View Full Version : Dice mechanics for a new system

2013-04-02, 05:55 PM
I'm working on a new game system for my next campaign that will have a pretty steep power curve. I've found that when this happens in something like D&D, the issue is that the relative randomness decreases as you get better at things (d20 + static modifier). White Wolf's pool of d10s system solves this in part since the standard deviation grows as sqrt(dice pool), but has the problem that as you get better at things you're rolling more and more dice.

My thought was the following system:

You have Traits and Skills. Skills start at 10 for common skills, 5 for uncommon skills, and 0 for trained only; skills can be increased with xp or whatever. Traits tend to be from 2 to 5 and don't increase.

When you roll a check you roll a number of d10s equal to your Trait. A result of 6+ on each d10 counts as a success. If you have zero successes, you are still considered to have 1 success unless there's a 1 somewhere in your roll, in which case you 'naturally' botch (e.g. your result will be 0 whatever your skill might be). You then multiply the number of successes you obtain by your skill rating, and then add any static circumstance modifiers to the roll (e.g. due to items or whatever).

I think this has the mathematical properties I want (standard deviation remains proportional to the mean regardless of how good you get at a skill), but it still feels a bit clunky. Any thoughts, suggestions, or ideas how to improve the system while keeping it simple and retaining this scaling?

2013-04-02, 08:40 PM
d20+modifier is an affine system, not a linear one.

+0 is to +5 as +10 is to +15 as +20 is to +25.

If your system is based off of opposed rolls, be they opposed by another persons roll or 10+some modifier that scales like roll bonuses, then the power impact of bonuses is roughly exponential (well, hyperbolic).

Suppose you roll 1d20+X against an opponent who rolls 1d20+Y. Your target number in each case is 11+Y and 11+X respectively.

And suppose it takes K successes to "win", and the other side needs K successes for you to "lose". How many such challenges can you be expected to "win" before you "lose"? I'll assume other side successes accumulate (like damage would).

This system is clearly determined by the value X-Y. So without loss of generality, we'll look at Delta = X-Y.

Delta = +0 is an even match. Average of 1 win per loss.
Delta = +1 is a 1.22:1 match. Average of 1.2 wins per loss
Delta +2 is 1.5:1
Delta +3 is 1.9:1
Delta +4 is 2.3:1
Delta +5 is 3:1
Delta +6 is 4:1
Delta +7 is 5.7:1
Delta +8 is 9:1
Delta +9 is 19:1

A decent approximation of this is 1.25^Delta, an exponential power curve. (The curve is actually hyperbolic, but exponential is easier to work with).

Changing this to 1d20+X rolled against 1d20+Y mostly just flattens the curve a tad, the exponential nature of the delta remains.

Now, if you lose control of modifiers, and do not treat each cumulative +1 and +2 as a precious treasure, but instead hand out +2 and +3 bonuses like candy on Halloween after the characters already have a +20 bonus, then yes, 1d20+modifier does break down in the way you describe.

It can be easier to deal with a system where you can hand out "bigger numbers" easier, and where the measure of your character's capabilities is some linear number rather than an exponential measure of power like it is in an opposed d20 based system.

Your system tries to give a linear scale of power by taking some random number seed (flip coins for traits, add up number of heads, with a critical failure system tacked on, and using d10s for whatever reason), then multiplying it by some constant number. The downside is that it actually takes a non-trivial amount of time to multiply 17 by 4 compared to other operations, and the granularity of your resolution system (68) overkill.

It takes as much mental effort to deal with that 8 as it does the 6 in 68, yet the importance of the 8 is way lower than the 6. Ideally, a system shouldn't end up accumulating unimportant digits like that.

The same problem rears its ugly head in a DnD like linear HP-linear damage game, where the granularity of HP is fine at level 1 (where 3 and 4 HP of damage is a huge difference), but by level 20 it is way too fine (where a 137 HP and a 138 HP wound is something that is nearly indistinguishable, yet the system still requires that you track it).


As a more direct critique, if you are rolling Xd10, don't just count "number over some threashold", actually use the dice to do something. Collect matches (pairs, triplets), runs (1234 whoot!) -- do something with all of that pattern you threw down on the table. Don't turn them into a pile of glorified weighted coins.

That doesn't mean throw the kitchen sink at it, but do more than the bare minimum. WW roll-and-count is boring not just because you end up rolling a ridiculous number of dice.

As for "traits vs skills": When doing two-dimensional resolution, really be careful about it. You'll note that WW tried it where one source determined the number of dice, the other the target number, before they abandoned it because they couldn't figure out what should increase one, and what should increase the other. In your case, I'm guessing your Traits end up defining the equivalent of your "class" in D&D terms?

2013-04-02, 09:25 PM
I think it's a little bit complicated. It must be tested first and observed if it will be effective.

2013-04-02, 09:32 PM
To clarify, this is intended to be used for an online campaign, which means that doing stuff with the dice becomes more onerous than it would in an in-person campaign (because Maptool and Roll20 have a tendency to hide the details of rolls). I agree that the granularity of this system is pretty rough. As I've written it, someone with a 15 in a skill trying to hit a flat DC 35 sees no benefit until their skill reaches 18 (at which point they need one fewer success to pass the roll). These skill deadzones are invisible to the players because they won't know what DCs are going to commonly occur.

I've come up with what I think is a better variation:

Traits are described by a die type (d6, d8, d10, d12). A roll looks like:

(Trait die)xRate + Skill rank. To avoid the multiplication it could be (Rate)d(Trait). Edit: Though doing it with multiple dice does mean that the randomness decays like sqrt(Rate), so its not actually equivalent.

The tricky bit is that there's a relationship between skill rank and Rate. Every 10 points of a skill increases Rate by 1. This way at least the one division can be precomputed and written down on the sheet, and everything else can be reduced to rolling multiple dice and performing addition.

2013-04-02, 09:43 PM
Assuming I'm reading it correctly, where 1s are only autofailures if you have no successes, the expected number of successes from Xd10 is .5X+.5^X - .05^X.

E(successes) = Probability of N successes + Probability of the minimum 1 success
E(b(X,.5)) + 1 * P(b(X,.5) = 0) * P(b(X,.1) > 0)
.5X + .5^X * (1 - .1^X)
.5X+.5^X - .05^X

EDIT: For the OP. I was ninja'd by TPAM