It is said that no amount of mages can pinpoint what pushes magic to flow. Arithmeticians believe that it can be broken down to simple mathematical equations. With them, they are able to manipulate magic to the situation that it is needed. Only after years of study is it easy enough to break down and figure it out on the fly. Being this way makes a person very precise and articulate in everything they do. These calculating strategists employ the principles of arithmetic law to pinpoint targets for their attacks. The arithmetician is more than just a spellcaster; they are a walking supercomputer, a master of universal constants and applied mathematics, translating complex equations into devastating battlefield effects. Unlike traditional mages who draw power from arcane words or divine favor, the arithmetician manipulates the very fabric of reality by identifying and exploiting the numerical patterns that govern existence – be it a creature’s current HP, remaining turns in combat, the turn order, or even environmental factors like elevation or distance. Their unique brand of “Arithmetic” allows them to target allies or enemies with unsettling precision based on these numerical conditions, delivering calculated buffs, debilitating debuffs, or perfectly placed damage that bypasses conventional resistances. Often seen as eccentric and detached, viewing the world as a grand, solvable equation, the arithmetician is the ultimate strategist, turning the seemingly arbitrary numbers of the game engine into their most potent weapon, making them an indispensable, albeit highly specialized, asset to any party.

Role: The arithmetician is often in a position to determine whatever role they choose. As a master of spellcasting, an arithmetician may fulfill many roles for the party in attack, defense, healing or utility. The srithmetician is a unique and often indispensable strategic lynchpin, wielding the power of pure mathematics rather than magic or brute force. Their role revolves around unraveling the complex equations that govern combat, resource management, and even the natural world. They are the party’s analytical mastermind, capable of predicting damage output, optimizing resource allocation, calculating the precise trajectory for a critical hit, or exploiting statistical probabilities to buff allies and debuff foes based on their numerical weaknesses. More than just a bookkeeper, the arithmetician manipulates the very fabric of the game’s mechanics, turning raw data into decisive tactical advantages and ensuring the party operates at peak efficiency, making them an essential asset for any group that values precision and strategic depth.

Alignment: Any

Hit Die: d6

Starting Wealth: 2d6 × 10 gil (average 70 gil.) In addition, each character begins play with an outfit worth 10 gil or less.

Class Skills
The arithmetician’s class skills (and the key ability for each skill) are Appraise (Int), Craft (Int), Fly (Dex), Knowledge (all) (Int), Linguistics (Int), Profession (Wis), and Spellcraft (Int).

Skill Ranks per Level: 4 + Int modifier.

Table: Arithmetician

Level	Base Attack Bonus	Fort Save	Ref Save	Will Save	Special	MP	Spell Level
Type	1/2	Bad	Bad	Good	—	—	—
1st	+0	+0	+0	+2	Flexible Spellcasting (1 spell), Spell Proficiency, Mathematical Casting, Limit Breaks	3	1st
2nd	+1	+0	+0	+3	Arithmetic, Talent	4	1st
3rd	+1	+1	+1	+3	Magical Theorem	5	2nd
4th	+2	+1	+1	+4	Talent	6	2nd
5th	+2	+1	+1	+4	Clear Mind I, Magical Theorem, Flexible Spellcasting (2 spells)	8	3rd
6th	+3	+2	+2	+5	Talent	11	3rd
7th	+3	+2	+2	+5	Arithmancy, Magical Theorem	15	4th
8th	+4	+2	+2	+6	Talent	20	4th
9th	+4	+3	+3	+6	Cup of Life, Magical Theorem, Flexible Spellcasting (3 spells)	26	5th
10th	+5	+3	+3	+7	Clear Mind II, Talent	32	5th
11th	+5	+3	+3	+7	Split, Magical Theorem	39	6th
12th	+6/+1	+4	+4	+8	Advanced Talent	47	6th
13th	+6/+1	+4	+4	+8	Calculating Mind, Magical Theorem, Flexible Spellcasting (4 spells)	56	7th
14th	+7/+2	+4	+4	+9	Advanced Talent	65	7th
15th	+7/+2	+5	+5	+9	Magical Theorem	75	8th
16th	+8/+3	+5	+5	+10	Advanced Talent	86	8th
17th	+8/+3	+5	+5	+10	Mathematical Manipulations, Magical Theorem, Flexible Spellcasting (5 spells)	98	9th
18th	+9/+4	+6	+6	+11	Advanced Talent	110	9th
19th	+9/+4	+6	+6	+11	Soul Bind, Magical Theorem	122	9th
20th	+10/+5	+6	+6	+12	Clear Mind IV, Advanced Talent	135	9th

Class Features

All of the following are class features of the arithmetician.

Weapon and Armor Proficiency

Arithmeticians are proficient with the dagger, sling, power rod, power staff, and quarterstaff, but not with any type of armor or shield. Heavier armor interferes with an arithmetician’s movements, which can cause his spells with somatic components to fail.

Limit Breaks (Su) 

At 1st level, the arithmetician receives the Limit Breaks (Defensive Numbers and Null Zero Effect).

Defensive Numbers (Su): This Limit Break allows the arithmetician to divide damage coming at him and his party. The arithmetician and all allies within a 30-ft.-radius of the arithmetician takes half damage from any source for a duration of 1 round + 1 round per four arithmetician levels after 1st. This limit break requires only a swift action.

Null Zero Effect (Su): This Limit Break allows the arithmetician to cast spells without any spell exhaustion. For a duration of 1 round + 1 round per four arithmetician levels after 1st, any spell you cast doesn’t incur any spell exhaustion. This limit break requires only a swift action.

Spell Proficiency (Ex)

Arithmeticians are considered to have the Precise Shot feat while casting spells, using class features that require ranged touch or using any magical items that require ranged touch.

Universal Weaver (Ex)

At 1st level, an arithmetician may learn any spell from spell scrolls or other sources as if they were on his spell list, and count as having all spells in the game for using magical items and crafting purposes. 

Flexible Spellcasting

At 1st level, an arithmetician is able to craft and build his spells on the fly (see below). Starting at 1st level and every four arithmetician levels thereafter, an arithmetician is able to memorize a spell with all its components calculated (by 17th level, he can have 5 of these spells memorized). He gains a -1 discount to the final component cost of the entire spell when casting this specific set of spells, plus an additional -1 discount per four arithmetician levels after 1st (this discount applies to both the required and effect components when calculating the cost). After 8 hours resting, the arithmetician may change out the set of memorized spells.

To cast a spell, the arithmetician must have an Intelligence score equal to at least 10 + the spell level. The Difficulty Class for a saving throw against an arithmetician’s spell is 10 + the spell level + the arithmetician’s Intelligence modifier. In addition, an arithmetician gains additional MP for having a high attribute (Intelligence). An arithmetician cannot craft spells with a component cost higher than 10, this limit increases by 5 every odd level after 1st. For example, a 3rd-level arithmetician can only craft spells up to 15 component cost.
Note. Arithmeticians can cast spells of higher levels than what is listed on the Class Table when using Flexible Spellcasting, for all other purposes they are limited by what is listed on the Class Table.

Table: Flexible Spellcasting Level

Level	Component Cost
0	0-4
1	5-8
2	9-12
3	13-16
4	17-20
5	21-24
6	25-28
7	29-32
8	33-36
9	37+

Mathematical Casting (Su)

Mathematics is the fundament by which the arithmetician quantifies everything including magic. Each day he can use this ability a number of times equal to half his arithmetician level (minimum 1) plus his Intelligence modifier, the arithmetician can cause his spell to tap into the fundamental mathematics of reality. This is a free action that does not provoke an attack of opportunity. 

The arithmetician gains one “Parameter” at 1st level and every four levels thereafter to a maximum of 5. Parameters are countable aspects of reality that can be found in combat-based scenarios. Some examples are [Initiative, Strength Score, Base Attack Bonus, missing Hit Point or even Number of Limbs]. No matter what the choice, it must be something that every person in combat would potentially have a number for.

