## An analysis of dice mechanics

What does one need to make a good dice mechanic? What would an ideal dice mechanic look like?

To understand this, consider what your game statistic and dice model in a game you are playing. Specifically, if you have two characters and the first character has a stat of 10, and the second character has a stat of 12, you know that the second character is better at doing what that stat models than the first character. So what happens when a person gets “better” at something. Primarily there are two things:

- They become more accurate
- They become more precise.

Now, to fully get what I’m saying you have to grasp the difference between accuracy and precision. For starters this link may help. But to illustrate imagine your going to see a surgeon. You want that surgeon to be accurate, as in able to perform admirably, but you also want the results from that surgeon to be specific. Similarly a marksman at a firing range needs that is good not only shoots near the bullseye, but does so consistently. For my part I am considered an expert programmer. That means that not only does my code tend to be good, my code is consistently good. I don’t sometimes write brilliant algorithms and sometimes terrible algorithms, but I consistently write good algorithm. When I was first programming on the other had I would average mediocre algorithms, but that average ranged between Good algorithms and Terrible algorithms.

Which brings up one more point. That is that the very best so outclass the amateur that pitted against each-other it should be no contest. Most games seem to work from a design principle that the best specialist should be double the dice range outside the amateur. For example in Fate, the dice range from -4 to +4, and the stats range from 0 to +5. That means the very best is just out of reach from someone with no training. D20 is harder to scrutinize for various reasons but seems to keep a similar pacing. Consider in D20 for example that a Combat specialist consistently has 2x the ability to hit as a magic specialist. At level 20 the Mage has a BAB of 10, and the Warrior has a BAB of 20 which puts them within half the dice range of each other, but bonuses of various sorts is likely to double that for each of them putting the Warrior at exactly the Dice range above the Mage.

My inclination is that the very best should be outside the dice range of an expert, and that an expert should be outside the dice range of an amateur. That means the skills need to scale to at least 3x the dice race, and even more if one considers scaling the game into supernatural realms.

The last element we want out of a Dice Mechanic is simplicity. With enough mathematical complexity we could model anything, but we need the system to be easily workable during play. How do we measure simplicity?

The easiest dice system is boolean, for example “Is it a 6”, followed by Dice Matching “Are these two dice equal?”, followed by comparison with a fixed number “Is the face larger then 4”, followed by comparing dice “Is this dice bigger than this dice”, followed by summing dice “What is the total of these three dice”, followed by lookup tables, followed by other math. The Summing method is probably the maximum complexity that one should allow for a generic mechanic.

That gives us the following four design goals:

- An increase in skill should increase accuracy
- An increase in skill should increase precision
- An expert should completely outclass an Amateur
- The system needs to be simple.

So what are our options?

## Roll and Add

The most frequently seen mechanic is a Roll and add mechanic. Equivalently there is Roll Under. Roll and add is any mechanic where a fixed set of dice is used and then that number is modified in some way by a statistic and difficulty. D20, Fate, and GURPS all use a variation on this. The differences with what the average is and what sort of shape the distribution of numbers is actually rather tangental. While the Bell curve can help us achieve principle 3, and the system already succeeds at 1, the system does nothing to reflect an increase in precision as the skill of the user increases. Looking at those three system specifically, all three of them actually fail at #2, and #3. They all succeed at #1, and the mileage varied relative to #4. There is a tendency with these sorts of systems to end up needing to add a whole lot of modifiers before rolling, which often adds to the complexity.

## Pooling Targets

Under this system a number of dice based on your skill is rolled, and a certain target number is required to be on the face of the dice. The number of dice that hit this is your “margin of success”. Difficulty sometimes is used to change that target number, or sometimes subtracts the dice you can use, or sometimes requires a certain number of dice to come up above that target number. This system is featured in the World of Darkness games and also in Shadowrun.

Like all sensible dice systems it does fine at #1, though even in this respect it’s not great. Specifically a +1 in one of these systems is less valuable the higher your stat already is. Going from a 2 to a 3 is more valuable (increases accuracy more), than going from a 4 to a 5.

That might be okay, if it weren’t for the fact that it utterly fails at #2. Unlike Roll and Add, this mechanic has the unique feature of actually reducing the precision as the character becomes more proficient at a skill. Meaning as the character becomes better, the less they are able to rely on their skill providing consistent results.

