Comparing Dice Mechanics

Here we go!

I am quite aware I am biased towards simulationist systems and styles of play. That doesn't mean I think any of them are any good! If I did, I wouldn't be making my own! In fact, your favorite game is probably a lot better than most of the simulationist ones that are out there. But, the mechanics of both systems are a real problem for me, and here is why! Narrative systems have neat properties, but don't produce the granular results that simulationist players need! I want both!

Simulationist systems attempt to focus on simulating results according to the physics of the fantasy world in a way that mirrors our own world. The idea is to make it more believable and more immersive. Ideally, the player does not deal with any mechanics and simply makes choices from the standpoint of their character. In a simulationist system, the focus is on the character and describing the character abilities in detail. There is a lot of measurement going on so that you can show how the character progresses through increase of numeric statistics, and sadly often just vertical progression. The player is simply the actor controlling the character and adlibing the lines. Combat generally uses hit points.

In a narrative system, the players are co-directors and sometimes co-creators of the world. There is very little focus on character ability because the focus is on shared world-building and co-creating the stories. There are often mechanics that allow a player to simply not accept failures in exchange for narrative consequences later. Resolution mechanics tend to be low granularity, and this is why combat uses wounds. In may cases, the players remind me that its just a game,and we're telling a story with depth and meaning, so we don't care about how much blood is gushing from this wound or exactly where everyone is standing. This works well with the common aversion to numbers! You'd be surprised how many people are counting dots rather than writing a 3 or a 4! I can write and understand a 3 easier than I can count stupid dots!

So let's talk about something simple. How about a simple boon to a roll. How do various systems handle that?

Simulationist: Roll High (ex: d20)

Every bonus grants a +1, changing the probability of any given result by 5%. This is nice for character progression (D&D plans for 20 character levels. 5% * 20 = 100% ... its not a coincidence!), but +1 feels like crap for a situational modifier.

• Easy Task: DC 12
• Masterful: DC 24
• Assume +2 attribute and +2 proficiency bonus:
  • DC 12 - need to roll 8+ or 65% chance
  • DC 24 - need to roll 20 or 5% chance
• Extra +1 grants 5% to all results equally, making 10% and 70% chances
• Because 5% is not normally noticeable, the change to "Advantage" was used
  • DC 12 w/advantage, an 8+ is 88%, or 23% improvement for easy tasks, like a +4.5!
  • DC 24 w/advantage, a 20+ is 10%, or only 5% improvement for harder tasks, a +1!
  • First advantage die grants significant benefit (median value goes up by 3.3, not a +5!). Diminishing returns to not upset game balance
• Single die resolution means flat resolution. Degrees of success will not follow the frequency of result distribution

Simulationist: Roll Under (ex:d20)

At first glance, this is way easier because you don't have to set a DC! Just roll under your skill! However, this now begs the GM to decide what the definitions of Easy and Masterful are! And is 2 a better result than 8 if both succeed? There is no way to know because the statistics don't favor anything. Let's say that we set this up exactly like what we have above, so we move the +2 attribute and +2 proficiency bonuses to our skill and make it a 14. Rolling under (not equal to) 14 is a 65% chance, so this is actually our "Easy" mark! Our DCs 12 apart, so masterful is a -12 to our skill. Did the math get confusing yet?

• Easy Task: roll under 14. 65%
• Masterful: -12. 5%
• All the problems above, extra confusion, and opposed rolls requires you to subtract, basically converting it to a roll-high system!
• Few systems apply an advantage/disadvantage mechanic to allow a modifier with diminishing returns

Honestly, this feels like it should have been done as a narrative game! You get the same benefits without the issues that a roll-under system implies.

Simulationist: Roll Under (d%)

• All the problems of both systems above
• D20's +1 modifiers felt too insignificant, now we have to give a +5 just to get that!
• Is 00 a zero or 100? If 00 is zero, then rolling equal to the number is a fail. Consider 99% is 1% fail. So if 00 is 100, then 100 is your 1% fail, and rolling equal is a success. Not only is this really confusing for most players, I have seen game designers get this wrong!
• Two digit numbers to deal with
• No diminishing returns modifiers. Every modifier is a fixed modifier of two digits.

The only thing I can think of is that the author didn't want to explore mechanics too deeply and just went simple. If the chance is 30%, we write that and thats what it is. It just doesn't have any of the safety nets and scalability features that other dice systems have.