Also, at 1st level and every six levels thereafter, the arithmetician gains a new “Number”. He must choose one of the following:

• Three
• Four
• Five
• Any Prime Number 7 or higher 

These numbers will select the targets of the arithmetician’s mathematically altered spell. By selecting one Parameter he knows and one Number he knows, the spell the arithmetician now casts affects everyone (ally, enemy and himself) within the spell’s range that has that Parameter at a number evenly divisible by the Number he chose. 

Ex. If one chose limbs and 4 for his spell, it would affect all party members that have 2 arms and 2 legs, as well as the spider they are facing that has 8 legs (creatures that have 0 of the given parameter, such as an ooze with 0 limbs, are unaffected).

Arithmetic (Ex)

At 2nd level, an arithmetician can solve any mathematical equation almost instantly. He gains the ability to solve any mathematical problem as a free action. In addition, his analytical mind quickly accesses situations, allowing him to act while others are still debating the appropriate courses of action. The arithmetician may add his Intelligence modifier in addition to his Dexterity modifier to his initiative rolls.

Magical Foundations (Ex)

At 2nd level, an arithmetician receives a +1 bonus on all Spellcraft and Use Magic Device checks. This bonus increases by +1 every other level thereafter, to a maximum of a +10 bonus at 20th level.

Numerical Talents (Ex or Su)

As an arithmetician gains experience, he learns a number of talents that assist him in manipulating spells and other forms of magic. At 2nd level and every two levels thereafter, the arithmetician gains one Numerical talent. An arithmetician cannot select an individual talent more than once. Talents marked with an asterisk add effects to an arithmetician’s spellcasting ability. Only one of these talents can be applied to an individual spell and the decision must be made before the spell is cast.

• A complete list of numerical talents can be found here: Numerical Talents

Magical Theorem (Su)

At 3rd level and every other level thereafter, the arithmetician learns how to apply one type of mathematics to his spells. Magical theorems are divided into five disciplines (Algebra, Geometry, Calculus, Topology, and Statistics). The first magical theorem in each discipline may be learned by any arithmetician, but subsequent theorems may only be learned once the preceding theorems in the discipline have been mastered.

Algebra

• Subtraction: The arithmetician simply subtracts energy from the sum total of what is required to alter his spells. When applying a metamagic feat to a spell he casts, he subtracts 1 MP the metamagic feat imposes upon the spell (which also reduces the spell level of the spell) to a minimum of 1.
• Addition: The arithmetician adds additional energy to his spells, rendering them more effective. He adds one to each dice of variable numbers in the spell’s description.
• Equation: By mastering algebra, the arithmetician gains the ability to link two creatures together in an equation. As a standard action, he may designate two creatures, who each receive a Will save (DC 10 + half of the arithmetician’s level + his Intelligence modifier). If both creatures fail their saving throw, they are linked together for one round per class level the arithmetician possesses. If one of the linked creatures takes damage, loses hit points, heals damage, or suffers a status effect, the other creature is affected as well, suffering the same effects, taking the same amount of damage, or healing the same amount of hit points. If one of the linked creatures dies, the remaining creature must immediately succeed at a Fortitude save against this ability’s DC or die. If one of the creatures is immune to a form of damage or a status effect, both creatures are immune.

Geometry

• Euclidean Space: The arithmetician gains a better understanding of distances and spatial relations. He adds 5 feet for every two levels of the arithmetician class he possesses to the range of each of his non-Touch spells.
• Riemann Manifolds: The arithmetician’s understanding of geometry is such that he is able to curve his spells around obstacles. When casting any spell requiring a ranged touch attack, the arithmetician can ignore any benefit the target gains from cover, and never risks harming an ally in melee or grappling with a target.
• Lobachevskian Dimensions: The arithmetician understands the curvature of the multiverse and can warp it, allowing him to reach his target from safety. He may cast any of his “Touch” range spells as if they had a range of “Close,” though doing so requires a ranged touch attack rather than a melee touch attack.

Calculus

• Integrals: The arithmetician can integrate his spells, making them more cohesive and difficult to break down. The DC to dispel an arithmetician’s spells increases by +4.
• Derivatives: The arithmetician can differentiate his spells, allowing them to function in non-continuous units of time. After a spell is cast, the arithmetician can choose to differentiate his spell as a move action, causing the spell to become suspended. While suspended, duration does not elapse for the spell. He may recall his spell as a move action, at which point it continues from the point at which it had been differentiated. The arithmetician may differentiate each spell only once. 
• Time Variance: The arithmetician understands how time functions and can break down spells cast upon him. When a spell is cast on the arithmetician, as an immediate action he can halve or increase by half the duration of the spell.

Topology

• Manifolds: The arithmetician can create complex figures by combining copies of similar figures. When determining the area of any shapeable spell, the arithmetician increases the area by one half (+50%).
• Homeomorphism: The arithmetician learns how to transform variables from one set to another set while still preserving the values of the original. He may alter any area-affecting spell he casts so that it affects an area different from its normal area, as selected from the following list: Cylinder (10-foot radius, 30 feet high), Cone (40 feet long), Cubes (four 10-foot cubes), or a sphere (20-foot radius spread). The spell works otherwise normally in all respects.
• Knot Theory: The arithmetician understands mathematical knots, allowing him to twist, tangle, and shape his area effect spells. The arithmetician can alter any of his area effect spells so that they exclude any square or squares within their area of effect, as determined by him.

Statistics

• Above Average: The arithmetician learns to skew the law of averages, and may take 11 on any action on which he would normally be able to take 10. In addition, he may choose to take 11 on caster level checks, including Concentration checks, dispel checks and checks made to overcome spell resistance.
• Eschew Dice: Whenever the arithmetician casts a spell with variable effects, he may choose to take the average on each dice instead of rolling (d3 = 2, d4 = 3, d6 = 4, d8 = 5, d10 = 6, d12 = 7).
• Outliers: The arithmetician learns that occasional values are created which exist beyond the accepted range of results, and manipulates such values to his benefit. For a number of times per day equal to the arithmetician’s Intelligence modifier, he gains a +20 on a single skill check or caster level check he makes.

Clear Mind (Ex)

At 5th level, an arithmetician can regain his MP quicker. The arithmetician must be relaxed and must be free from overt distractions, such as combat raging nearby or other loud noises. For example, he could be riding in the back of a carriage and benefit from this ability. The arithmetician does not gain this recovery if he is asleep or unconscious. The arithmetician regains 1 MP per hour. This increases by 1 for every five arithmetician levels after 5th.

Targeted Mathematics (Su)

At 7th level, as a swift action that does not provoke an attack of opportunity, the arithmetician chooses one creature he can see. He selects one Parameter and Number he knows, if the Parameter is a number evenly divisible by the Number he chose for the creature, all spells he casts that only target that creature gain the same discount that Flexible Spellcasting provides his memorized spells. This effect lasts for one minute, or until you use this feature again. The arithmetician can use this ability a number of times per day equal to his Intelligence modifier.

Cup of Life (Su)

At 9th level, the arithmetician can make sure that nothing in the equation goes to waste. Whenever an arithmetician casts a spell that heals damage, if it puts himself or an ally over their max, the remaining HP is given to the next closest ally, within 30 feet, that isn’t at full HP. So long as there is extra HP remaining you can continue to do this until there are no extra targets. 

Split (Su)

At 11th level, an arithmetician sees incoming spells as numbers and with just a thought, can split the numbers in half and transfer them to other people, including the original caster. As an immediate action when targeted by a spell, the arithmetician can make a Spellcraft check (DC 15 + double the spell’s level), if successful, the spell’s healing or damage is halved, now targeting an additional creature within range of the original spell for the same amount. Any spell that requires an attack roll that hits the arithmetician will automatically hit his intended target. Any saving throws required will be based on the caster who cast the spell. The arithmetician can use this ability a number of times per day equal to 3 + his Intelligence modifier.

Drop Remainder (Su)

At 13th level, when an arithmetician witnesses an effect that damages or causes death to any number of creatures, as an immediate action, he may spare those so weak to be negligible in a fight. Any creature that their hit die is both less than his own and 10 or more less than the creature causing the effect (assume traps and environmental effects have hit die equal to their CR) takes no damage and does not die from the effect.

Any given creature may only benefit from this ability once per day. 

