Sinter RPG: Dice Mechanics

Though not all tabletop roleplaying games use dice, the majority do. And most players consider dice to be the lifeblood of the genre. Part of the appeal of D&D in my childhood was rolling all those funky four-, eight-, ten-, twelve-, and twenty-sided dice. Dice introduce probability into roleplaying, for better or worse. Even the mightiest wizards and warriors have a slim chance of falling on their swords or botching a spell. The threat of great success and great failure keep an RPG lively and fun.

Prior to researching RPG design, I did not realize how important die mechanics are to the overall balance of a game. When and which dice a player rolls are not arbitrary–or they shouldn’t be. Each die (or group of dice) carries its own probability curve, which can skew the game in unexpected ways. Unexpected, of course, if you don’t look at the underlying math.

Modern D&D and its many clones rely on the d20, or twenty-sided die, for most rolls connected to combat, saves, and skill checks. In combat, for instance, a player will make their attack roll with a d20, comparing it against the enemy’s armor class (AC). If the result is equal or higher, they hit. The player then rolls for damage on another die (typically not a d20).

Why a d20? Rolling a single twenty-sided die produces a linear probability distribution, meaning that a player has an equal chance (5%) to roll any number on the die—assuming that the die is uniform and balanced. And since the d20 has twenty individual sides, there’s a nice range of values that a player can land on. That range means that players can improve over time. At level 1, a player’s character has a tougher time landing hits. In a narrative sense, their character is weaker, less trained, and equipped with poorer weapons or skills. As they advance, their chances improve.

However, chance does not scale by graduating players to larger dice. Instead, D&D and its ilk add modifiers. Advancing to level 2 might give the player a +1 modifier to attack rolls. In other words, they roll the d20 as usual, then add one to the result. That slight bump increases the probability of success. The player gets stronger, is more likely to hit, and so on.

The d20 works well for combat and skill checks, but most systems opt for alternatives during character creation. In D&D, most attribute scores are derived from sequential rolls of 3d6, i.e., rolling a six-sided die three times and summing the results. As such, attribute scores range from 3 (poor) to 18 (exceptional).

Why the dice change? If we look at the distribution of 3d6 vs. 1d20, we can see that we now have a classic bell curve instead of a line. Adding multiple dice to the attribute pool changes the odds in a significant way: players are more likely to land somewhere in the middle; exceptionally poor and exceptionally excellent scores are less likely than ‘average’ scores. In other words, your fighter’s strength will probably be 12 rather than 17. And it is practically impossible (though not improbable) to roll a character with all 18s.

In character creation terms, the bell curve makes a lot of sense. In D&D fiction, scores of 8-10 are typically ‘normal’ human capability. Anything above is heroic. According to our curve, most player rolls will be at or above the normal human range: approximately 48% of 3d6 rolls will land between 9 and 12. Characters will be better than average, but not grossly overpowered. There is also just a 0.5% chance to roll an 18, far less than the chance to roll the highest value on a d20. If players rolled ability scores on a single d20, both players and GMs alike would be frustrated with the results. The linear probability distribution would ensure that scores were all over the map–some players would get screwed, others would be unbalanced killing machines. The bell curve keeps things average, fun, and fair.

In my previous Sinter post, I outlined six attribute types and their six corresponding character trades. The core tenet of my world is bond between characters, so I wanted to choose dice mechanics that reflect that design value. I chose to maintain the number six as a theme, but opted not to rely solely on the d6. The multiple-d6 distribution works well, but I wanted a slightly steeper probability curve and a slightly wider range of possible values—in other words, a compromise between d20 and d6. I settled on the d12.

Rolling 2d12 for character generation produces a triangular probability distribution. Scores are likely to group near the center, like the 3d6, but there’s a steep slope on either side of the value 13 instead of a gentle bell curve. Doubling the die size also increases the range of values, from 3-18 to 2-24. However, rolling a 2 or a 24 is slightly more likely (0.7%) than rolling a 3 or 18 (0.5%) thanks to one less die in the pool. And since the 2d12 strikes a nice balance between 3d6 and 1d20, Sinter can use 2d12 for both character generation and combat rolls, saves, and skill checks (assuming I have saves and skill checks—I’m still undecided). I like the idea of uniform rolls for multiple mechanics. Not to mention that a d12 looks cool and is easier to roll than a d20.

The tricky part of using 2d12 for combat is balancing for modifiers. Adding a +1 to a 2d12 roll has different effects than adding the same for a 1d20 roll. Modifiers on the ‘edges’ of the triangular curve have less impact. If, for example, a player must roll a 15 or above to complete a challenge, they have a 38.2% chance to succeed. A +1 modifier bumps their chances to 45.8%, a +2 yields a 54% chance of success, a +3 grants 61.8%, and so on. In other words, there are diminishing probability returns for modifier bonuses. Each bump up provides a smaller percentage change in success. As such, modifiers near the center of the distribution have a more significant impact. Statistically, completing ‘average’ tasks becomes much easier with a positive modifier (and vice-versa). Proper balancing will require careful attention to the target difficulties and where they fall within the triangular distribution.

I’ll talk more about dice mechanics in the future, but this hopefully provides a little insight on how and why probabilities are tied to the larger Sinter fiction. I like that the d12 is a multiple of 6. Of course, no system is perfect and ultimately, attaching random die results to a world is mere abstraction. But keeping mechanics tied to fiction results in a richer, more robust game.