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In Barbarians of Lemuria, on p49

Spells of the first magnitude [...] are utility spells; they allow the sorcerer to perform activities that anyone with the right training and equipment could manage. Spells of the First Magnitude are usually either moderate [0] or tricky [-1] task resolution rolls. [...] Cost: 5 Arcane Power [AP]...

Spells of the second magnitude later mentions smashing a door as a spell of the first magnitude, and on p35's task resolution example breaking down a door is hard [-2 vs Strength].

Say the sorcerer really needs a door out of her way. She has gotten her spell Someone in there Owes Me Money spell down to 2AP via Line of Sight, Obvious Technique (a complicated series of finger snaps), and a Special Item (a brass ring engraved with "Pay Me"). The door is tricky [-1].

Lets negate the option to make the door disappear with a spell of the second magnitude by giving her 5AP currently.

Can the sorcerer better ensure success by spending additional APs (say up to 5, regardless of APs available) to improve her chances, or can she only use Hero Points in the event of a failure?

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I don't know the official answer, but that seems easy enough to house rule. Again if you spend more AP are you approaching the threshold of a third magnitude spell? If so you are talking about a lot of magical power that usually requires a lot more preparation and requirements. So there would be a balance there.

Maybe spend two more AP for a small bonus, but cap it there. You could also add an additional difficulty penalty or a requirement, like more time concentrating to gather that power...

I don't think BoL is a game that I'd kill myself over details and getting the rules just right. You are given a framework to run with. Run with it but where it falls a little short for you fill in as best you see fit.

If it really bugs ask Simone himself on Champions of Lemuria...

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