Mathematical Manipulations (Su)

At 17th level, as part of casting a spell an arithmetician can reduce the radius of a spread or burst effect or shorten the length of a cone. All changes must occur in 5-foot increments, to a minimum of 5 feet. Alternatively, the arithmetician can change the area of effect of a cone spell to a line with a length equal to the spell’s range. In addition, the arithmetician can bend the line of a spell that has a line area of effect up to 90 degrees at any single point along the line’s length.

Soul Bind (Su)

At 19th level, the arithmetician begins to understand that even the body can be broken down in equations and slightly altered. Whenever he takes physical damage, if it is a multiple of the ‘Number’ he knows, as an immediate action, he is healed for half (rounded down) of the damage while the attacker takes that much damage.

Axiom (Ex)

At 20th level, as a free action, an arithmetician may push the next spell he casts to the limits of reality, doubling the maximum number of components he may use for the spell, and automatically passes the Spellcraft check for casting it. He may only do this once per day.

Favored Class Bonuses

Instead of receiving an additional skill rank or hit point whenever they gain a level in a favored class, some races have the option of choosing from a number of other bonuses, depending upon their favored classes. The following options are available to the listed race who have arithmetician as their favored class, and unless otherwise stated, the bonus applies each time you select the listed favored class reward.

• Aegyl: The arithmetician gains +1/6th of a talent.
• Al Bhed: The arithmetician adds +1/3rd of an additional use of Mathematical Casting per day.
• Antica: Get a -1/5 bonus to the component cost of the Silent spell component in the Metaspell category. To a possible component cost reduction of -4 (final cost of -2) at level 20. 
• Bangaa: Add +1/4 to caster level checks made to overcome a creature’s spell resistance.  
• Dwarf: Select one item creation feat known by the arithmetician. Whenever he crafts an item using that feat, the amount of progress he makes in an 8-hour period increases by 200 gil (50 gil if crafting while adventuring). This does not reduce the cost of the item; it just increases the rate at which the item is crafted.
• Elvaan: Add +1/4 to caster level checks made to overcome a creature’s spell resistance.
• Galka: Select one item creation feat known by the arithmetician. Whenever he crafts an item using that feat, the amount of progress he makes in an 8-hour period increases by 200 gil (50 gil if crafting while adventuring). This does not reduce the cost of the item; it just increases the rate at which the item is crafted.
• Genome: Add +1/6 bonus to Knowledge (all) skill checks.
• Half-Breed: The arithmetician gains +1/6th of a talent.
• Hume: The arithmetician gains +1/6th of a talent.
• Kindred: Any elemental resistance that a creature affected by the arithmeticians spells has is considered +1/4 less when determining damage from elemental spells he casts. 
• Lambkin: Add +1/6 bonus to Knowledge (all) skill checks.
• Mandragora: Reduce Spell Exhaustion suffered by +1/6. 
• Mithra: Add +1/4 to the arithmetician’s initiative rolls.
• Moogle: Select one item creation feat known by the black mage. Whenever he crafts an item using that feat, the amount of progress he makes in an 8-hour period increases by 200 gil (50 gil if crafting while adventuring). This does not reduce the cost of the item; it just increases the rate at which the item is crafted.
• Mutant: The arithmetician gains +1/6th of a talent. 
• Nu Mou: Add +1/6 bonus to Knowledge (all) skill checks.
• Orc: The arithmetician gains +1/2 Strength. (+1 Strength every two times you select this option.) 
• PuPu: Add +1/2 bonus to Craft skill checks.
• Seeq: Add +1/5 to the arithmetician’s Fortitude saving throws.
• Shindroid: Reduce Spell Exhaustion suffered by +1/6. 
• Sylph: Reduce Spell Exhaustion suffered by +1/6. 
• Tarutaru: Add +1/2 bonus to Craft skill checks. 
• Tonkin: Add +5 feet range to the arithmetician’s Limited Telepathy racial trait.
• Vanu Vanu: The arithmetician adds +1/3rd of an additional use of Mathematical Casting per day.
• Velkk: Add +1/4 to caster level checks made to overcome a creature’s spell resistance.
• Viera: Reduce Spell Exhaustion suffered by +1/6. 

Flexible Spellcasting

Components: Components are the building blocks of spells. The number of which determines the strength of the spell. They are a measure of the spells and the Arithmeticians limits, not a resource pool. Much as an artist uses paint to create a mural or a weaver uses colored thread to create a tapestry, an arithmetician uses components to create a spell. The arithmetician creates spells by choosing the proper components to generate the outcome the arithmetician wants. Two major categories of components exist, Required Components: Area, duration and range, and Effect Components: Control, Force, Summon and more. 

Note: Just as the arithmetician spends points on different components for his spell effects, he can create a spell with multiple effects from the same component. For example, the arithmetician can create a spell that cures blindness and hit point damage at the same time (two Heal component effects), or a spell that throws an enemy around and damages them protects against fire and ice (two Force component effects). Pay for each effect separately.

Components costs, required vs effect.

Area, Duration and range are Required Components — the arithmetician always has to know what the magic is going to affect, how long it’s going to last and how far it reaches. Add their costs together, this is the minimum the spell can cost to cast, but their components are not added to the effect components cost.

Effect components are all other component types listed below (Core, Heal, Illusion, etc.), they are what effect the spell has on what it is targeting.  If the arithmetician wants to make a bandit run in fear, add a Control component. If he  wants to pick the bandit up and throw him against a tree, add Force components. If the arithmetician wants to learn his darkest secrets, add a Divination component. With enough practice, the arithmetician can build a spell that does all three of these things at once, or even more. The only limits are his imagination and skill at manipulating the components of magic. When determining the cost of the spell add up the cost of all of the effect components separately from the Required Components, if they are lower than the required components then use those to determine the spells level. Otherwise, if the effect components add up to be higher than the required components total, use that value to determine the spell’s level.

Example: So, if one was to make a spell that is a 100-foot cone, originates from caster and is instantaneous, its minimum level would be 4, with a required cost of 18 components. If its only effect component was to heal all creatures in range for 1d6, its effect component cost would be 1, far lower than the minimum still making it still a 4th level spell. You would still use its minimum level of 4. but if you had it heal for 40d6 instead, then you would use its effect component cost of 40, making it a 9th level spell.

Building Spells: To build a spell, follow these steps.

1. Decide what the arithmetician wants the spell to do.
2. Look at the component descriptions (below) to find which components are appropriate for his spell. 
3. Add together the Area, Duration and Range components for the minimum component cost and spell level.
4. Separately from required components add together the number of points the arithmetician will spend on all the effect components. If it is higher than the required component cost, use it for the spell’s component cost and spell level.

That’s it! If the arithmetician likes the spell he designed, write down its effects and component costs so he doesn’t have to build it again from scratch; doing so is especially handy for spells that he uses often, and required for memorized spells.

Steps for Spellcasting: To cast a spell, follow these steps.

On his turn, use an action appropriate to the spell’s casting time.

1. Provoke an attack of opportunity from all adjacent opponents.
2. Increase his current spell exhaustion by the spell’s exhaustion rating, if any.
3. Spend MP according to its spell level.
4. When the arithmetician finishes casting the spell, he makes a Spellcraft check (DC 10 + the component cost of the spell he is casting) to see if he successfully casts the spell. The arithmetician can take 10 on this. If the arithmetician fails this check, he fails to cast the spell. If the arithmetician succeeds, he moves to the next step.
5. Apply the effects of his spell.

Note: if you are interrupted while casting a spell, whether by outside means or via your own choosing, you do not cast the spell, expend MP, or gain spell exhaustion. 

Aspects of Flexible Spells

Casting Time: By default, casting a spell is a full-round action. Certain components can speed up or slow down one’s casting time. 

Words and Gestures: All spells require verbal and somatic components. 

Attacks and Saves: A spell allows an unwilling target to resist its effects with a saving throw, and any spell that targets individual creatures makes either a melee or ranged touch attack as well. A spell’s save DC is equal to 10 + the spell level + his Intelligence modifier. Choose the save type when you build the spell. All creatures can choose to fail their save against an arithmetician’s spells. 

