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View Full Version : game theory: the sides of dice and how they affect game play



Noje
2015-02-25, 10:28 PM
So I have been looking at a few different systems to run for a group of friends, and I found that they all had different ideas of what sided dice to use for what and when. Some of the mainstream games, like D&D, use the d20 to solve conflict and the other dice for damage, generation of stats, etc.. Some other games made by one-man teams like Warrior, Rogue, and Mage seem to take an approach of using the d6 or some other dice for anything that needs some randomness in the decision.

My question is, as stated in the title of this thread, is how do the different sided dice affect game play and what are each of the dice useful for?

johnbragg
2015-02-26, 09:33 AM
So I have been looking at a few different systems to run for a group of friends, and I found that they all had different ideas of what sided dice to use for what and when. Some of the mainstream games, like D&D, use the d20 to solve conflict and the other dice for damage, generation of stats, etc.. Some other games made by one-man teams like Warrior, Rogue, and Mage seem to take an approach of using the d6 or some other dice for anything that needs some randomness in the decision.

My question is, as stated in the title of this thread, is how do the different sided dice affect game play and what are each of the dice useful for?

There isn't a ton of difference. Compared to d20 systems, d6-based systems produce fewer extreme results because they use multiple dice, which makes the median results more likely.*

d20 systems almost always treat modifiers as a flat + or - to the die roll. D6 systems often use extra dice for modifiers. (each extra die is, on average, +3.5 to the roll)

The biggest evolution was from 2nd to 3rd edition D&D. Before 3rd edition made almost everything a d20 roll, D&D used a wide variety of dice-rolling methods for different tables, with little rhyme or reason. Rolling for a random treasure item? Roll percentile dice to see what kind of item it is--you get a scroll! Now roll d6, on a 1-2 it's a divine scroll, 3-6 it's an arcane scroll. etc etc.

* I'll use d12 vs 2d6 because the math is easier to follow. You can write out a 6x6 chart of the outcomes of rolling 2d6. There are 36 outcomes, 2 x 1, 3 x 2, 4 x 3, 5 x 4, 6 x 5, 7 x 6, 8 x 5, 9 x 4, 10 x 3, 11 x 2, 12 x 1.

IF you roll 2d6 for 2-12, you'll get between a 6 and an 8 16/36 of the time, 44%. If you roll a d12, you'll get between a 6 and an 8 3/12 of the time, 25%.

With a d12 roll, you'll get a 12 1/12 of the time, 8%. With a 2d6 roll, you'll get a 12 1/36 of the time, 3%.

Say you need to make a 10 or better on your roll to win. With 12 as the max, that's pretty unlikely. But how unlikely?
With a d12 roll, you have a 25% chance (10, 11, 12).
With a 2d6 roll, you have a 16% chance (6/36)

Single-dice systems produce a flat probability curve. Multiple-dice systems produce bell curves.

johnbragg
2015-02-26, 09:36 AM
The dice mechanics shouldn't play a big role in what game you and your friends decide to start. Plenty of d6-based systems changed over to d20-based systems when the Open Gaming License came out, and there wasn't much of a pushback from old-school players at converting extra dice to +3 bonuses. (Although that might be because they just kept on rolling fistfuls of d6s no matter what the books said, which is easy enough to do.)

Freelance GM
2015-02-26, 10:09 AM
Part of it is also a matter of theme.

Dark Heresy uses Percentile Dice so that the players know exactly what their odds of success and failure are, which reinforces the grittiness of the setting. Star Wars: Edge of the Empire uses symbols instead of numbers in its dice pool to encourage a more narrative play style, which fits the lighter theme of Star Wars.

Grod_The_Giant
2015-03-02, 10:58 AM
Long story short:

The more sides on a die, the more random the result.
The more dice you roll at a time, the less random the result.


So a single-die system like D&D will have very random random number generation. To get consistent results, you need large numeric bonuses and/or rules like taking ten. A die pool system like Exalted will have fairly consistent random number generation, where smaller bonuses can matter more.

Maglubiyet
2015-03-02, 03:06 PM
Long story short:

The more sides on a die, the more random the result.
The more dice you roll at a time, the less random the result.



There was a RPG in the 80's or 90's where character generation was done by rolling 10d10 for each of the stats. The developer felt that in the real world everyone was "pretty average" and exceptional values should be exceedingly rare.

Yeah, that game sucked.

