## Design Advice: How do I choose my Dice Mechanic

So you’ve decided to design your own Role Playing Game. You now want to figure out the best dice mechanic to use. You ask yourself “Should I use a d20, or a dice pool?” or some variant of that question.

How do you decide? I’m here to guide you through that decision process.

## Does it matter?

Why have you decided to write your own system in the first place? If your game is about “The social dynamics between adventurers exploring ancient ruins”… well, what is it about that game that requires its own system? The thing is that there are tons of systems out there that you can leverage to implement RPG’s dealing with all sorts of game elements, and most of them legally let you publish your work. Examples include: d20, Fate, Action!, Fudge, Dominion, OpenD6, Traveller, etc…

Even within the context of using one of these game systems, you have the ability to modify the system or add a subsystem. In the case of the design in question you might start with d20, and add a mechanic like “During character creation you define a social dynamic between your character and two other characters. You also gain an action point to start. Anytime your characters have a meaningful relationship interaction you gain another action point. Action points can be spent whenever you and the other person engage in teamwork”. Meanwhile you construct the world and classes in a way that emphasizes interpersonal relationships.

If your design goal really is to create a game dealing with something narrowly scoped like this, your best bet is going to be either making a very light system entirely focused on that or leveraging an existing system with new rules to emphasize the gameplay you’re looking for. In this case the question of the Dice mechanic is obviated. If you still want your own system, but your design goals don’t reflect a need for a specialized system, then simply pick the one you’ve enjoyed the most from another game.

## When does it matter?

Dice mechanics communicate specific ontological realities about the game, and facilitate certain playstyles. If your design goals include facilitating sorts of play the dice mechanic can be relevant. It’s entirely possible that your design goals do require a specific sort of dice mechanic, the following all being examples:

– An increase in skill should have decreasing marginal returns

– Rolling the dice should be “fun”

– An increase in skill should represent exponentially larger differences

– It should scale to represent the difference between extremely poor skill and godlike skill

– It should have very precise measurement showing even tiny differences

– It should only involve d6’s so that people can play by stealing dice from their board games

– Probabilities should hold “over time”, meaning if you succeeded recently you should be more likely to fail

– People should be able to trump the result of their randomizer with resources.

– The mechanic should be able to represent people who have absolute ability (unstoppable, immovable, etc)

– Luck is more important than skill

– The game involves magicians, so skill means manipulation of luck

– A more skilled person should be able to trade likelihood for amount

– I don’t care about representing peons, my game is about godlings

At this point I’m going to assume you’ve decided that you do need your own system, and you need a specific dice mechanic, so I’m going to help you decide.

## Dice Precision / Resolution

Should you choose 1d4 or 1d100? It doesn’t matter in most cases. A +1 on a 1d4 is the same as a +25 on a 1d100. So if you design the game around a 1d100, and then want to switch to a 1d20, a 1d12, or whatever, you are simply decreasing the resolution you are working in. The first game I ever designed used a 1d100, but when play testing I realized everyone always rounded to the nearest 5, so it was for all intents and purposes a 1d20 system. I moved the system to using a 1d20.

This also applies if you are summing multiple dice. In this case the value of a +1 is determines by the Standard Deviation. So 3d6 your +1 is 1/2.96 and your 5d8 is 1/5.12. This you have the same concept of precision as you do with a uniform distribution.

(To get Standard Deviations use anydice.com)

## Proportionality

Whether you use an additive pool, single dice, a dice pool, or anything else; you have a probability distribution that reflects the likelihood of getting a specific number given a specific roll. The most important ones to look at here are:

– Uniform: if you have 1 dice

– Triangle: if you are adding 2 dice

– Gaussian: if you are adding more than 2 dice

– Binomial: if you are counting dice above a number in a pool

– Pseudo-Exponential: if you have exploding dice.

Each of these has improtant properties when talking about the proportions of numbers. Let’s consider the case of having a skill of 10 on a system where you add a roll of 1d20 to your skill. Well a skill of 11 is a 5% better in terms of probability, but only 10% better in terms of proportion – the same system comparing a 1 and a 2 the two is still 5% better in terms of probability, but 100% better in terms of proportion.

This is in contrast with an exponential distribution. To get a true exponential distribution: flip a coin, keep flipping so long as you get a “head”, sum the number of heads you get. This is a “pure” exploding mechanic. When dealing with an exponential dice mechanic the difference of proportion is the same for every +1. In the case of a coin flip every +1 is 100% better proportionally because the fixed probability is equal to the proportional change. Most exploding dice are not “count number of times it explodes”, which makes their mechanic a mix.