Schools: All spells an arithmetician casts fall into at least one, if not multiple spell schools. Some components will list in parentheses what schools and subschools are usually appropriate (such as mind-affecting for all components listed under Control), but there will be plenty of times where they won’t, so it is up to the arithmeticians with DM’s approval to choose what schools and subschools a spell is. 

Spell Exhaustion

While others stick to tried and tested spells, Arithmeticians manipulate reality on a fundamental level without normal limitations, this unique way of casting is both physically and mentally taxing. When the arithmetician successfully casts a spell, take its component cost and subtract twice his arithmetician level + the arithmeticians Constitution modifier [lvl * 2 + Con] (treating results less than 0 as 0). This number is the spell’s exhaustion rating (SE). Every time the arithmetician casts a spell, add its spell exhaustion rating (if any) to his current spell exhaustion and take non-lethal damage equal to the amount gained. For example, after casting three spells with SE 5, his spell exhaustion is 15. A fifth-level arithmetician with a +4 constitution modifier can cast three 14-point spells in a row without penalty as each one has an spell exhaustion rating of 0 (14 – 14 = 0), whereas two 18-point spells (SE 4 each) put him at a spell exhaustion of 8.

Whenever you would recover MP, if you have any points of spell exhaustion you reduce your spell exhaustion by that amount instead, only regaining MP after your spell exhaustion has been reduced to 0.

Note: Overflow is regained, if you would gain 5 MP and have 1 SE, you reduce your SE to 0 and regain 4 MP.

Averting Spell Disruption: When the arithmetician is casting a spell, taking damage forces him to make a Concentration check to cast the spell. If the arithmetician fails the check, his spell is disrupted, and he stops casting. The arithmetician does not lose any MP or increase his spell exhaustion rating for a disrupted spell.

Ending Spellcasting: The arithmetician may interrupt his own spellcasting at any time. Doing so does not take an action (he can even do it when it is not his turn), cost MP or add to his spell exhaustion rating. In effect, ending a spell is totally “free.”

Dismissing Spells: The arithmetician may end one of his ongoing spells at any time as a standard action. Doing so does not cost MP, increase his spell exhaustion rating or provoke attacks of opportunity. The arithmetician may dismiss a spell at any range.

Component Summary: 

This section gives detailed explanations of the sorts of things each component can do when added to a spell. These are examples and are by no means comprehensive lists of what each component can do — that would be impossible and work against the goal of the flexible spellcasting system. If the arithmetician wants to create a spell and the exact effect he is looking for isn’t described here, use these effects as guidelines for how many component points his spell should cost and work with your DM. The following summaries include rules clarifications for certain components.

Required Components:

Area: Determines how many creatures or how much space the spell affects.

Range: Determines the distance that the spell affects, and where its origin point is. 

Duration: Determines how long the spell lasts. The Duration refers only to ongoing magical effects, as the consequences of these effects may last much longer than the spell. For spells with a duration longer than 1 round per level, it is recommended to use the next shorter time increment when determining recurring effects. (For a damage over time spell that’s duration is measured in days, the damage recurs every hour, not every round.) 

Effect Components:

Core: These components are core aspects of a spell, how potent it is, how taxing it is to cast, how long it will take to cast.

Control: This component covers mind control and emotions. 

Divination: This component reveals or conceals information. Information revealed by a spell is accurate, but may become inaccurate. Future circumstances may change, and knowledge of the future makes such a change even more likely (for example, intervening if one knows a friend is going to die within the hour); divination spells determine the most likely outcome based on current circumstances.

Enhance: This component improves qualities of its target, even to the point of being permanent inherent bonuses. Some components can grant a creature new powers beyond their normal capabilities. 

Force: These components inflict the arithmeticians’ will upon reality with force. They can move, damage, or negate certain aspects of the world around the arithmetician. By default, a spell deals bludgeoning, piercing or slashing damage. Damage reduction affects this sort of damage. The damage a spell does can be changed to be non-lethal, non-elemental, or to an energy type. Common energy types are earth, fire, holy, ice, lightning, shadow, water, and wind damage. Spells made with energy types count as being of the appropriate school type (for example, a spell that deals fire damage would be of the elemental (fire) school.)

Heal: This component heals injuries and other afflictions.

Illusion: This component creates false images and sensations. Illusions appear real but do not exert force, though the arithmetician can compensate for this drawback with other components. (For example, the arithmetician can create an illusionary beast coupled with Force components so that it can affect the world around it.) A witness to an illusion gets a save only if he interacts with it in such a way to suggest it is unreal, such as by touching or passing through the illusion. A witness who makes this save realizes the illusion is unreal, though he may still have instinctive reactions to it or choose to act as though it is still real to fool others.

Summon: This component creates or summons objects or creatures. Conjured objects cannot have any moving parts unless they are masterwork, and more complex items (like a lock) requires the arithmetician to have the skill to craft such an item and make an appropriate Craft check. The arithmetician can be either conjuring creatures from other planes, using raw magic or a suitable substrate to form them. Conjured creatures, usually called “minions” are under his control and will do as he commands without question; the arithmetician can modify the minions’ nature and abilities by using minion templates. It is easier to conjure a minion if the arithmetician has a “substrate” for that minion — appropriate material to create a minion of that type. For example, if the arithmetician wants to create an earth elemental, he could use the sands of the beach he stands on, or instead pull from the ocean to form a water elemental. Minions summoned using substrates are made out of said substrate, and any damage they sustain is also dealt to the substrate.  

Apocryphal: Effects that may or may not be allowed by a DM, do not expect to use these. They are listed as guidelines if the DM wishes to allow them.

Component Cost Reading Guide:

If a number has nothing else listed with it, that is its cost, you may take it only once.

If a number has a + in front of it, it can be taken multiple times by adding the listed value each time it is taken. 

If a number has a – in front of it, it reduces the component cost of the spell. It only affects the Required Component cost calculation if it is listed in a Required Component, and only affects the Effect Components cost calculation if it is listed in an Effect Component. You may take it only once, and any components that would conflict – such as the time it takes to cast a spell – cannot be taken in tandem.

If a number has a * behind it, it is a cumulative component cost, each increment costs the listed value plus the cost of all lesser values leading up to that value. For example, in Enhance, a +1 Will save bonus costs 1 component, a +2 save bonus costs 3 (1+2), +3 costs a total of 6 (1+2+3), +4 costs 10 (1+2+3+4) and so on.

Note: The points below are supposed to be used as is, and are balanced around normal play to make for easy spell building that should remain reasonable. In saying that, they are still guidelines, and if certain components or component combinations are found to be excessively strong or weak – especially when compared to what other spellcasters have available to them at your table – the arithmetician player and DM should work together to find more balanced costs for their spells. Certain combinations can have their spell level increased or decreased outside of what its component cost would recommend, or just not possible at all if they are found to be problematic. 

Required Components

Area
Component Cost	Effect
0	Affects the arithmetician; no target required; or creates or conjures the target.
+1	Five-foot-square wall, one inch thick.
+2	Each additional target beyond the first.
+2	20-foot line.
+3	10-foot cube.
1	One target.
2	Five-foot radius sphere or 10-foot cone.
4	10-foot radius sphere or 20-foot cone.
8	20-foot radius sphere or 40-foot cone.
16	50-foot radius sphere or 100-foot cone.
20	100-foot radius sphere or 200-foot cone.
24	200-foot radius sphere or 400-foot cone.
28	400-foot radius sphere or 800-foot cone.
36	Line of sight

 

Range
Component Cost	Effect
Divide Range Cost by 2	Divination Effect Components only
1	Affects only the arithmetician (also called “personal range”).
2	Affects a creature or object the arithmetician touch. If the target is avoiding his touch (as in combat), the arithmetician must make a melee touch attack to touch the target and release the spell.
2	Originates from the arithmetician (normally used with area-affecting spells where the arithmetician wants to be ground zero for the effect).
3	Close (25 feet + 5 ft./2 levels).
8	Medium (100 feet + 10 ft. levels).
12	Long (400 feet + 40 ft. levels).
16	One mile
24	Unlimited on plane

 

Duration
Component Cost	Effect
–1	The arithmetician must concentrate on the spell to maintain the effect. When his concentration ends, the built-in Duration of the spell (if any) begins. For example, the arithmetician can build a spell with that lasts for his period of concentration plus one round per level; the Duration component cost is –1 point for concentration and 1 point for one round per level for a total of 0 points in the Duration component.
–1	The spell has no effect until a creature fulfills a triggering condition that the arithmetician specifies (such as touching the target or reciting a password). The Duration begins when the arithmetician casts the spell, but its effects don’t activate until the trigger occurs. The spell ends at the end of the built-in Duration whether or not someone has triggered it. +2 per extra time it can trigger after the first.
0	Instantaneous.
0	A one-use effect that occurs on or before the arithmetician’s next turn (such as a spell that grants him a bonus on his next attack roll).
2	One round per level.
4	One minute per level.
6	10 minutes per level.
10	One hour per level.
16	One day per level.

