Probability and Chosen Tools

A.K.A. Physical Mechanical Decisions (reupload)

When we play a TTRPG, every mechanic that involves a die roll is just a game of chance. Sometimes we're able to manipulate that chance to our favour, sometimes we're not.

I've seen aversion to the idea of "flat checks" to determine outcomes, and I myself have even had initial distaste for the OSR's attachment to using a d6 in such circumstances (usually calling for a 4+ or 5+)- but I think it's finally "clicked" in my mind, and I've come to appreciate the virtues of simplifying the mechanic as much as is reasonable.

Let's take an example from Pathfinder 2e, since it's a very math-heavy game (and likely what my audience is most familiar with): The creature building rules provide example ACs for monsters at levels -1 through 24, and while it does vary, generally the values are set such that a dedicated martial, fully investing in their ability to hit creatures, will have a baseline ~50% chance to hit. It's basically a flat check.

Now, we have to inspect and appreciate what nuances are allowed by a system before we can deconstruct it. Just because the values in Pathfinder tend towards a 50% success rate doesn't mean we can just start rolling d6s and hitting on a 4-6. With the example of Pathfinder, using a d20 gives us, well... 20 results. A wide spread of numbers that can then be meaningfully interacted with, as each point of bonus or penalty is worth a 5% statistical modification. Additionally, the +-10 critical success/failure system gives these points secondary values in modifying crit chances, and nat 1s/nat 20s a static 5% bump chance.

If we were to try to reduce the to-hit system down to a d6 then, what do we lose? Or more specifically, what changes? Well, modifiers either become much stronger and potentially much more necessary- each point is now worth 16% (over three times as much!), and depending on the game balance, a high modifier may now be necessary to even hit a creature. Critical results too lose something in this adaptation- maintaining the +-10 system makes modifiers the only way to reasonably achieve critical hits, and dumping it in favour of nat 1/nat 6 once again over triples the chances of a crit one way or the other.

In many important ways here, something quite important has been lost. Much agency and much nuance are jettisoned in favour of smaller numbers.

But let's take another look at Pathfinder now, and specifically its flat checks. Pathfinder has a variety of actions, effects, and miscellania that rely on the roll of a flat d20 to determine their results, usually at DCs 5, 11, and 15 (75%, 50%, 30%). As far as general play is concerned, these DCs don't shift and players don't get modifiers for them, so they function purely as statistical values. In this case, replacing them with a d6 system may in fact function fine. Setting the ranges to 3+, 4+, and 5+ (66%, 50%, 33%) results in nearly identical mathematics, and a functioning game system nonetheless. Flat checks, additionally, do not have critical successes, which leaves the other primary benefit of a d20 system out of the equation.

So why, then, does Pathfinder use a d20? I'm sure there are plenty of reasons. A d20 still has more manipulatable results, allowing for potential DC variance a d6 cannot emulate. A d20 is the primary chance die used elsewhere in the game system. A d20 is iconic.

But to circle back and round out my thoughts here, die rolls are, ultimately, nothing but chance. Without other systems interacting with (and creating results off of) their values, the method of delivery by which you achieve your chance is all but irrelevant. In such cases, what's most important is how easily one can access and adjudicate the levels of chance. A d20 with 5% per value might be quite intuitive to some, while others might prefer the more pie-like 16% of d6s. A 1 and a 20 are relatively rare on a d20, while a 1 and a 6 on a d6 are relatively common.

Always examine the tools you use, what they're doing for you, how they interact with your systems, and how you might be able to better achieve whatever goals you seek out at your tables. It makes for easier, better games.