, but it's exceedingly rare.

How rare? Well, it's (7/20)^10 = 0.0028% of the time. So, every 100,000 times you roll a series of 10 d20s, you'll have them all be under 8 only about 3 of those 100,000 times. That's pretty freaking difficult.

And if you meant "8 or lower" that's still only (8/20)^10 = 0.0105%, which is once in every 10,000 times. Still very, very uncommon.

But the spirit of your points stands: With a flat distribution, you'll randomly get some streaks here and there, more often than you might expect. You'll roll below an 8 three times in a row about 4% of the time, so that's something we've all experienced.

Thanks, you're right, I should have been more discriminating with the math there. 10 in a row is probably a bit exaggerated; 3 or 4 in row less so, as you've noted.

Love the comments from everyone so far on dice systems they've tried.

I'm toying with house ruling (probably more of a large re-write) of Savage Worlds to use a different die mechanic.

I like the "Die number as skill" and the "Wild Die," but instead of having an either/or resolution mechanic, actually adding the numbers together. Also, only the "Wild Die" would explode, and could explode a maximum of one time.

I've looked at a basic probability calculator for the math, and it seems to be fairly solid, depending on how target numbers would be set up (obviously this is the big part that would have to be changed). The numbers would range from maybe 1-15, or 1-20, increasing in increments of 1 (1 being so absurdly, stupidly, easy you'd only fail under extreme adverse circumstances, 15 being the limit of human capability).

This does a couple of things; first it changes the probability to a normal distribution rather than flat. I don't like how GURPS implements some of their checks, but to me, a normal distribution better represents reality--if you want to succeed at "average" stuff, you do need to have skill, but if you want to succeed at the hard stuff, you have to REALLY be good--but I like that the "luck die" has one open-ended iteration.

I'd also like to add a couple more levels beyond a standard D12 before PCs get a static bonus--like, after d12, they then get 2d6, 2d8, 2d10, etc. I'd have to look at the math on that a little more closely though, because even though adding a second die gives better average results, it makes it harder to hit the high end. Rolling 1d12 + 1d6 is a different set of probabilities than rolling 3d6. Also, once you go to 2d8, it increases the maximum roll by 4 each increment, instead of just 2 (although maybe that's the point of being really skilled LOL).

One thing that's interesting to me is that as I've studied dice mechanics, it becomes apparent that one isn't inherently better than another--it's all based on what the player expects the results should model, and how the GM "feeds back" the result to the player.

If D20 DC's were all adjusted upward, suddenly having a +10 or +15 in something doesn't feel all that "skilled." Likewise, if you change the default target number in Savage Worlds from 4 to a 5, the entire paradigm of mechanical success changes.

Maybe that's a thread to fork from here: how do you set player's expectations of "power" and "skill" to fit the paradigm you want the resolution mechanic to represent?

 

[Bluenose]

So here's a list of all of the dice mechanics that I'm currently aware of, from any systems I've ever studied in any detail. I'm sure there are others out there that I'm not aware of, feel free to add them to the list.

FATE / FATE-based systems:
Have no experience with this yet.

1d6 -1d6
Add the result to your skill and try to exceed a target number. If you beat the number required to succeed then you'll get shifts, which allow you to gain extra benefits from the action.

Warhammer Fantasy RPG:

No experience

3rd edition? That's a dice pool system, with several different types of dice. How many you roll varies. You count successes against failures, and if you''ve more successes than failures you succeed. Some of the dice give extra benefits or penalties additional to whether you succeed in the attack.

Pendragon

1d20
roll under the character's ability to succeed, if it's an opposed roll then the higher score that's a success wins.

Qin: the Warring States

Roll 2d10
add the difference between them to your Aspect + Skill. Beat a target number or the number rolled by your opponent in an opposed test. If the score on both dice is the same, this is an extraordinary success; unless both dice score 0, when it's a critical failure.

Traveller

2d6
+ skill (+ attribute*) to roll higher than a target number.
*depending on edition, this may not apply.

 

[Asmor]

I can't speak for Feng Shui, but the mechanic described is used in Weapons of the Gods (which is based on a Hong Kong comic book series). You can choose to save rolled dice in your "River" in hopes of achieving greater results on future rolls. Starting characters have two slots intheir River to store dice.

You are correct. I remembered what Feng Shui's system was at work today...

You roll 2d6. One is always positive, the other negative, so you get a bell curve centered at 0 and that can give anywhere from -5 to +5. Actually a pretty neat system with a lot going for it. Since the average and most common result is 0, a given character's average roll is equal to their score.