Effect Components

Core
Component Cost	Effect
-8	The spell can only affect creatures whose HD are half the arithmeticians CL (rounded down) or lower.
+1*	Per +1 increase to the spell’s save DC.
+1	Reduce Spell Exhaustion gained from this spell by –2 per increment of this effect.
+2*	Increase the dice from the spell effect; such as healing, damage or poison, by one die size. (1d6 to 1d8, then to 1d10, then to 1d12, which is the maximum). If the spell has multiple separate dice sizes, like d6’s alongside d4’s, they all go up by one step per time this component is taken.
Casting Time
-8	Casting the spell takes one week. The arithmetician is concentrating while casting.
–5	Casting the spell takes one day. The arithmetician is concentrating while casting.
–4	Casting the spell takes one hour. The arithmetician is concentrating while casting.
–3	Casting the spell takes 10 minutes. The arithmetician is concentrating while casting.
–2	Casting the spell takes one minute. The arithmetician is concentrating while casting.
-1	The arithmetician casts the spell as a one round action.
0	The arithmetician casts the spell as a full-round action (this is the default).
1	The arithmetician casts the spell as a standard action.
12	The arithmetician casts the spell as a quickened spell; doing so is a swift action. (The arithmetician may cast only one quickened spell – or use one other quickened effect – once per round even if he has multiple swift actions. Quickened spells do not provoke attacks of opportunity.)
Metamagic
2	Silent spell: the spell requires no words to cast. The arithmetician can cast it in an area of magical silence or if unable to articulate.
2	Still spell: the spell requires no gestures to cast. The arithmetician can cast it even if the arithmetician is restrained. (Casting while paralyzed requires the spell to be silent and still.)
4	Selective spell: An area spell affects only targets the arithmetician designates.
5	Covert spell: All obvious magical effects of the spell appear to come from a mundane source. For example, a bolt of electricity being turned into a lightning bolt, or a poison spell appearing to be from a snake bite, a fly spell appears to be the result of artificial wings or other mundane contraption, and so on. Some effects for which no realistic explanation is possible (such as a person turning into an animal) cannot be cast as covert spells. Any evidence a Covert spell leaves behind stands up to scrutiny of any surveillance and investigation, but detect magic while the spell is still ongoing will show its magic.
6	Disintegrating spell: If a creature is killed by this spell or object destroyed, it is disintegrated entirely. Spells that affect an area do not leave residue, the only evidence left behind is the lack of whatever was targeted.

Control
Component Cost	Effect
3	Target is shaken. (Fear)
5	Target is frightened. (Fear)
7	Target is panicked. (Fear)
8	Target is charmed and regards the arithmetician as a friend. (Charm)
8	The target falls asleep. Damaging a sleeping creature instantly wakes them up. To awaken a sleeping creature nonharmfully takes a standard action. (Compulsion)
8	Inspire a non-overwhelming emotion or feeling in a creature. Such as hunger, joy or apathy. Emotions or feelings that are inappropriate for the circumstances (such as hunger right after a meal or dread for no discernible reason) may arouse suspicion. (Compulsion)
+16	You overwhelm a target with a specific emotion: Send a creature into a rage inflicting Bezerk. Befuddle a target inflicting Confusion. Cause a fit of laughter to inflict Stunned on a target, etc. (Enfeebling)
16	Implant a suggestion of an action or course of actions one wishes a target to perform, they must be simple enough that the arithmetician can describe it in a sentence or two. The target automatically resists the spell if the suggestion is an obviously self-harmful act. The suggested course of activity can continue for the entire duration. If the suggested activity can be completed in a shorter time, the spell ends when the target completes the activity. A very reasonable suggestion gives the target a –2 penalty on his save. If the proposed activity is out of character for the target they will be suspicious if they succeed their save or after the spell ends. (Compulsion)
20	*Compel the target to perform a service or refrain from an activity for the Duration. This effect cannot compel the target to perform acts that will result in certain death or are a gross violation of its nature. The arithmetician can assign difficult tasks, but impossible tasks cause the spell to fail. (Compulsion)
20	Limitations on Compulsion effects that would not allow suggestions or commands that would cause self harm, suicidal actions, impossible request, or other such limitations can now be ignored, so that a target will attempt to perform such actions.
36	*Dominate the target. The target cannot resist his commands unless they would result in the direct harm or death of the creature itself. If the target is humanoid or beast only, the cost is 24 instead of 36. If the arithmetician must directly control the target by forsaking his own actions, either through mental puppetry or a form of possession, reduce this component’s cost by 4. (Compulsion)
*If the target of a spell has more Hit Dice than the arithmetician does, the target gains a +4 bonus on his save.

 

Divination
Component Cost	Effect
-3	Answers for divination are limited or vague; like riddles, metaphorical visions, or single word answers.
4	Reveals information that requires some scrutiny if determined by non-magical means, cannot find information that could not be found within the duration or would require any check with a DC higher than 20. Examples: Learning a person’s name, finding a lost object or secret door, speaking and understanding a foreign language, detecting lies, finding an address.
6	Reveals information about the future*, up to one hour from now.
8	Reveals information that cannot be determined without interrogating the subject or using magic. Examples: Determining if the target is an undead creature, learning a magical item’s properties, remotely viewing (scrying) a creature or location, finding the quickest path from one location to another, learning someone’s greatest desire or fear.
10	Asks questions of the dead. This effect requires a dead body or the haunting presence of a dead spirit. The arithmetician may ask one question per round. The dead creature can only recall things from before their death.
10	Reveals information about the future*, up to one day from now.
12	Reveal information about a location’s past, such as by asking the animals, foliage or even the earth itself to reveal that which it was there to witness.
16	Tells the target if they are being scryed upon or watched, magically or not.
16	Magically conceals the target from divination magic, regardless of what sort of information is desired.
16	Asks questions of entities beyond this world, such as demonic spirits or deities.
25	Reveals information about the future*, up to one week from now.
The component values listed here are recommendations for what is described that they may do, using other, unorthodox components from other groups is encouraged, such as using a control effect on top of speak with dead to force the dead to tell what they know.

  

