Exponential scaling problems in RPM

[GurpsObserver]

Different elements of the RPM system have very different scaling patterns with increasing amounts of energy. As in computing, for large values of energy the asymptotic costs dominate: those properties with exponentially improving performance have game-breaking effects, while those with linear or log improvements are left utterly behind.

Sample super-spells

Petropower Lesser Create Matter (6) Weight 4.4 billion tons (25) Duration 5 years (26) 57 energy (57*1). This spell conjures a lake of high-quality petroleum equal to the Earth's annual production. The oil will continue to exist for 5 years (by which time it will have been safely consumed) before any unused oil disappears. Its market value at today's prices is over $3,000,000,000,000. Adding an additional energy point will triple the amount produced. Other versions of this spell can replace the world's agriculture, forestry, metal production, and fresh water supplies.

The End of Everything Greater Create Energy(6)+Area of Effect Planetwide (80) Damage External Burning (Indirect) 12d (12). 294 energy (98*3). This spell applies 12d burning damage to everything on Earth. An extra 60 energy will increase the damage to 27d.

28 days later Greater Control Mind(5)+Area of Effect Planetwide (80), Duration 1 month (11). 288 energy (96*3). The vast majority of living creatures (who fail a resistance roll) are compelled to kill any human they can find for 1 month.

Exponential scaling
Area of effect costs twice the size modifier, so 100 energy points is enough to cover the entire planet.

Speed and range also use the same exponential table.

Weight costs 11 energy for 1,350 tons and triples for each additional energy point. 130 points are enough to move the entire planet.


Linear scaling
Duration over 1 year is linear at 1 point per year plus a small constant.

Damage per target is linear (total damage is exponential, because one can affect many targets with minor damage).

Grants of advantages are linear in character points.

Logarithmic scaling
Bonuses or penalties require exponentially increasing energy to deliver linear performance boosts. One example spell produces a ST score: a broad +10 bonus to strength rolls would cost 2,560 energy points, far more than enough to throw around galaxies at near lightspeed.

Additive constants
The spell effects, like sense or transform, all cost 8 or fewer base energy. For large spells this is trivial relative to the total cost.

Multiplicative cost factors
The modifiers for lesser vs greater effects (and some other minor modifiers like trappings) multiply the total cost of a spell.

For the linear scaling effects, a 3x cost multiplier cuts the effect size to about 1/3rd, e.g. going from 31d to 11d damage. For the exponential effects, the same multiplier cuts the effect size to its cube root. For area or volume the change is x^-6 or x^-9.

Exponential apples and linear oranges
Many example spells of modest utility in the RPM supplement have costs in the hundreds of energy points, usually because they are using linear or log effects (granting bonuses or advantages, or doing damage or afflictions). They might give a useful advantage, do heavy direct damage, or incorporate multiple greater effects.

A caster able to cast these spells in the basic system could also cast world-shaking exponential effects that use a single, like dropping mountains on cities or pushing the Earth into the Sun, mind control on the global population, inflicting modest (just enough to kill) damage on every human on Earth, changing the global temperature or weather to stop all agriculture, and so on.

On the positive side, Create Matter could be used to supply all the world's needs for food, fuel, and similar consumables. With 100 year durations most non-consumables could also be provided in this way, and Transform Matter could provide permanent gods with massive mining and construction effects. Eliminating all pollution would be easy. Spells to eliminate all disease everywhere are easy, as are teleportation gate networks. Mind and chance can be used to give modest bonuses to the global population, detect and stop crime and violence everywhere, and so on.

Limiting factors
One way to avoid a setting being destroyed by such spells lies with the path of magic spells (which happen to have good exponential scaling). One could use Greater Path of Magic to block a particular kind of ritual worldwide. To work the banned ritual anyway would require applying as much energy as was used in the ban spell, and so long as defenders outnumber attackers by a large enough margin any particularly annoying spells could be banned by global magic.

Or one could have gods or Elder Things casting such spells to regulate the overall magical situation (all sorts of "laws of magic" could actually stem from such spells, backed with more energy than mortals could hope to overcome). Of course then one may ask why such global spells haven't solved most other problems too.