Gaussian distributions act more like uniform distributions when the numbers are close, and get even more extreme than exponential distributions when they’re far away. So it makes small differences seem very unimportant, but many small differences accumulate into a huge difference. For example a 1d10+5 and a 3d6 have a similar amount of “variance” equal to about 3 and the same mean. However the 9, 10, 11, 12 rolls are more likely with the 3d6, the outlying rolls are more likely with the d10 and the far outliers aren’t possible with the d10 and are with the 3d6. https://anydice.com/program/100a9

Dicepools use a binomial distribution, which is a lopsided Gaussian distribution. The more important factor here is the the deviation changes with skill, which gets to the next point.

This is all a lot of technical detail. The summary is that if you are using a “roll and add” there are two questions: Do you want it to be possible for a person way less skilled to beat the better even if it’s unlikely? If so choose a Gaussian. Do you want a person significantly worse, but still in range to have a good chance of beating their better? Then choose a uniform distribution. If you want both choose an exploding uniform distribution. If you want something in between choose a triangle (2 dice) distribution.

## Variance with skill

The thing about roll and add mechanics is that the variance is fixed. This has the advantage of making things easy to reason about. However if you want the variance to increase when your skill increases, you need to choose either a Step Dice mechanic or a Dice Pool mechanic. What this means is that as your skill increases, your average increases but so does the randomness. Step Dice will give you features similar to a Uniform distribution but with increasing variance, and Dice Pools (count successes) gives you features similar to a Gaussian distribution but with increased variance.

If instead you want the variance to decrease, you have two basic options here. If you want features like a Uniform distribution, use step dice but make low rolls better than high rolls. If you want features like a Gaussian distribution, have a fixed number of dice you keep (say 3), but increased ability increases the number of dice you roll.

Both the dice pools mentioned here also have the feature that they have decreasing marginal returns. That is to say the increase in your probability of success is reduced for each +1. However all of these also have scaling problems, in that you quickly hit practical limits of what you can describe.

### Variance in Contests

Many games have Attack and Defender roll. Be careful here because it increases the variance whenever you do this. This may be a desired feature, but you should make an explicit decision when you want to do this. This is a weird design feature in Fate when combined with the Bronze rule, because it means the dice variance is determined by whether you decided to model something as a character.

## Weird Randomizers

There are other weird randomizers you can choose that have their own features. You could have a mixed set of dice that are interpreted in different ways, you might do this because it’s fun and your game is silly. If you have an Old-West game you might choose cards.

### Inventing a Unique Dice Mechanic

Sometimes you have specific design goals that require being inventive. An example might be “I want people who have good rolls recently, to have bad rolls later”. Cards are a good way to model this “probability over time” aspect. If you want increasing variance you could have the player have “all cards up to their ability number” so an ability of 3 has a {1,2,3}. Or if you want it to have decreasing variance, then they remove those cards, so a 3 has {4,5,6,7,8,9,10}. When you do this note the practicality – if you do this you can’t reasonably have them construct a new deck for every action, so how do you handle different skills? Making new mechanics is hard, and usually not worth the effort you put into it – there are lots of game designers who have experimented with lots of game mechanics, and most don’t work very well. The last innovation I saw in this space was One Roll Engine’s dice mechanic (count matching dice), and that only really works in the context of superhero’s and the mechanics they built around it.

## Living Myth’s dice mechanic (a worked example)

If you go looking through this blog you’ll see a lot of different design goals for the core mechanic. You’ll also see the construction of a unique mechanic. All of these were dropped due to needless complexity, and because a more important feature emerged.

The final decision for a dice mechanic was a desire to express exponential change. People are pretty good at estimating differences of percentages, but it’s confusing if your difficulty is based on “every 5 feet” when you are talking about something 100 feet out. So onc eI decided that everything was measured on a log scale, I knew I wanted a dice mechanic that reflected this. The straightforward way to do this is “exploding coin toss” as mentioned above, but it’s onerous. It also needed to be positive and negative which is a “Laplace Distribution”. The final choice was an exploding d10 minus another exploding d10 which is a reasonable approximation of the same thing. This is very similar to the dice mechanic in Feng-Shui, except d10’s are used instead of d6. Why d10’s? Because it makes an getting 11 10% as likely as getting a 1, and a 12 10% as likely as getting a 2. With a d6 it’s 12 is 16% as likely as getting a 6 which is in no way intuitive.

Comparison of a true Laplace distribution vs Living Myth: https://anydice.com/program/100ae

## Final Thoughts

Your dice mechanic is hopefully the least interesting part of your game. Unless you have very specific reasons to design a specific mechanic, you should stick to the basics. You should be able to figure out in a few minutes what to use by deciding:

– How does variance change with skill?

– Do I want an Exponential, Triangle, Gaussian, or Uniform distribution?

– Do you want to handle exponential differences?

– What level of granularity makes the most sense?

With these three questions and playing with the dice to see what feels right you can get your core mechanic squared away and get to the business of what really differentiates your game whether that be unique mechanics, an interesting setting, or fascinating narrative elements.

## Leave a Reply