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One of the major advantages of GURPS is creating your character the way you want, since the rules let you create anything. And the spell-casting system is arguably too complex or boring.

Putting together those two ways of thinking, there is a sub-system that I inherited as GM where the players can cast spells without the casting time. Plus they don't have to learn spell by spell to do something like tossing a fireball; there is a "Fire Manipulation" generic spell where the PC that acquires it can freely manipulate fire (or any other element - according to the skill) having the cost in mana scale up to how much he wants to manipulate.

That's obviously too OP, but I managed to balance it with the encounters in the adventures so far. The problem is that I'm reviewing the rules of this sub-system we are using, and I'm having trouble calculating how much it would cost in character points for such a spell.

Such a spell would combine multiple spells of the basic system into one, plus remove the combined casting times. To exemplify: One could cast a fireball at cost of 1 mana, or cast a wall of fire having the cost in mana depending on how many hexagons it would occupy.

How many character points would such a skill cost?

This ruleset could apply to 3rd or 4th editions.

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You seem to be looking for very freeform control of an element. That is not normally achieved through the basic magic system (single-skill-per-spell magic, also sometimes known by the tautological title Magic magic). Nor does your description seem to match the magic of ritual paths in Basic Set (not to be confused with the other, standalone ritual path magic). You should look for the Create and Control Advantages found in GURPS Powers. The rules for them, due to their wide scope, are too big to quote, though.

Alternatively, you might be interested in the more freeform types of magic found in Thaumatology, such as Realm Magic and many others.

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