Narrative (ex: roll d6's; count 1's)

The simulationist examples just keep getting worse! Let's try this narrative situation. You roll a die for every "plus" and count how many come up as 1s. Let's assume 2 dice for attribute and 2 dice for skills and see what kind of numbers we get!

• Easy (1 success): 52%
• Masterful (4 successes): 0.08% !!

Okay, if we want to compare to what we had above, we need to bump this up. Let's add a die to the attribute and a die to the skill. 6 dice total.

• Easy (1s): 66% - Adding two dice gave us 14%, or 7% per die
• Master (4): 0.87% - Adding twice dice gave us roughly 0.8%.
• Let's try with an extra +1 (die) bonus ...
  • Easy: 72% (Added 6%, slightly less than before)
  • Master: 1.76% (Added <1%)

So, where D&D was giving a flat 5% for everything, requiring a "fix" of the advantage mechanic, here the narrative dice pool has a similar slope basically built-in to every +1. However, we just rolled 7 dice to get the effect of the d20 advantage and our difficulty levels just slammed into a brick wall at a difficulty level of 4. This should explain why a "wound" based system works better than hit points in these systems. There just isn't a lot granularity. As for gating, D&D would have given us a 0% chance for a DC of 25, basically the 0.87% we see here.

Once you get rid of the idea of strict pass/fail, we have a curve here and degrees of success is mapped out for us very nicely and quite literally! Easy 1, Normal 2, Hard 3, and Master 4. You'll need at least twice as many dice as the difficulty to have a chance of making it, and this rule of thumb is pretty consistent for most dice pool systems. This makes it easy for the GM to describe the actions and set difficulties and degrees of success. It also shows a general avoidance of details, very abstract design (you roll all these numbers just to throw them away!), and you can see why the narrative style of play matches up so well to this type of dice mechanic.

But, we don't get to see a really nice looking bell curve with a range of values until you get up into just crazy numbers of dice. With a simulationist system, we can pre-compute modifiers for less math, but sorting dice can't be helped. Fewer dice means successes match degree of success but skills and attributes must be kept low. Attributes of 0-4 might be paired with skill values of only 0-6. We've all seen D&D characters with skills approaching 20. You sacrifice detail. Add more dice and now you basically have to set difficulty levels and decide your degrees of success while rolling 20-30 dice.

The main difference isn't in the mechanic itself, just what the more abstract thinking leads to. Narrative systems are great for shorter games where the skill progression can be shorter and less granular. So this leads to games that are shorter to learn, easier for reviewers to review, lower barrier to entry ... all good stuff ... and often highly disassociative mechanics. The majority of the people playing these systems are looking for a shorter experience, less attachment to the character, and are not focused on a deeply immersive or realistic experience. It's "just a game".

Fate / D8

The Fate system (formerly "Fudge" from a decade earlier) is basically using a narrative system with both positives and negatives on the dice such that results average out to zero. There is a similar idea called the D8 System that is basically [0 0 1 1 1 1 2 2] which nicely makes the average roll equal to the number of dice rolled and allows for a lot more granularity. These systems won't be discussed in detail here, but the Virtually Real capacity system was found to be more flexible.

PbtA

PbtA is a roll-high system, but its designed to be ultra-low granularity and most people agree it fits in the narrative style in spite of using a roll-high system. Fundamentally, the dice system is similar to Virtually Real in that the most common roll is 2d6, but the similarities end there. Everything else is about as diametrically opposed as you can imagine.

Virtually Real

It's not just a game! It's Virtually Real!

So D&D had one type of bonus for stats and skills, and then conditional modifiers were done with extra dice, like a narrative system, but they only allow one extra die. Virtually real takes a roll-high simulationist approach and puts it in a blender with a bunch of things learned from narrative systems. And that's actually more than just the dice mechanics (Intimacies, Aspects, etc) but those things follow from the mechanics. We also have a very consistent probability curve for trained skills with a totally random (but lower) set of results for people that are untrained. The consistency of results really helps with immersion because you know how well you usually do. Your rolls can be seen as typical or uncharacteristic, and this changes both the mood of the player and the character in similar ways. The narrative systems get this down too, but they don't focus on immersive role-playing. Sure, there are other systems with roll-high multi-dice probability curves, but do those curves change? You'll want to read Chapter 1 to see how Virtually Real's capacity system handles this!

• Easy Task: DL 8
• Masterful Task: DL 16
• Notice the slightly smaller numbers, less granular than D&D (8 steps vs 12), more granular than narrative systems.