Enhance
Component Cost	Effect
+1*	Per +1 enhancement bonus on checks with a single skill.
+1*	Per +2 enhancement bonus to an item’s hardness.
+2*	Per +1 enhancement bonus on a weapon’s attack and damage rolls.
+2	Per +5 feet enhancement bonus to one type of movement (land, fly, swim and so on).
+2*	Per –1 penalty on all d20 rolls.
+2*	Per +1 bonus on all d20 rolls.
+4*	Per +2 enhancement bonus to an ability score.
+10	Per +1 Inherent bonus to an ability score (max +5).  Duration component of this spell is Instantaneous, with a cost of 25 instead of 0.
+10	Reroll one d20 roll (you may only reroll any given roll once, and may only roll a number of d20’s equal to the number of times this component is taken).
Immunity
6	The target is immune to fear effects for the duration. An instantaneous spell with this component dispels fear effects on the target.
10	The target is immune to compulsion and charm effects for the duration. An instantaneous spell with this component dispels compulsion and charm effects on the target.
10	Immunity to poison. This effect cures existing poison the creature may be inflicted with.
12	Immunity to suffocation. A creature currently suffocating is no longer hampered by the effects of suffocation, but only while under the effects of this spell. This is commonly how arithmeticians emulate underwater breathing.
Alterations
Component Cost	Effect
+4	The target gains a natural attack such as a bite (1d6 damage) or two claws (1d4 damage each). The target is proficient with this natural attack. The arithmetician can use multiple components to give the target additional attack as long as it has suitable limbs (for example, the arithmetician cannot give a hume more than four claw attacks because a hume has only four limbs).
4	Opponents have a 20% miss chance when attacking the target, and vice versa; for example, this effect could result from portions of the target phasing in and out of reality.
6	Telepathy. This is two-way communication that respects the privacy of both creatures’ thoughts; one target must think at the other to send a thought, and vice versa.
6	Low-light vision.
8	Silence. Affected creatures cannot make noise of any kind, including casting spells that require speech (though the silent Metaspell effect easily compensates for this).
8	Levitate at a speed of 20 feet/round. (This effect allows vertical motion only, though the target can maneuver laterally if he is adjacent to a wall or stable object).
8	Opponents have a 20% miss chance when attacking the target, but the target can attack without penalty; for example, this effect could result from a defensive shield that deflects incoming ranged attacks but doesn’t affect his ability to attack.
8	Disguise. Changed the target’s appearance – including clothing, armor, weapons, and equipment – look different. You can seem 1 foot shorter or taller, thin, fat, or in between, but most still remain with your general body structure. This is purely cosmetic, none of the creature’s statistics change. Otherwise, the extent of the apparent change is up to you. The spell does not provide the abilities or mannerisms of the chosen form, nor does it alter the perceived tactile (touch) or audible (sound) properties of you or your equipment. If you use this spell to create a disguise, you get a +10 bonus on the Disguise check.
9	Darkvision 60 feet.
+10	Flight speed of 15 feet/round; maneuverability poor. Increasing by 15 feet/round and increasing a maneuverability stage (poor to average, average to good, etc). The target can rise at half speed and decline at double speed; a medium or heavy load reduces his speed by half.
10	Shapechanging. The arithmetician gives the target a new shape. The target does not get any supernatural powers of the new form and retains its own ability scores, but may use the new shape’s locomotive and breathing abilities (flight for birds, swimming and water breathing for fish, etc). The arithmetician can make the target look like a different person – changing their voice, appearance and the space they take up – even a specific person, though the change is not detailed enough to duplicate fine details such as fingerprints. This sort of disguise gives the target a +10 bonus on Disguise checks to pretend to be that person. (The arithmetician does not have to build a separate skill bonus into the spell to gain this benefit.). You may not change a creature into a form that is dramatically stronger than they are.
10	If the target makes a full attack, he gains one extra attack at his highest base attack bonus, perhaps because he moves with extraordinary speed.
10	Opponents have a 50% miss chance when attacking the target, and vice versa.
10	Transform an object into a different material (Stone to sand, dirt to gold, etc), size or amount is based on the area component.
+12	Increase or decrease size by one size category.
20	Opponents have a 50% miss chance when attacking the target, but the target can attack without penalty.
20	Advanced shapechanging. The arithmetician gives the target a new shape. This effect carries all the features of the cosmetic shapechanging effect plus exceptional senses such as low-light vision and scent as well as exceptional natural abilities such as a poisonous bite. An advanced-shapechanged target is physically indistinguishable from the original (including fingerprint, voice). Gaining the new form’s increased ability scores requires Enhance magic, which the arithmetician can include in this spell. The target reverts to its original form if killed. You may not change a creature into a form that is stronger than they are.
Protection
+1*	Per one point of energy resistance or five points of energy protection against one type of energy.
+1*	Per +1 bonus on a single saving throw (so +1 on all three saves costs three).
+1*	Per +1 enhancement bonus to natural armor.
+2*	Per +1 deflection bonus to AC.
+5	Per +1 point of type-less damage reduction (DR 1/–).
10	An aura that prevents creatures from directly attacking the subject unless they resist the spell with a Will save (a creature makes one save against the spell; success means it can directly attack the target, failure means it cannot). This aura ends if the subject attacks, and it does not prevent creatures from attacking the target with area effects.

 

Force
Component Cost	Effect
+1	Per 1d6 points of damage. To a maximum of your Caster level in d6. (max CL d6). Damage over time effects cost double.
+2	Per 1d6 points of damage. Damage over time effects cost double.
3	Add Caster Level (to a max of 5x the spells level) and Intelligence modifier to damage.
+8	Per 1d3 Pool resource lost. (The target loses Pool resources; the arithmetician must declare which when he makes the spell.) If the resource poll is MP reduce cost by -2 per.
+8	Per damaging poison effect (Fort negates, 1d2 damage to one ability score, 1/round for 6 rounds, cure 1 save)
10	Nauseated. Target may take only one move action per round. (Enfeebling)
Type Adjustments
–1	The spell manipulates the energy of the area to deal energy damage. For example, the spell causes the flames of a bonfire to shoot out at a target. (Elemental)
-1	Damage type becomes Non-lethal
1	The spell creates energy to deal energy damage (instead of bludgeoning, piercing or slashing damage). (Elemental)
2	Add Status effect, costs 1 less if spell does appropriate type of damage for status, (IE Fire with burning).
4	Damage type becomes Non-elemental.
Nullify
+1	Dispel magic. Choose a single spell or magical effect. Roll 1d20 and add the number of Metaspell components the arithmetician spends on the dispel attempt; the DC is 11 + the creator’s Hit Dice. If the arithmetician succeeds, the spell or magical effect ends.
12	Antimagic. Supernatural effects (hostile or friendly) do not work on the target or in the spell’s area. Arithmeticians and other supernatural creatures immediately sense when they enter an antimagic area. Antimagic can be dispelled. Overlapping antimagic effects are still antimagic (they do not cancel each other to create a “normal” area where they overlap).
20	Block teleportation in the area (or on the targets).
Movement
0	Forcefully move up to a tiny creature or object at speed 20 feet/round. Particularly dense/light creatures or objects may count as a size larger/smaller at DM discretion.
+1	Per movement speed of 10 feet/round on forced movement.
+2*	Per size category larger of the target on forced movement.
Cost as double Range Component	Teleport. You can bring along objects as long as their weight doesn’t exceed your maximum load. You may also bring one additional willing Medium or smaller creature (carrying gear or objects up to its maximum load) or its equivalent per three caster levels. A Large creature counts as two Medium creatures, a Huge creature counts as four Medium creatures, and so forth.  The distance the arithmetician can teleport the target depends on the spell’s Range components.
Cost as double Range Component	Teleport 100x the distance of the ranged component, with accuracy of teleport just as the spell Bend Space and Time

 

Heal
Component Cost	Effect
–2	Parasitic; the spell damages the arithmetician for the amount of damage the target recovers.
+1	Per 1d6 hit points of healing.
3	Add Caster Level (to a max of 5x the spells level) and Intelligence modifier to healing.
+2*	Per 1 point of Fast Heal.
+1	Per 1d6 temporary Hit Points that last for the duration of the spell.
+4	Per 1 point of ability drain cured.
2	Vampiric. The spell heals another target within range for the same amount of hit points that the damaged target takes.
6	Cure exhaustion (the exhausted condition, not spell exhaustion).
15	Cure blindness or deafness (magical or not).
15	Cure supernatural affliction, such as a curse or magical disease.
22	Resurrection, as Raise
32	Resurrection, as Arise
42	Resurrection, as Full life

Illusion
Component Cost	Effect
1	Target is dazzled.
+1	Audio illusion, per 20 decibels of noise. Without this component, the illusion is utterly silent. An illusion cannot cause harm due to noise unless the arithmetician includes Damage and Energy components.
+1	Thermal illusion. One component is sufficient to duplicate the sensation of warmth or cold without pain or damage. An illusion cannot cause harm due to heat or cold unless the arithmetician includes Damage and Energy components, but adding a thermal effect is usually sufficient to convince a casual witness that the illusion is real.
+2	Olfactory illusion. One component is sufficient for all moderate odors (food, a flower garden, a kitchen garbage can, human body odor), two for strong odors (skunk musk, sewage). An illusion cannot cause debilitating effects (such as nausea) due to stench unless the arithmetician includes the appropriate components.
+3	‘Create illusion of one object or creature up to Small or smaller size.
+6	Create illusion of one object or creature up to Medium size.
+10	Create illusion of one object or creature up to Large size.
+20	Create illusion of one object or creature up to Huge or larger size.
1	Creates a false aura that fools supernatural perceptions, such as making an ordinary object seem as if it had a supernatural property or concealing a supernatural object’s aura so it appears to be mundane. Supernatural scrutiny of the target always allows a Will save.
3	Scripted illusion. The illusion performs a pre-set series of actions that the arithmetician specifies when he casts the spell. These actions repeat or stop (his choice) when the script reaches its end.
16	Invisibility (normal).
24	Invisibility (greater).

