Advanced Dungeons and Dragons Second Edition: Wizard: Exceeding the Spell Level Limit
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Exceeding the Spell Level Limit

It is possible, but difficult for a wizard character to learn and cast spells of a higher level than he would normally be allowed to know.
Before a character can memorize a spell that’s over the level he can normally cast, he has to learn it first. This means that the character must find, purchase, or otherwise stumble across a spell of the level in question and attempt a learn spells check to see if he can master it. However, when a character is dabbling in matters beyond his depth, his learn spells chance of success is halved for a spell one level higher than he should be able to use, and divided by 10 for a spell two levels higher than the maximum normally allowed. If a character does not succeed in learning the spell at this point, then he can try again at the level that he normally gains the spell. Under no circumstances can a character learn a spell three levels higher than his normal maximum — it’s just too difficult, and he’ll have to study his art for a while longer before he can make heads or tails of it. Also, because the spell is so difficult to learn, the wizard must memorize it as a fixed magick.
If the character succeeds in learning the high-level spell, he can then select it normally by using his spell points to memorize it. However, since the spell is extraordinarily difficult for the character, he must pay twice the listed normal fixed magick cost to memorize it. For many low-level characters, this will make the spell prohibitively expensive in any event; a 2nd-level specialist wizard only has a total of 12 spell points available, so he could just barely memorize a single 2nd-level spell of his specialty school. Note, a 2nd-level mage doesn’t have the spell points available to attempt this feat.
Wizards of medium to high level have a better chance to use a spell that would normally be out of reach for them. For example, a 6th-level wizard normally is limited to 3rd-level spells, but with effort he can learn a 4th-level spell and cast it for 30 spell points, which is twice the normal cost of 15 spell points. Since a 6th-level mage has 55 spell points available, he actually has a few points left over to select other spells — although it’s a very costly privilege!
Note, all level-based characteristics of a spell depend on the caster’s true level, so even if a 3rd-level wizard somehow acquired a fireball, it would only do 3d6 damage. (And he wouldn’t have the points available to memorize it, anyway.)

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