The Gaming Den

This is a one-off post.

When we discuss rules and mechanics in TTRPGs we have to assume that there are only a finite number of finite tasks associated with carrying out any given rule or mechanic. So as cool as it is to say "there's infinitely many different schemes for rolling dice", only a finite number of those are actually usable by human beings.

That finite number might be big.

I watched The Banach-Tarski Paradox on YouTube last night. In setting up the premise it distinguished between 'countable infinity' and 'uncountable infinity'.

I agree with your premise. If you have to roll 30+ dice in sequence to determine your action, that's not practical at the table. If you need to roll dozens of the same type of die at the same time (ie, 25d12) that's also not practical. Rolling solutions that include fewer steps, fewer processing steps, and fewer physical dice are generally preferred. That does still allow for a lot of 'gimmicks' that can make a rolling scheme feel different - different effects on particular rolls (ie, max value [critical success], min value [fumble], doubles, exploding dice, subtracting dice).

Gimmicks are attractive because it is a way of portraying your game differently. If done right, they can contribute to the 'feel' of the game in a positive way. If done badly they can negatively impact the play experience or complicate things without actually mattering.

Oh, yeah, if you restrict it to "practical mechanics" the domain is even SMALLER. But we can restrict it to "humanly possible" and get finity.

Also, mechanics are gonna be a countable infinity! Because we demand that they're communicable in language.

There are infinite numbers between 1 and 2 There are infinite numbers between 2 and 3.

Infinity does not just come from discrete rules, but from minor variations on those rules.

The ideaspace of all possible houserules is essentially infinity, not because "roll a a billion d one million" is a practical possibility, but because of infinitesimally minor variations that arise organically within a play group, which are probably not big enough to be actual written rules.

hyzmarca wrote:There are infinite numbers between 1 and 2 There are infinite numbers between 2 and 3.

Infinity does not just come from discrete rules, but from minor variations on those rules.

The ideaspace of all possible housefules is essentially infinity, not because "roll a a billion d one million" is a practical possibility, but because of infinitesimally minor variations that arise organically within a play group, which are probably not big enough to be actual written rules.

In practice: there's an lower bound on how minor a variation of a houserule can be. To actually quantify this you'd need a representation of a "rule" or a "houserule" but it's pretty clear that, since we're finite beings who do finitely many things at any given point, there are only finitely many rules that we can ever carry out. You only get infinities when you can increase without bound (but we will die) or you can refine without bound (but we can't do things every 1e-10 seconds).

There are infinite numbers between 1 and 2 but a finite amount of numbers that differ down to 1e-100.

Is there a reason the cardinality of the set of possible rules is interesting? I think we can agree that it is large, for a particular maximum length of rules text is finite, and for unbounded texts is countable but unreasonable because past a certain point you run out of dead trees to print it on.

Pixels wrote:Is there a reason the cardinality of the set of possible rules is interesting? I think we can agree that it is large, for a particular maximum length of rules text is finite, and for unbounded texts is countable but unreasonable because past a certain point you run out of dead trees to print it on.

Hell no there's no reason, I just personally get a big ol' hard-on for pedantic mathematical clarifications

Cervantes wrote:

hyzmarca wrote:The ideaspace of all possible housefules is essentially infinity, not because "roll a a billion d one million" is a practical possibility, but because of infinitesimally minor variations that arise organically within a play group, which are probably not big enough to be actual written rules.

In practice: there's an lower bound on how minor a variation of a houserule can be.

This lower bound apply game per game; when you create a houserule, it will differ from the original rule by at least this lower bound. But the distance between two houserules used by two different table may be smaller than this bound.

Example: the difference between fractional save bonus in D&D3, and Pathfinder PrC save bonus, is bullshitly small and in one given game you'll use only one of those two rules (or the original rule). Still, those are different rules in the DesignSpace.

Mathematically: consider the the DesignSpace as a affine space, your original game contains a point/rule X, and your houserule is another point X+deltaX1. What you're saying is that norm(deltaX1) > some lower bound b. I agree, but this doesn't prevent another group to use the houserule X+deltaX2, with norm(deltaX2)>b and norm(deltaX1 - deltaX2)<b.

(In the other hand, the DesignSpace is limited by the number of word we can reasonably use to describe the rules. Hence it is finite. But I guess your original questioning wasn't about something as obvious as "any usable ruleset can be described with less that a gogolplex of words, and you can only write a finite number of different stuffs using that amount of words")

I didn't use an argument from "language is finite so rules are finite" because I'm actually not sure if you can't use finitely many letters to express infinitely many rules. "Fighters get +X to Strength at level 20, where X is an integer". So I went with the fact that rules are subject to use in practice to get the finiteness.

I think there's probably some lower bound b across all tables, so that norm(deltaX1 - deltaX2) > b.

Serious question, is 0 finite? I've yet to see the game with mechanics that weren't flawed to the point of being barely playable. There are differing degrees of shit but there's shit in all of it.

Cervantes wrote:This is a one-off post.

When we discuss rules and mechanics in TTRPGs we have to assume that there are only a finite number of finite tasks associated with carrying out any given rule or mechanic. So as cool as it is to say "there's infinitely many different schemes for rolling dice", only a finite number of those are actually usable by human beings.

That finite number might be big.

Correct, which is why much of game design outside of RPGs revolves around how to limit the number of possible options and tasks to begin with. Indeed, RPGs to a large extent are messy things because of the genre’s insistence on “freedom”, rather than considering the insight that players do not necessarily want freedom.

Rather, what they want is to have a good experience; based on preconceived expectations of what their choices should result in.

The set of rules that humans can implement is quite finite, although establishing the boundaries would be quite difficult.

Every requirement you apply to rules narrows that set even further.