This is the all-important chapter on randomness. I feel like it needs more detail and rigor about statistics, but that’ll require me learning more about statistics and probabilities. Right now this chapter is a lot about how randomness fits into the overall experience. There’s a short section I want to do but haven’t yet on “other uses for dice,” with things like using them as counters, stacking, roll-and-spend (a la *Dogs in the Vineyard*), etc.

The vast majority of RPGs make extensive use of randomness, and most of those use dice to achieve that randomness. Randomness isn’t a necessity, but it’s deeply ingrained and legitimately useful. It introduces a level of controlled unpredictability that can keep gameplay popping. However, it’s important to also think about where the randomness slots into the overall experience, and be aware of what the actual odds are.

## Doing the Math

If you’re going to make a game where probability plays a role, you need to understand the math involved and make it work as well as you can before you even begin playtesting. Games tend to have enough moving parts that it’s hard to anticipate *everything*, but that’s all the more reason to begin with a sound theory. My own preferred approach is to keep the math simple and the numbers low. That’s partly because I don’t have that much of a head for numbers, and partly because it makes it that much easier to figure out what’s going on and fix things that aren’t working right.

A traditional RPG has an action resolution system, which is to say a set of rules to determine whether a given discrete action succeeds. From 3^{rd} Edition onward, D&D’s action resolution system has had you roll a 20-sided die and add whatever applicable modifiers you have, and you succeed if your total matches or exceeds a target number. In the case of an attack, you add your attack bonus, and you hit if you can reach the target’s Armor Class, while for skills you add your skill bonus and need to reach a Difficulty Class. That mechanic itself is simple enough, but the things that go into it get a bit complicated, since a character’s attack bonus comes from a mathematical formula involving around 2 to 6 different numbers. Thus, the designers at Wizards of the Coast have the rather complex task of making sure that the bonuses that characters get add up to something that leads them to have a suitable ratio of success to failure.

There are many different types of dice (and other randomizers) that RPG designers have used over the years. The most important distinction is between flat and curved probabilities. If you roll a single die, each possible result has an equal chance of coming up. On a d20, the numbers 1 through 20 each have a 5% chance of coming up on any given roll.[1] On the other hand, if you roll two or more dice, it creates a probability curve, and results in the middle are more likely to show up because there are more combinations that can produce them. If you roll two six-sided dice, you only have a 1 in 36 chance of rolling a 2, but a 1 in 6 (or 6 in 36) chance of rolling a 7. This is because there’s only one combination of two dice that can add up to 2, whereas there are six different combinations that can add up to 7.