Singularity

[malonkey1]

Has there ever been a time, or is there a theoretical possibility, that somehow a mathematical singularity should appear in the rules?

To be clear, a mathematical singularity is basically, divide by zero. What I mean is, as a result of random die rolls and mathematics inherent to the game, somehow, can a division by zero crop up, and if so, what might happen? This question applies mostly to Pathfinder and 3.5, but it could really be asked of all D20 systems.

[Someonelse]

Could you please clarify your question? I'm confused. What do you mean by a division of zero cropping up?

[Promises Kept]

While there are a number of possible infinities as a result of rule interactions, division by any variable value is, to the best of my knowledge, not present in the 3.5 ruleset. Of course, I may be wrong, but I think the designers have avoided the possibility of such a thing.

[NichG]

There are implicit divisions in the calculations of probabilities of events that cause singularities. The generalization of the d2 Crusader is an example of this - imagine a dX Crusader and calculate the expectation value of damage dealt.

The recursion relationship is: <damage> = (<damage for a single roll>) + Prepeat * <damage>

So <damage> = <damage for a single roll> * 1/(1-Prepeat)

So as Prepeat approaches 1, there is an implicit mathematical singularity in the expected damage.

[Necroticplague]

Nothing in dnd is ever divided by a variable, only by constants (though variable/constant does exist). As such, you can't get any divide-by-zero. The closest you can get is ratios, which aren't quite the same (for example, effect/cl)), as having a 0 on the "denominator" does produce a result (like in that example, you would get 0 effect if your cl was zero).

[Arbane]

ISTR someone jokingly made a Plane Of Powergamers, where samples of the worst rules-combos were imprisoned. One was a d2 Crusader frozen in mid-attack against a Frenzied Berserker: one does infinite damage, one can take infinite damage. Since they can never stop rolling damage, time doesn't progress for them...

[Chronos]

The d2 crusader is not forced to continue rolling damage: There's a "you may" in there. So once he's gotten it up to a trillion or whatever, he can just choose to stop re-rolling.

I think the omniscificier's trick might be a forced infinity, though.

[Bakkan]

The d2 crusader is not forced to continue rolling damage: There's a "you may" in there.

Can you provide me with a citation? I'm looking through the text of Aura of Chaos and Imbued Healing and I'm not seeing it, unless you're referring to the line "You can continue to reroll as long as a die shows its maximum possible result". The use of "can" is ambiguous in natural English, but I believe its primary meaning is "is capable of". The previous line, "When one or more of your damage dice show a maximum possible result, reroll each such die and add its result to the original damage total", seems to indicate that the reroll is required.

[weckar]

Usually when such a thing would crop up, the game provides the answer. Such as when, say, you can use an ability CHAmod times per day, it will give you the minimum.