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Any core class can be a spell caster, by devoting a chunk of feats and skill points to the task. These rules cover the basics.
Each type of spell caster has its own feat, which you must take in order to have access to those spells. You may specialize in one, gaining ever more powerful spells (the usual specialist approach), or spread out among several and content yourself with more variety and lower levels (the usual adventurer approach).
Being a spell caster requires a lot of dedication: to be good at it will consume most of your feats and many of your skill points. In return for this, however, you can tinker with the basic forces of reality...
Forgotten Realms: For forgotten realms, the "types" of spell caster are: arcanist, bard, druid, paladin, priest, ranger. Each gives access to the appropriate spell lists (priest allows a choice of spheres, just like the cleric class does; arcanist gives access to the Sor/Wiz lists).
Spell Caster Feat: Each type of spell caster has a special feat which you take to become one. The first time you take this feat, you gain access to 0-level spells; each additional time you take this feat, you gain access to spells one level higher.
You may never cast spells more than half your level (rounded up).
It costs 1 skill point to know a spell, or 2 skill points to master it. If you are researching the spell on your own, this takes 7 days (8 hours per day) per skill point. If you have a spellbook with the spell in it, this only takes 1 day (8 hours per day) per skill point.
You may put points into your spell casting skill with the usual level limits on skills. The spell casting skill is different for each type of spell casting, and is named after the spell caster type (thus, a diviner has a divination skill; an illusionist has an illusion skill).
You may cast any spell you know. This takes one full action and requires the usual components for the spell. You then make a spell casting skill check, with the following DCs:
DC 10 + (spell level x 4) base casting difficulty
add damage taken if hit while casting
(halve if this is continuing damage, such as from an acid arrow
add the save DC-10 (min 0) of a distracting spell (such as flash)
add +10 if grappling or pinned
add +5 for violent motion (galloping warhorse, small boat in white water)
add +10 for incredibly violent motion (large earthquake)
add +5 if casting defensively
these rules replace the Concentration skill
Against Magic Resistance, the spell only affects the target if you exceeded the target's resistance number with your spell casting check.
Once you have cast the spell, make a Will save against DC 10 + (spell level x 2). On failure, the caster becomes Winded (STR -2, DEX -2, can not run). If already Winded, caster becomes Exhausted (STR -4, DEX -4, can not move faster than a walk). If already Exhausted, caster falls unconscious. Caster may recover by one stage per hour of rest.
If you have mastered a spell:
+2 competency bonus to the spell casting skill check and the Will save vs fatigue.
+2 competency bonus to related rolls (such as spellcraft to identify the spell).
+2 to DCs for others to save vs your spells (or disbelieve for illusions).
A 5th level spell caster should be able to cast level-0 and level-1 spells all day long with little or no difficulty. Level-2 spells will be somewhat chancy, and level-3 spells may be close to impossible for any but a specialist. Regardless, the highest level spells a spell caster can use will tend to fatigue the caster very quickly, while the lowest level spells will tend to not be fatiguing at all.
Will this result in magic missile machine guns? In a combat heavy game, likely so. However, this is hardly different from a similarly leveled warrior (who averages considerably more damage per round), and is unlikely to disrupt combat much. And on the other hand, it means that mages will be more likely to keep an unseen servant running constantly to step and fetch for them, and similar wizardly things... but they will be very, very hesitant to throw meteor storm just because things are a little hairy.
The diviner uses spells to open her mind to the surrounding world and expand her perceptions of it. By enhancing her intuitions and extending the reach of her natural and mystical senses, the diviner develops knowledge as a finely honed tool.
Divination magic can include knowledge spells, second sight, consulting spirits and even consulting the dead, if they are willing.
Glamour is the natural magic of the fey, and exists purely in the minds of those held in its sway. Glamour can alter emotions, influence decisions and manipulate perceptions. Although skill in this is rare among mortals, those who possess it are often rightly feared for their ability to play with the very essence of who a person is.
The healer uses magic to affect the life essences. Although the primary use of this is (as the name implies) healing, it can also be used to strengthen, alter and damage the life essence.
Illusion centers around the creation of phantasmal constructs, semi-real objects and things which fool the senses. As the illusionist grows in power, the constructions take on stronger reality, even fueling their own strength with the belief of those who perceive them, and can become quite powerful.
Although illusion magic seems related to glamour magic, it does not directly affect the mind; the illusionary construct is actually present, reflects light, and so on. It simply isn't entirely real. Belief can impact it, but the illusion is there even if no one can see it.
Infernalism uses magic to establish contact with the infernal realms. It centers are hellish gates, demonic summonings and dark contracts. The infernalist can use demons to animate corpses, rend his enemies, discover secrets, provide advice, build towers, fulfill wishes and more... but the creatures of the abyss have their own agendas, and those agendas are dangerous to the mortal's very soul.
The magus uses magic to command the elemental forces themselves. With the greater spells, the magus may bring down lightning to sunder foes, shake the very earth and fly as a bird. The magus possesses a great deal of raw power, although she lacks subtler forms of magic.
The priest is the mirror opposite of the infernalist, using magic to commune with the divine. The spells of the priest are simple pleas for small miracles, and the priest often has a long-term relationship with particular servants of his god.
Although it may seem odd, it is possible to be a priest and an infernalist, so long as the priest is very careful in his dealings and use of infernal forces... and always remembers that those forces are very interested in corrupting him.