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.

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.