Virtually Real differentiates between primary training and secondary training. This is sort of like your proficiency bonus, except that virtually real doesn't not treat skills as extensions of attributes. Let's assume a [2] 8/1 skill since it matches the "average first level characters" we've been using above.

• Easy Task: Need a 7. 58%
• Masterful: Need a 15 (on 2d6): 1.85%

However, very quickly, most of our skills will go up. In fact, 2 scenes gets us to [2] 10/2.

• Easy: Need a 6. 72% (+14%)
• Masterful: Need a 14. 2.3% (+0.45%)

We clearly have the right ballpark. The "tail" on our curve is even smoother than the narrative dice system due to the exploding dice mechanism. As for settings the DLs, this is actually Easy = 8, Normal = 10, Hard = 12, Difficult = 14, Masterful = 16. So, granularity is sort of right between the two approaches.

Let's try that +1, but we need to look at a +1 on a skill, and a +1 advantage. Like D&D, these are different. So, let's begin with the +1 to a skill. The only time this happens is when a skill goes up in level, which we actually just saw, but let's bump it again to [2] 16/3!

• Easy: 85% - Improvement of 13% on easy tasks (less than before!)
• Masterful: 2.8% - Improvement of less than 0.5% on masterful tasks
• This shows a really interesting progression that shows how the DLs within the playable range of the character show massive advancement so the character notices the level change, but this does not make significantly more difficult tasks much easier!
• Similar to D&D, a low number rolled is a critical fail. The +1 of skill level does not change this, but this IS changed by skill "training" to make up for this. So, we have a fixed curve and we just bump this nice "getting better at this skill" curve up the number line.

Because critical failure rates don't change, the +1 fixed modifier that looked great for skill progression, looks horrible for simulating conditions like fighting in slippery mud. Let's see what happens when we apply a mechanic similar to D&D advantage to this! From the [2] 10/2, but with advantage on the roll.

• Easy: Need a 6. 89% (+17%)
• Masterful: Need a 14. 6.2% (+4%)

This a much more significant modifier, especially on the higher end. D&D Advantage gave us +23% and 5%, so just slightly less impact than D&D advantage. In Virtually Real, you can have multiple advantage and disadvantages on a single roll. As far as median values, the change is +1.6, +1.1, +0.8, +0.6 ... steadily decreasing. This means we can stack these without breaking the game which is really important for situational modifiers. What we need to see is a change in extremes ...

Let's look at critical failure rates. At no advantage 2.8%, with 1 advantage it's 1.9%, at 2 advantages it drops to 0.4%, and 3 advantages 0.08%! This means that we can avoid critical failures by stacking conditional modifiers. For penalties, we have 2.8% go up to 7.4% with disadvantage, at 2 disadvantages it goes to 13% (almost as high as an untrained person's 16.7%), at 3 it's 19.6%, at 4 it's 26% and more than 1/4 of all rolls will critically fail!

For skill training, we have secondary (no training) skills are 1 die, random probability, median 3.5. Primary training is 2 dice, triangle probabilities focused on a median of 7, and elite training of PHDs and olympic athletes are 3 dice, with a bell curve centered around a median 10.5. Even the degree of swing is controlled, with combatants actually taking more damage on average when they reach elite skills, even if everything else is equal. And how genetics, attributes, skills, and experience all intermingles is spelled out in Chapter 2

Degrees of Success

• 1-2 is close enough, succeed with complication
• 3-5 is the next degree, minor failure
• 6-9 is the next degree, major failure

This follows the skill point bonus table. Not all skills or results will have a table for this, but the progression of degrees of value are based on how these degrees interact with the probability curves. And the rest is magic!

Conclusions

The Virtually Real system combines some of the best aspects of both, not only from a mathematical standpoint but from a psychological one. The simplest systems, such as D% where the number is your chance of success, are obviously easiest to understand, but actually put the absolute most work on the GM! Opposed rolls require conversion, modifiers don't self-scale, and to make them fair, you end up basically having to adjudicate every situation separately. The narrative systems would have some great properties, if you were rolling 100 dice! The more dice-heavy systems are adding curves rather than flat values, which provide more boost where you

Simulationist systems work best with targets between 10-25, depending on the size of the dice of course, but many seem to target this range, perhaps for historical reasons. Narrative systems are best when your targets are 1-4. Virtually Real is targetting 6-14 for typical novice fantasy play, and then 12-20 for the elite levels of play (when this happens is adjustable). It actually scales to god-like proporations with gods rolling above 25 as an average skill check before advantages or magic, and that is what the capacity system is doing. With magic, you could double that!