Summon
Component Cost	Effect
–5	Harmless minion.
–2	Appropriate minion substrate.
+1	One day’s worth of simple nutritious food or water for a medium creature. The Duration must be at least one day for the spell to provide any lasting effect, or the nutrients decay before providing any real nourishment. (Living off summoned food or water with a shorter Duration eventually results in starvation or dehydration, though a creature that consumes summoned sustenance with a duration more than an hour won’t notice it vanishing, just their hunger or thirst returning.)
+1	Per cubic foot of raw material, such as wood, stone or iron. Add the material’s cost (below) separately. When creating walls, you must take this once per use of the wall Area component.
4	Creates shadow or light fog that gives all within it a 20% miss chance.
+4	Per minion template.
+4	Masterwork object.
+4	Per additional copy of the summoned creature. (one can use dice for summoning, use the average result of dice for the equivalent number of creatures summoned. Ex, 1d3 = 2 on average for +4 CP + base cost, 1d4+1 = 3.5 on average for 10 CP + base cost)
6	Wood object.
10	Creates darkness or thick fog that gives all within it a 50% miss chance.
10	Stone object.
12	Iron object.
12	Minor minion.
16	Lesser minion.
24	Greater minion.
28	Superior minion.
4	CR ¼ creature.
8	CR ½ creature.
12	CR 1 creature.
+4	+1 CR. Can only be added to the “CR 1 creature” component.

 

Minion Statistics: Minions come in four general types: minor, lesser, greater and superior.

• Minor Minion: CR 2; Medium animal; HD 3d8+3, hp 16; Init +2; Spd 30 ft.; AC 15, touch 12, flat-footed 13; Base Atk +2; CMB +4; CMD 16; Melee Bite +5 (1d6+3); SV Fort +4, Ref +5, Will +0; Str 15, Dex 15, Con 13, Int 3, Wis 8, Cha 3. Skills and Feats: Perception +5; Weapon Focus (bite).
• Lesser Minion: CR 4; Medium animal; HD 6d8+24, hp 51; Init +3; Spd 30 ft.; AC 18, touch 13, flat-footed 15; Base Atk +4; CMB +7; CMD 20; Melee Bite +8 (1d8+4); SQ darkvision; SV Fort +8, Ref +8, Will +3; Str 17, Dex 17, Con 17, Int 3, Wis 12, Cha 3. Skills and Feats: Perception +10; Power Attack, Toughness, Weapon Focus (bite).
• Greater Minion: CR 6; Large animal; HD 10d8+60, hp 105; Init +2; Spd 30 ft.; AC 18, touch 11, flat-footed 16; Base Atk +7; CMB +16; CMD 24; Melee 2 Bite +12 (2d6+5); Space/Reach 10 ft./10 ft.; SQ darkvision; SV Fort +12, Ref +9, Will +4; Str 21, Dex 15, Con 21, Int 3, Wis 12, Cha 3. Skills and Feats: Perception +14; Combat Reflexes, Power Attack, Toughness, Weapon Focus (bite).
• Superior Minion: CR 8; Large animal; HD 14d8+98, hp 161; Init +2; Spd 30 ft.; AC 20, touch 11, flat-footed 18; Base Atk +10; CMB +20; CMD 28; Melee 2 Bite +16 (2d8+6); Space/Reach 10 ft./10 ft.; SQ darkvision; SV Fort +15, Ref +11, Will +5; Str 23, Dex 15, Con 23, Int 3, Wis 12, Cha 3. Skills and Feats: Perception +18; Cleave, Combat Reflexes, Power Attack, Toughness, Weapon Focus (bite).

Minion Templates: Templates are quick and easy ways to customize minions. A minion template is just a few quick adjustments to a minion’s statistics, giving the effect and feel of the appropriate minion without a ton of work.

• Advanced Template: +4 to all ability scores.
• Air Elemental Template: Immune to poison and wind. Attack deals +1d6 wind damage. Darkvision 60ft. +20 bonus to speed. Fly at its (modified) ground speed (perfect maneuverability). Weak to Ice. An air elemental typically looks like a tornado.
• Demon Template: Immune to poison. Earth resistance 10, ice resistance 10, fire resistance 10, lightning resistance 10. +4 bonus on damage rolls. +4 bonus on saves against spells and supernatural abilities. Darkvision 60ft. Weak to Holy.
• Earth Elemental Template: Immune to poison and earth. +5 natural armor bonus to AC. Improved Bull Rush. Darkvision 60ft. –10 penalty to speed. Weak to Wind. An earth elemental typically looks as if it is made of earth and stone; when still, an earth elemental looks like a statue.
• Fire Elemental Template: Immune to poison and fire. Attack deals +1d6 fire damage. Attacking it with natural weapons or unarmed attacks deals 1d6 fire damage to the attacker. Darkvision 60ft. +10 bonus to speed. Weak to Water. A fire elemental looks like an animate flame or a “special effect” of a creature made of fire; it can stand perfectly camouflaged within fires of its size or larger.
• Harmless Template: The minion is unable to directly cause harm — it cannot attack, use weapons, drop rocks on people from a rooftop and so on, but it could push a button that detonates a bomb. If attacked, a harmless minion does not retaliate (which makes it a good decoy for unintelligent enemies, as it lets its opponent chew on it until it expires).
• Holy Elemental Template: Immune to Holy. In areas of light, holy elementals become translucent. They gain a +6 to hit rolls and a dodge bonus to their AC while in bright light, reduced to a +3 while in normal light. In shadowy illumination, a holy elemental loses this translucence, having a faint glow that produces Dim Light out to 60ft. Weak to Shadow. Holy elementals look to have a radiant glow to them, almost as though they were made of light. 
• Ice Elemental Template: Immune to poison and ice. +5 natural armor bonus to AC. Improved Bull Rush. Darkvision 60ft. –10 penalty to speed. Weak to Fire. An ice elemental typically looks as if it is made of ice and snow; when still, an ice elemental looks like a snowman.
• Lightning Elemental Template: Immune to poison and lightning. Attack deals +1d6 lightning damage. Darkvision 60ft. +20 bonus to speed. Weak to Earth. Fly at its (modified) ground speed (perfect maneuverability). A lightning elemental typically looks like an animated jagged bolt of lightning.
• Shadow Elemental Template: Immune to Shadow. Attack deals +1d6 shadow damage. In any condition of illumination other than bright light, a shadow elemental disappears into the shadows, giving it concealment (20% miss chance). A shadow elemental can suspend or resume this ability as a free action. Darkvision within line of sight. Weak to Holy. A shadow elemental looks like an animate shadow, almost like an optical illusion as its two dimensional darkness takes a 3d shape.
• Skeleton Template: Immune to mental attacks (including charm and compulsion effects), absorbs shadow, poison, Con damage, and stunning. Damage reduction 5/bludgeoning. Darkvision 60ft. Weak to Holy. When lying still, a skeleton looks like any other (dead) skeleton.
• Water Elemental Template: Immune to poison and water. +5 natural armor bonus to AC. Darkvision 60ft. Swim speed equal to its ground speed +20. Can breathe underwater. Weak to Lightning. A water elemental looks like a free-standing wave, camouflaging perfectly into water.
• Zombie Template: Immune to mental attacks (including charm and compulsion effects), poison, absorbs shadow, Con damage, and stunning. +2 hit points per hit die. Damage reduction 5/slashing. Darkvision 60ft. Weak to Holy. All movement speeds are halved. When lying still, a zombie looks like any other dead body in the same state of decomposition.

