PbtA games (Powered by the Apocalypse) are sometimes summarized as 2d6 games, due to the 2d6+stat dice mechanic popularized by Apocalypse World: a 10+ is an unmitigated success, a 7-9 is a mixed success, and a 6- (6 or less) is a failure.

But some PbtA games use other dice mechanics.* I was particularly fascinated by the action rolls of Blades in the Dark, which use dice pools where only the highest die is considered: “They might succeed at their action without any consequences (on a 6), or they might succeed but suffer consequences (on a 4/5), or it might just all go wrong (on a 1-3).” Depending on the dice bot you use, this might be notated as 2d6b (“keep best”) or 2d6kh1 (“keep highest 1”) or 2d6D1 (“drop lowest 1”).

I wanted to better understand the relative probabilities of dice pools where you keep only the highest result vs. traditional 2d6+N modifiers.

A single d6 has almost the same chance for success (6) as a 2d6 does (for 10+): 17% vs. 16%, though the chance of a mixed success (4-5) is 9 percentage points lower: 33% vs. 42% for 2d6 (7-9). The 2d6kh closely approximates 2d6+1: 31% chance of success vs. 28%, and both have a 44% chance of a mixed success. The 3d6kh also closely approximates its counterpart, 2d6+2: 42% chance of a full success for both, 45% vs. 42% chance of a mixed success. The 4d6kh is close to the runaway success of 2d6+3: 52% chance of full success vs. 58%, 42% chance of mixed success vs. 33%. The dice pool falls even further behind the 2d6+modifier at 2d6+4: 60% chance of full success vs. 72% chance.

The dice pool isn’t great at the other end either: To approximate 2d6-1, you need to roll 2d6 and keep the lowest number.

The sweet spot is clearly mimicking 2d6+0 through 2d6+3 with 1 to 4 dice, keeping the highest.

Dice probabilities of 2d6 vs d6kh pools

The advantages to me of d6 dice pools where only the highest counts include:

  • The results are bounded. You’re never going to roll a 15 (as might happen with 2d6+3).
  • Rolling more dice is fun!
  • Carrying a +1 forward to your next roll (a common PbtA mechanic) can be accomplished by placing an additional die on your character sheet as a reminder.
  • There’s some science that comparing quantities is more innate: pre-verbal children already have comparisons as a “proto-quantitative skill”, that comparison is easier than addition, and that addition is easier than subtraction.
  • The progression of the increase in the probability of success is similar enough to 2d6, 2d6+1, 2d6+2, 2d6+3 for me.

*Quick Aside: Examples of Other Dice Mechanics in PbtA Games

Just for illustrative purposes, here are some of the PbtA games that use dice mechanics besides 2d6:

  • d6 dice pools – Blades in the Dark (which started as a PbtA hack), but with the added complexity of its action roll mechanic
  • d6 vs. 2d10 – Ironsworn
  • 2d6 with different ranges – Liberté and Apocalypse Keys, where 7- is a miss, 8-10 is a success, and +11 is an excessive success
  • 2d10 – Flying Circus and Kult; 2d10 supports more granular stats
  • diceless – Belonging Outside Belonging and Firebrand Framework.

Hard Knock World Dice Probabilities

When I was creating Hard-Knock World, I started out with the six classic stats for characters [also see Attributes/Stats for Characters in Old School RPGs] and used the standard 2d6+stat dice mechanic. Now Vincent Baker recently wrote about what he sees as the biggest weakness of PbtA: “What the PbtA system or philosophy wants you to do is, it wants you to create a whole new game. It won’t help you adapt a game in play — it thinks you should make a new game instead. It won’t even really help you make new playbooks or things for existing games — it thinks that those games are already finished.”

The more I worked on Hard-Knock World, the more it diverged from its inspiration. I came to realize that the 2d6 mechanic and the 6 stats were overkill for this system. Stats are great when you have a wide variety of moves, with categories of moves that can be modified by a stat (for instance, social moves being modified by Charisma). Hard-Knock World has only 20 moves, and a player will never have more than 11 moves available. So instead I decided to switch to d6 pools where each move specified how many dice a character could roll; rolling low on a move earns XP and every 7 XP earn the player another die to assign to a move for their character.

So I ran the above numbers to make sure I was comfortable that the math would align. And, despite my desire for a Yahtzee! like roll of 5 dice, I decided to cap the dice pool size at 4.

I did consider using the dice pool for the damage from monsters but decided I did want creatures that could do more than 6 points of damage.

You can download a copy of Hard-Knock World from my Itch.io account or read more about it here.

Photo by Moritz Kindler on Unsplash.

Reflections on PbtA Design book coverYou can download this and other essays in my free ebook, Reflections on PbtA Design.