Botches
One problem with numerous defensive global enchantments is that casting and maintaining them would lead to botches, which could have world-shaking exponential effects.

And of course regular workings also pose such risks.

How attainable are mega-spells?

This app allows calculation of energy costs for planet-cracking spells. And this one computes the results of an energy gathering process for a given skill level and target.

A caster with high effective path skill and bonuses and appropriate trappings can easily reach catastrophic power levels.


Risk-taking in RPM makes exponential scaling MUCH worse
RPM allows casters to take risks of a critical failure to go for bigger spells. For linear spells that's fine, but for exponential spells the impact can be overwhelming. Say that normally casters limit themselves to a 5% chance of a critical failure. Someone willing to risk a 40% chance of failure can cast spells with 10 times the energy cost. Since 200-300 energy points are enough for planet-cracking, that means any world in which witches can get off 30 point spells reliably is one in which someone willing to take a 40% risk of doom can become a multi-trillionaire or destroy the world.

[DangerousThing]

How would you suggest the problem be solved?

[Dwarf99]

Personally I like these numbers. They set up a scenario where the BBEG is a very real threat.

[sir_pudding]

I think the problem is more with the rule that non-living subjects can't resist. If the Earth could resist it would get HT (probably at least 12) + 43 to resist anything cast on it. Of course in an animistic setting Gaia (or equivalent) would get a resistance roll even by RAW.

[GurpsObserver]

Originally Posted by sir_pudding

I think the problem is more with the rule that non-living subjects can't resist. If the Earth could resist it would get HT (probably at least 12) + 43 to resist anything cast on it. Of course in an animistic setting Gaia (or equivalent) would get a resistance roll even by RAW.

I don't think resistance helps much. One target resisting doesn't save others, and a high skill spell will still get most targets on Earth. And creation spells aren't resisted (post-scarcity economy and so on).

[DangerousThing]

Originally Posted by GurpsObserver

I don't think resistance helps much. One target resisting doesn't save others, and a high skill spell will still get most targets on Earth. And creation spells aren't resisted (post-scarcity economy and so on).

There are a few poisons that don't take much to kill people, and I assume animals. Botulism poison is one of them. Any mage that could target the area of the Earth with a create matter spell could probably kill near 99% of all mammals at least.

This sort of thing should have been spelled out in the RPM book along with possible solutions. I have to figure out the extent of the problem and if I need to fix it for my system, which borrows a lot from RPM.

[sir_pudding]

Originally Posted by GurpsObserver

I don't think resistance helps much.

It helps with doing anything untoward to planets.

One target resisting doesn't save others, and a high skill spell will still get most targets on Earth. And creation spells aren't resisted (post-scarcity economy and so on).

What about having Magery cap the more troublesome sources of extra energy? Like maybe you can't get more than Mageryx3 (or x5 or whatever) from any Energy Source and only as many caster can Work Together as the highest Magery among them?

[Refplace]

Its the same with many sections of GURPS, at large ends you can have broken powers for less then it seems approrirate.
GM needs to just adjuticate it.
For example casting a spell like that and people or Gods will notice and take countermeaures.

[DangerousThing]

Originally Posted by Refplace

Its the same with many sections of GURPS, at large ends you can have broken powers for less then it seems approrirate.
GM needs to just adjuticate it.
For example casting a spell like that and people or Gods will notice and take countermeaures.

I think the problem is that many spells which can target huge areas with nastiness cost less energy than a spell to increase somebody's ST by 10.

And the way I figure it is that a spell disturbs the manasphere in proportion to its energy. And the gods might not notice a creation spell the same way they'd notice a direct damage spell. Afterwards, of course, the mage would be toast, because they'd probably notice their worshippers being dead.

And in a modern game, what are the gods like?

[GurpsObserver]

Restrictions on maximum spell power can cut out the world-cracking and economy-breaking post-scarcity spells, but they will throw out a lot of cute linear spells. E.g. if I can turn someone into a frog for 1 day, then I can replace the world's supply of food, fuel, and raw materials.

"Sylph Form," an RPM Grimoire spell to take on a Body of Air, costs more than killing or mind controlling almost everyone on Earth.