Hi.

My name is Sean Landis. I’m a professional software engineer, and aspiring game design.

In Search of the Holy Action Resolution Grail

holy-dice-grail.jpeg

So, a little while ago, I tried to create a variant of Dungeons & Dragons, 5th Edition specifically tailored for a Sci-Fi setting. The variant mostly spun out of the opinion that once a society invents modern medicine, medicine becomes the domain of Intelligence not Wisdom. But if the main ability tied to healing becomes Intelligence, Wisdom doesn’t really have a use except for Perception (and Insight) ability checks. Perception is arguably one of the most important skills, so you can’t just drop it… Wait, hang on, this post is not about that. I’ll write about that thought processes another time.

However, after some playtesting, I wasn’t satisfied with the standard d20 System’s action resolution mechanic (not in general, just in this setting). I began experimenting with 2d10 instead of 1d20, but it started to get quite complicated—rolling different dice for different actions, adding dice together, etc. Then I read this article from The Angry GM and was inspired.

The Hunt for Climatic Dice Rolling

The thrust of the article is that an ideal Tabletop RPG action resolution mechanic would be one in which not just the player picking up the die (or dice), but everyone at the table knows exactly what needs to be rolled to succeed. Then, when the die/dice land, everyone immediately knows if the action was successful or not. This creates the climactic tension Angry discusses. As the dice are picked up, everyone holds their breath in anticipation, and then when the dice land, everybody collectively exhales and the tension is released.

While reading the article, I was reminded of the final, climatic scene in the first D&D episode of Community (RIP), when (Fat) Neil wants to throw his sword at the amulet “around the sad, old man’s neck.” Abed says that it’s a tough shot, so he’ll need an 18 or better. As Abed picks up the d20 and is preparing to roll, there are several close up shots of all the characters—praying, wishing, and watching very intently. Abed rolls, and the camera snap zooms on a 19, and the table goes crazy! The players at the table (and the audience at home) all knew what Neil was trying to accomplish, they all knew the stakes, knew the chances, and new the consequences. The whole scene only works as a dramatic scene for exactly the reason Angry talked about (also, notice there’s no damage roll).

So, if we want to achieve this ideal, there are some conditions we need.
1) When the player grabs the die to roll, they need to know what they are trying to roll. So we can’t have a hidden success target.
2) The other players, and GM, should also know what the acting player needs to roll. This means their success can’t rely on adding modifies or abilities to the result of the roll, which people around the table may not know and/or have forgotten. This doesn’t mean character abilities shouldn’t effect the roll, it just needs to happen before the roll, at the dice pick up part, not after the roll.
3) Similar to the previous point, the success of the roll needs to be quickly, and easily verified. Thus, needing to add or subtract modifiers to the number on the die to know the final result, or dice pools that involve canceling things out, need to be avoided.

Daddy Needs a New Pair of Shoes!

You know, there is already a game that’s pretty close to this ideal: craps. When a craps player picks up the dice, everyone around the table typically knows exactly what the player is attempting to roll, or at least what he or she is hoping not to roll. Often the player is attempting to roll as specific value, in which case everyone needs to add the face value of the two dice together to get the final result. But sometimes, the player is attempting to roll a pair… I’ll come back to that. First, lets dissect the anatomy of a generic action resolution roll in more detail.

In most (all?) systems, there are three fundamental components to determining success for any given action. The first is luck, embodied in the act of rolling a die or dice. In D&D, this is the d20 rolled to resolve an ability check, saving throw, or attack roll. The second is the capabilities of the character. Typically, this is a positive or negative number that is added to the roll, often called a modifier. And finally. there is the inherit difficulty of the task being attempted. In D&D this is represented by the Difficulty Class, a number that the player must meet or exceed by rolling a d20, and adding their relevant modifier(s) to the face value.

So, with all the preamble over, here is the idea I came up with for my new* action resolution system. In my system, success is rolling a pair. The specific number doesn’t matter, all the matters is that at least two dice show the same number. The human brain is very good at recognizing patterns, so noticing a pair, even when more than two dice has been roll, is relatively easy for us smart monkeys**. At least as easy as very simple addition. The difficulty of the task determines how many dice you roll. Easier tasks mean the player rolls more dice, increasing the chance of at least one pair. Finally, capabilities of the character determine which type of dice is rolled. Dice with less faces (a d4, for example), are more likely to roll a pair than ones with more faces. So, as a character’s capabilities increase, the dice they get to roll goes from d20 -> d12 -> d10, etc.

With all those ideas in mind, it was time to put them to the test with MATH!

Tables, Tables and Percentages Everywhere!

First, I calculated the standard D&D DC’s with various modifies to use as a baseline/point of comparison (a relatively easy exercise, since in the d20 system, a one point increase in DC or a one point increase in ability modifier equals a 5% increase in the chance of success)

Probability of Meeting or Exceeding DC with given Modifier
DC Task -1 0 +1 +2 +5 +10
5 Very easy 75% 80% 85% 90% 100% 100%
10 Easy 50% 55% 60% 65% 80% 100%
15 Medium 25% 30% 35% 40% 55% 80%
20 Hard 0% 5% 10% 15% 30% 55%
25 Very hard 0% 0% 0% 0% 5% 30%
30 Nearly impossible 0% 0% 0% 0% 0% 5%

Next I calculated the chance of rolling at least one pair with various numbers of the different polyhedral dice:

Probability of Rolling at least One Pair
Task # of Dice d20s d12s d10s d8s d6s d4s
Very easy 6 56% 78% 85% 92% 98% 100%
Easy 5 42% 62% 70% 79% 91% 100%
Medium 4 27% 43% 50% 59% 72% 92%
Hard 3 15% 24% 28% 34% 44% 63%
Very hard 2 5% 8% 10% 13% 17% 25%
Nearly impossible 1 0% 0% 0% 0% 0% 0%

Right away, you can tell the distribution isn’t linear, but it seems linear-ish, and they are not wildly different from the D&D probabilities. Also, unlike the D&D system, as long as you are rolling two dice, there is always a chance of success, regardless of the type of dice rolled, but if you are only rolling one, it is literally impossible. However, this does hint at some ideas for some high level class abilities. Something that gives an extra die to roll, allowing the impossible to become possible.

Regardless, the probability distribution was encouraging enough that I began revamping my Sci-Fi variant rules to use this new action resolution system instead of the d20 system, and it quickly became apparent that I had to change EVERYTHING. Funny that. When you change the central mechanic of a system, literally none of the subsystems work anymore. Anyway, that’s a topic for a future post I will totally definitely write…

After revamping the rules enough to make it playable, I started a new campaign with my regular D&D group. Thus far, the reactions to the new pair-based action resolution system have been very positive. My players grasped it quickly, and have been enjoying it. Once I polish the system more, I will post it on my blog so you all can give it a try and tell me what you think. Until then, let me know in the comments what your initial thoughts on my new system are, and/or if you have any interesting action resolution systems of your own.

Until next time!

* Well, new to me. I’m sure this has been done by some system at some point in time. Nothing new under the sun, and all that.
** Yes, I know human’s are apes not monkeys, but monkey is a funnier word.

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