## Wednesday, June 2, 2010

### Less Dice for More Awesome

To be totally honest, I'm not entirely sure what a Blog Carnival is, but I'm really excited for The Bones to come out, so I'll take a swing. All it takes is a post about dice, right?

That's actually a daunting topic. I could go on at great length about dice bags, certainly. The dice we gave out as wedding favors. How my original D&D dice (the ones you color with a crayon) all met a terrible fate when I left the expert D&D box on top of a heater. But instead, I'm going to pick a trick I'm very fond of. See, it's very easy to come up with a pretty robust system of randomness when you have an unlimited number of dice to draw from, and it's with that in mind that it's always nice to travel armed with big stack of dice, but sometimes that's just not an option. Sometimes you need to pull a game together with just whatever fits in your pocket, so there are a few interesting tricks for getting a seriously broad range of outcomes with just a few dice.

Now, if you only have one six sided die, you're kind of hosed for variety. You can roll for the value from 1-6, or you can make a binary success or failure (usually on 3+, 4+ or 5+ depending) but there's only so much variety out there. Certainly, you can even make a weird sort of curve[1], with
1. Spectacular Failure
2. Failure
3. Partial Failure
4. Partial Success
5. Success
6. Dramatic Success
But with a single die, the randomness of that is crazy. Still, it's a useful chart as you manage to scratch up more dice.

With 2 dice, you start getting some interesting options. Just adding them together gives you a little bit more of a curve, but that's not the only trick. If the dice are different colors you can subtract one from the other to make a range from -5 to +5, as is done in Feng Shui or ad hoc fudge. Alternately, you could subtract the smaller die from the larger die to produce a small number from 0 to 5, weighted towards 1. Lastly, you can introduce some level of skill by allowing the roll of two dice and choosing the best one (or the worst one) for anything that you could do with a single die, including that success chart.

3 dice, though, is a magical number. If you have three six-sided dice, you can do almost anything.

Right off the bat, it's a 10 centered curve, which makes it a reasonable (if imperfect) stand in for a d20. Plus, in some ways, this makes for an even better way to generate a fudge-style curve than d6-d6. Many, many gamer have internalized the D&D stat curve[2], so they know a 12 is a +1 and a 6 is a -2 on such an instinctive level that they can read a 3d6 and turn it into a value from -5 to +5 with negligible thought.

There's another trick from fudge as well which can be useful here, called min-mid-max. When you roll 3 dice, depending on circumstances, you can take the lowest, middle or highest value. By itself, this allows a simple skill system (Untrained, trained and expert) which can be used with any of the resolutions you can use with a single d6, including that chart. Alternately, you can do a 7 step system that goes something like this:
1. Lowest die (average 2)
2. Middle die (average 3.5)
3. Highest die (average 4.9)
4. Lowest die + Middle Die (average 5.5)
5. Lowest Die + Highest Die (average 7)
6. Middle Die + Highest Die (average 8.4)
7. Sum of all 3 dice (average 10.5)

This is a fun one because while the averages progress in a reasonable fashion, the maximums have curious jumps. Being level 7 is the only way to get a result higher than 12, just a being level 4 is the only way to get a result higher than 6. This creates an interesting 2 tier model, where the best of one tier (level 3 and 6 respectively) are almost as good as the worst of the next tier (4 and 7) over the long run, but there are some things that they just can't do. I find there are a lot of things this models very well, especially in a game with a lot of competition, such as Amber.[3]

Now, this only scratches the surface of what can be done with a few dice, and doesn't even touch on fun things like bluffing or hidden information. But what I hope it illustrates is that dice, even just a few of them, are incredibly powerful and versatile. When you think about a system it might be fun to go deep into the dice bag to make things go, but when you need to make do with less, there are still a lot of options.

1 - Pretty sure this is stolen from Dying Earth
2 - Int((3d6-10)/2)

3 - One nice bonus there is that it makes "faking down" your level of ability entirely doable even with open die rolls. You simply take a lower set.

1. With 2d6 (added together), I toyed with a system that made doubles indicate critical success/failure based on whether or not the roll was a success or not. To make it interesting, the critical successes could be more effective the lower the roll was, and, likewise, the critical failures would be more devastating the higher the roll was.

So, if you needed a 8+ and rolled double 4s, that would be a more viscous critical than double 6s. And double 3s would be more dangerous than snake-eyes. This meant that the more skilled you were, the more you would expect more and better criticals (and less and more forgiving fumbles).

2. @Peter Nice! Shades of Unknown Armies, but with a nasty twist!

3. Also, I realized I forgot my newest favorite 3d6 method, the FFF method as well as other Dragon Age inspired approaches. 3d6 truly is a magic number (so to speak).

-Rob D.

4. Have you heard of the d66 or d666?
Just use your 6-sided dice as you would 10-sided ones to create percentage rolls.
A specialty of Croc, of In Nomine Satanis / Magna Veritas' fame.

5. @Stephane I have, but I had totally forgotten about it! One more excellent configuration (and the old WHFRPG also used it in a few tables).

6. Another one that works well (inspired by another of Croc's creations - Bloodlust): d66 for testing success and the "digit" die for measuring quality.

So, for a 44 difficulty, a 36 is a better success than a 12. It lets you combine attack and damage in one roll.

7. Oh, and success with a double is a critical success.

8. @Stephane Oh, fascinating - feels like a precursor to some of the ideas in Weapons of the Gods which otherwise kind of just riffs on Reign/ORE

9. You can also expand the min-mid-max system by considering what happens when dice are equal. If two dice roll the same then the sum is the min, mid, or max value, which allows for "lucky shots." For example a person with min skill who rolled three sixes would get an 18.*

You can also combine approaches, such as in ICE's Bladestorm and Silent Death where the sum of the dice is the attack roll and the damage is then min-mid-max (or in this case, Low, Middle, High).

[* Useful if you hold to the maxim that the opponent the best fighter is worried about is the worst fighter who doesn't know enough to realise that that attack shouldn't have worked...]

10. @rev oh, I like the mixed reading approach, and my brain is crackling with further complications based on mixing colors.

11. what about mid-min/max-min? average 1.46/2.91 with the possibility of zero.

12. med-min or max-med ~=0, 1.46, 5
min~=1, 2.04, 6
max-min~=0, 2.91, 5
mid~=1, 3.5, 6
max~=1, 4.96, 6
min*2~=2, 4.08, 12
min+med~=2, 5.54, 12
med*2~=2, 7, 12
min+max~=2, 7.00, 12
med+max~=2, 8.46, 12
max*2~=2, 9.92, 12
min+med+max~=3, 10.50, 18
max*3~=3, 14.88, 18