Furthermore, because of the way the system is designed, there is no means by which a character can completely outclass another character without introducing absurdly large dice pools. The only thing this system seems to have going for it is that it is a little simpler relative to the addition required in Roll and Add method mentioned above. However on every other metric is fails completely.

## Additive Pool

An additive pool keeps the pool concept but plays out similarly to a Roll and Add. The Additive pool involves rolling a number of dice set by the skill and then summing those dice together. While this does result in linear gains fulfilling #1, it still means that the more skilled you are the less precise you are, violating #2. Like the Roll and Add it has the capacity to fulfill #3, it rarely does, and suffers from the problem that scaling can result in enormous dice pools to be added. And unlike the Pooling Targets manages to be more complicated than Roll and Add, instead of less.

## Step Dice Mechanics

Step Dice mechanics associate ones skill with a certain sized dice. For example a master might roll 1d12, while a novice rolls 1d4. While this seems interesting, again it makes the more skilled a person is the less precise they are. Like the previous two it could be switched to a roll under system, but roll under is inherently counter intuitive and needlessly complex.

## Roll and Keep

Of the systems I will explore, this and the next one are the only ones that actually increase precision as the skill increases. In such a system a pool of dice is rolled, a number of dice are kept, and the total of those dice is the ability. For example 4d6 k 2, means your roll 4 six sided dice and keep the best two of them. In fact there is nothing requiring that all the dice are the same, it could be a pool of any arbitrary dice and a fixed keep number will always mean more accuracy and more precision. This is the system featured in L5R, but L5R actually breaks this system and shows the fragility of it. L5R realizing this doesn’t scale to high numbers made dice explode when they rolled a 10. This simple change actually removed the increase in precision, and returned the system to one where more dice actually reduced precision. Also, in terms of Principle #3, it failed to allow that kind of differentiation. The only way to do that is to change the number of Keep dice, however doing that dramatically drops the precision. This change might be acceptable if these different metrics measures different things like magnitude versus finesse, but because the dice are all summed together at the end all changes to the dice pool variables go to the same place. Nonetheless this system does manage to be at least as good as Roll and Add.

## Matching Dice

This is another mechanic that fulfills Principle #2. In this you roll a pool of dice, you then find matching dice and the number of matching dice determines your “success”. This system is featured in the One Roll Engine (Wildtalents, Godlike), and manages to meet #1, #2, and #4 quite well. Additionally it has the advantage of giving two separate values for a success, which allows one two get the How Much and How Well in a single dice roll. Unfortunately it has scaling issues. The first issue is scaling at the bottom, if d10’s are used as in ORE, then the low end “average” person has a mere 10% chance of getting a single success. Furthermore at the peak of 10 dice you get an average width of 3.5 – That means that the steps involved in scaling out the width of a task is reflecting an order of magnitude more difficult. The high of the dice on the other hand scales in a way more similar to what one expects in a Pooling Targets mechanic. So while the Width scales up in orders of magnitude quite well, it scales very poorly at the low end, and while the height scales well at the low end, it scales poorly at the high end.

## Conclusion

Of the mechanics presented here, Roll and Add and Matching Dice seem to be the best. Roll and Keep might be workable, but it’s not entirely obvious how to manage it. None of the dice mechanics presented reflect an ideal match to the criteria, nor do any of them give a lot of flexibility when it comes to giving the players better choices. Without a compelling reason to use an alternative dice mechanic I will likely stick with the Roll and Add because it seems to mostly meet the criteria and is immediately intuitive to both new and experienced players.

Do you have other criteria for dice mechanics? Do you have a favorite Dice Mechanic?

Leonard WilsonI believe I can meet all four of your criteria using a system I call “En Media Dice” En Media Dice is my compromise between gaming by freewheeling instinct and gaming with granular number crunching. The name comes from its similarities to FUDGE dice (or are the kids calling them FATE dice these days?), where the results measure divergence from a character’s average performance. The same thing could be accomplished with FUDGE dice, but it would magnify the limitations that inspired me to develop an alternative.