Knaight
2015-03-02, 03:26 PM
The sides on the dice matter a lot less than how the dice are used. 1d6+x, 1d8+x, 1d10+x, and 1d20+x all feel pretty similar. Rolling several d10 and taking the best 2 or 3, rolling several d10 and counting how many are of certain numbers, rolling several d10 and looking for matches, and rolling several d10 and adding them all up all feel substantially different despite all using d10. There are some systems where the dice themselves affect the feel significantly - Fudge and Fate are the obvious ones here - but there are a lot where they don't.

bookguy
2015-03-04, 12:28 PM
The sides on the dice matter a lot less than how the dice are used. 1d6+x, 1d8+x, 1d10+x, and 1d20+x all feel pretty similar. Rolling several d10 and taking the best 2 or 3, rolling several d10 and counting how many are of certain numbers, rolling several d10 and looking for matches, and rolling several d10 and adding them all up all feel substantially different despite all using d10. There are some systems where the dice themselves affect the feel significantly - Fudge and Fate are the obvious ones here - but there are a lot where they don't.

Knaight the bast way to think about it.

Although there certainly are other types of RPG systems, the ones I've come across the most you either need a target total or a target number of successes. For a total, there are things like 1d20+x, 3d6+x, xd6, 1dx, etc. For successes, you roll a certain number of dice and count how many are above a certain number. These two categories are quite different, but which dice you choose within a category don't really change the feel of the game.

If you're looking for recommendations on what game to play, don't focus on the dice. Focus on the overall feel of the mechanics, how much is left up to the GM, the setting, reviews, etc.

If you're making a system, I would recommend 1d20+x if consequences of rolls are strictly binary, and something else if they are not. Just be sure to pick something where you can understand the math.

A few other thoughts:
-Light d6 only systems are good for first-time RPGers who just want to try it out, since they probably have a few of them on hand and won't have to pick up new dice.
-Some people just don't like certain dice. I wouldn't want a system that uses d4's heavily, and a friend of mine dislikes d8's.

Knaight
2015-03-06, 11:34 AM
Although there certainly are other types of RPG systems, the ones I've come across the most you either need a target total or a target number of successes. For a total, there are things like 1d20+x, 3d6+x, xd6, 1dx, etc. For successes, you roll a certain number of dice and count how many are above a certain number. These two categories are quite different, but which dice you choose within a category don't really change the feel of the game.

Roll and add, roll under, and dice pools are the big three, and the first two are essentially the same mathematically but with representation differences. It is worth distinguishing between roll and add with one die and roll and add with multiple dice, but that still works out to effectively three big ones. The matching mechanic I listed is from ORE, as an example of a more esoteric use with a pretty different feel.

jqavins
2015-03-09, 12:08 PM
Some points that have been touched on but I feel are worth amplifying.

Smaller dice make for smaller ranges of totals, which increases the relative effects of bonuses and penalties. +1 in a 1d20 system is a bonus of one nineteenth of the total range, where +1 in a 1d6 system is one fifth, comparable to +4 on a d20. That means if you want to be able to have minor, medium, and major bonuses and penalties you need a decent total range. Personally, as you can probably tell, I prefer a good size range, like d20 (or more.)
Multiple dice centralize results, and the more dice the more centralized. One die gives a flat distribution, three or more give a bell curve which grows narrower relative to the total range as more dice are used. Two actually doesn't give a bell curve, but rahter a triangle; it wants to be a bell curve, but it's not curved. There are two effects of centralizing.

One is that, as has been said, the extremes of results come up rarely, and very rarely if more than two dice are used. (The chance of getting an 18 on 3d6 is about 0.5%, and of getting 17 or 18 is still only about 2%.) Some people find this too predictable and boring, some like it better for the perceived realism that most outcomes are about average. (But a 10 die roll is ridiculously over-centralized.) On that score, I prefer a mix; some things make sense to centralize and some don't. This is something that, in my opinion, D&D has had right since the first edition with multiple dice for ability scores and single dice for attack rolls, damage, saves, etc.
The second is that it distorts the effects of bonuses. With single die rolls, let's say 1d20, a +1 bonus increases your chance of success by 5% any time that the chance without bonus is anywhere in the middle. (When you need a 22 to succeed, +1 still leaves it impossible.) But with multiple dice, that same +1 bonus has little effect in the extremes and a much larger efect in the middle. It's partly for this reason that I prefer single dice for attack rolls etc.



All that said, Book Guy and others are absolutely right that this is not the thing to focus on when picking a published game.

(As an aside, there is a way of centralizing rolls a little but even less than two dice. Well, it is two dice, but two different dice. For example, one can change from 1d20 to 2d10 and keep the range about the same. But it that's too centralized for your preference, you can use 1d12 + 1d8; this gives a distribution that is trapazoidal, with unlikely extremes but a flat top where bonuses have a uniform effect. The more different the dice the wider the flat top. Using electronic dice, one can use dice of any size, so 1d12 + 1d8, 1d13 + 1d7, and 1d14 + 1d6 have progressively wider tops. I've never seen this used in any game but I might try it some time. Maybe I'll use 1d20 + 1d10.)