For the record, I departed from FUDGE dice because I was dissatisfied with how little room they left for character growth over the course of a long campaign, and by how deeply they cut into the roll luck could play in a situation. Basically, I just wanted more elbow room than they allowed.

The En Media Dice roll is +1d0, -1d10, to get a result that ranges from -9 to +9, with results weighted toward 0. When you’re setting a precise target number, add in the character’s skill and the situational modifiers. When you’re free-wheeling it, the roll’s deviation from zero is just a general indication of how much luck plays into the results you’d expect to see from a character of that skill in that situation. Personally, I very much like the fact that the most extreme results in either direction will each come up exactly 1% of the time, so it’s essentially like working with weighted percentile dice.

My rule-of-thumb descriptions of a character’s skill are +0 is a total amateur, +3 is a student, +6 is a competent professional, +9 is a noted expert, +12 is a true master of the field, +15 is world class, and +18 is legendary/mythical competence.

Target 1: Check, like any other roll and add.

Target 2: No. Again, like any other roll and add.

Target 3: Check. If you want the expert to be further out of reach, just set a different rule-of-thumb scale.

Target 4: Check, I like to think. That was definitely a core design goal.

That’s the base system as I normally use it. Now to cover Target 2, I’ll introduce a minor variant.

Character skill now represents two factors. First, it performs as noted above. Second, a player may voluntarily commit before the roll to shifting the outcome towards 0 by an amount equal to his skill bonus or less.

e.g.: Young Socrates engages in a debate using his Philosophy +4. Feeling he has the better of his untrained opponent, he chooses to stick to his best material, leaving as little as possible to chance, and commits to moving the roll 4 points toward zero. The dice come up a -2. Had he been playing things recklessly, that would have achieved a net result of 2 (4 skill – 2 luck). Instead, he achieves a net result of 4 (4 skill – (2 – 4, minimum 0) luck).

Target 2: Check. And hopefully I can still claim the simplicity needed for target 4.

February 4, 2016 at 3:00 am

sheavalentineClever.

February 4, 2016 at 5:00 am

Arturo OrigelI don’t know if you have checked EABA (especially EABA v2) from BTRC…it is a ‘dice pool’ and ‘roll and keep’, but not like in L5R, you always keep only 3 dice so there is a limit (grounded in ‘reality’ like in GURPS) of what you can achieve, there have rules to, when you get better in some skill can ‘reduce’ the dificulty and rules to ‘pass’ pretty easy obstacles without having to roll fo everything, for me EABA strikes as a perfect balance in ‘reality feel-ish’ and playability, but that’s because Greg Porter (the man who wrote the system) it’s a genius-game-designer (yeah, it’s the guy of ‘macho women with guns’ but actually, he have pretty awesome games, in cad, boardgames y rpgs it’s only that it’s a bit ‘idealistic’ so he doesn’t make any marketing other thant the mouth to mouth from his ‘fans’ -and I a convert from a few years until now, don’t work from him just to clarify- . I use to be a ‘GURPser’ but the I give EABA a try and never look back (but maybe this discussion it have his place in another zone in your blog..maybe in you ‘generic systems’ discussion…but back to the point, maybe you want check it, it have a nice probability curve and it’s easier put all the modifiers than in GURPS, so in play it runs pretty smooth. Well, I hope my poor english don’t be a problem for make me undesrtand. Salutes!

March 20, 2016 at 4:48 am

AlexanderYou could do a ‘dice pool’ where target number is 1-2, Attributes grant bonus dice, but skill reduces dice type. Difficulty is based on the number of successes required. Hmm, might have a poke around with numbers and see if this is workable for something…

April 12, 2016 at 11:24 am

MikeGreat analysis of dice mechanics. I settled on xd6 k3 where x is your skill level (1-10), then count successes. 1-3 Fail 4. 1 Success 5. 2 Successes 6. 3 Successes. Accuracy and precision both increase with skill and an expert outclasses an amateur. It’s also quite simple because you only need to count successes for 3 dice. Lastly, your success rate is over 50% so long as skill equals or exceeds the target number, at least until 7d6, which is quite rarified air in terms of skill level. This is neat for opposed skill checks because only one roll is needed. Deceive 5d6 has a 54.8% chance to succeed versus Detect Lies 5…

August 13, 2022 at 1:43 am