Apocryphal *The following are effects with cost as guidelines for those who wish to allow them, do not expect them to be allowed
Required Components
Component Cost	Effect
24	Permanent. The magic is ongoing; magic-negating effects can interrupt or break the spell. Cannot have damage or other negative status effects.
24	Curse. Allows negative effects on a Permanent effect so long as there is a conditional way to break it that a normal person could theoretically achieve.
36	Interplanar Targeting/Range
Effect Components
Component Cost	Effect
Double Final Component cost for the spell	The spell no longer provides a save or needs an attack roll to hit. It automatically affects all creatures it targets. Discuss with your DM price changes for only attack roll spells and for spells which are save for no effect.
16	The arithmetician casts the spell as an immediate action.
+16	Per round of stopped time, as Time Stop. (can use dice for rounds, use average result of dice for equivalent number of rounds. Ex, 1d4 = 2.5 rounds, 40 points.) (Chronomancy)
32	Resurrection, as Raise Dead
52	Resurrection, as Resurrection
65	Resurrection, as True Resurrection
36	Interplanar Travel / Astral Projection
*	Create pocket dimension (size is based off of area, with this effect being the areas cost +20)

Numerical Talents

Alongside his mathematical endeavors, an arithmetician will learn numerous talents that assist him in manipulating spells and other forms of magic. At 2nd level and every two levels thereafter, an arithmetician gains one numerical talent. An arithmetician cannot select an individual talent more than once. Talents marked with an asterisk (*) add effects to an arithmetician’s spellcasting ability. Only one of these talents can be applied to an individual spell and the decision must be made before the spell is cast.

Table: Numerical Talents

Numerical Talent	Prerequisites	Benefits
Additional Monster (Su)	—	The arithmetician summons a monster(s) with a spell he summons one additional monster. This talent stacks with Superior Summoning if the spell is being used to summon 1d3 or 1d4+1 number of monsters. When using this talent on a spell, increase the MP cost by ½ of the spell level, this does not increase the spell level.
Ambuscading Spell (Su)	—	During a surprise round, the arithmetician’s opponents that have not yet acted take a –2 penalty on saving throws against spells he casts. Creatures that have already acted take a –1 penalty during the surprise round.
Arcane Builder (Ex)	—	The arithmetician has an exceptional understanding of the theory behind creating magical items. He can select one type of magic item (potions, wondrous items, and so on); he creates items of this type 25% faster than normal, and gains a +4 bonus on Spellcraft checks to craft items of this type. He may select this talent multiple times; its effects do not stack. Each time he selects this talent, it applies to a different type of magic item
Attract Disciple	4th	The arithmetician takes a loyal Minion under his tutelage. The minion is a character with Lil’ Witch class level (can be one of the archetypes) equal to three-quarters of the arithmetician’s class level rounded down.
Cancel Out (Su)	8th	When you or an ally within 30 feet takes damage, you may use an immediate action to nullify certain values in the damage roll. An arithmetician chooses one of his known numbers, any die in that damage roll that shows the chosen number is treated as having rolled a 0 instead and does not contribute to the damage total. You may use this ability once per creature protected per day.
Chaos Theory (Ex)	12th	Once per encounter, as an immediate action, the arithmetician can push his mathematical prowess to its limits, practically predicting the future via deterministic equations. Choose one creature the arithmetician can see, if that creature makes an attack roll, skill check, ability check, or saving throw before the start of your next turn. You may choose to add or subtract half your intelligence bonus on that roll. At 18th level, the modifier increases to your intelligence bonus.
Cognitive Thesis (Su)	—	The arithmetician can condense and transmit highly complex information directly into the minds of others. As a standard action, he may telepathically impart a complete understanding of an abstract or complex concept—such as an advanced mathematical theorem, intricate philosophical argument, or obscure historical context—to a number of willing creatures equal to his Intelligence modifier. Targets must be within 60 feet. Upon receiving the information, the recipients comprehend it with perfect clarity and no ambiguity, regardless of their Intelligence score or prior knowledge. This does not grant skill ranks or abilities but allows perfect theoretical understanding.
Concentrate (Ex)	—	The arithmetician can reroll any concentration check he has just made with a +4 bonus. He must use this ability after the roll is made, but before the roll’s outcome is determined. The arithmetician must take the second roll, even if it is worse. The arithmetician can use this ability once per day.
Contingency Plan (Ex)	—	Once per encounter, if the arithmetician fails an attack roll, a skill check, or the use of a talent that requires an opposed check, he can move up to his movement speed as an immediate action.
Cup of Mercy (Su)	8th	Whenever an arithmetician casts a spell that deals damage, if it would reduce a creature’s hit points below 0, he can choose to let the damage reduce the creature to -1 HP and leave it stable. If he does so, the creature gains temporary hit points equal to the left over damage it was spared from.
Domain Exception (Su)	10th	Whenever a creature attempts to use a teleportation effect or summon a creature within 30 feet of the arithmetician, he may attempt to block the effect. Make an opposed caster level check (1d20 + caster level) as an immediate action. If the check succeeds, the spell or effect fails and is wasted; otherwise, it is unaffected. He can use this ability once per day plus one additional time for every five arithmetician levels he possesses beyond 10th.
Empower Disciple	Attract Disciple	Your minion now has Lil’ Witch levels equal to your class level, and gains an additional MP per level.
Familiar (Ex)	Caster Level 2nd. Must be chosen at 2nd level.	The arithmetician who selects this talent gains the Familiar feat.
Golden Ratio (Ex)	—	Use your Intelligence bonus instead of your Charisma bonus for any roll relating to your appearance (such as disguise, seduction, making a good first impression).
Immortality (Ex)	20th	The arithmetician discovers a cure for aging, and from this point forward, he takes no penalty to his physical ability scores from advanced age and cannot die from old age. If he is already taking such penalties, they are removed at this time.
In Desperate Need of Coffee (Ex)	—	The arithmetician treats non-lethal damage as lethal damage when determining if he can activate Limit Breaks, becoming fatigued after using a Limit Break in this manner.
Instruction Manual (Su)	—	The arithmetician gains the supernatural ability to speak with and understand any intelligent construct, even if they share no languages in common. Additionally, by observing a mindless construct for 3 rounds, the arithmetician can determine the nature of its instructions or programming, learning how the construct will respond to stimuli, like being attacked or approached.
Knowledge is Power (Ex)	—	The arithmetician’s understanding of physical forces gives him power over them. He adds his Intelligence modifier on combat maneuver checks and to his CMD. He also adds his Intelligence modifier on Strength checks to break or lift objects.
Lies, Damned Lies, & Statistics (Ex)	Above Average Magical Theorem:	The arithmetician may now take 11 on bluff checks. When telling a lie involving any form of math, he may treat it as the truth for any abilities or magic that detects or affects the truthfulness of the statement. (Eq, he can now say 1+1=3 under the effects of a zone of truth. This does not mean others will believe such obvious lies, and a check may still be required to convince them.)
Mage Training	—	The arithmetician may select an item creation or metamagic feat. The arithmetician must still meet all prerequisites for a bonus feat, including caster level minimums. This talent may be taken more than once. Each time, a different feat must be selected.
Magic Aid (Su)	—	As a standard action, the arithmetician can spend MP up to his maximum spell level to grant additional magic energy to an allied spellcaster within close range (25 feet + 5 feet/2 levels). If that ally casts a spell of an equal or lower MP cost before the beginning of his next turn, all level-dependent calculations and caster level checks the spell requires are made as if the ally’s caster level were 2 higher. If MP spent is at least twice the MP cost of the spell his ally casts, his ally’s caster level is treated as 4 higher instead. If his ally is able to cast more than one spell before the beginning of his next turn, only the first spell cast gains this bonus.
Mathematical Paradox (Su):	—	As a standard action, you force one creature within 60 feet of you to attempt to conceptualize a paradox or logical contradiction so baffling that it overloads their mind. That creature must succeed on a Will save (DC = 10 + ½ your character level + your Intelligence modifier) or be stunned for 1 round. This is a mind-affecting effect. This effect ignores construct immunities and they automatically fail their saving throw.  You may use this ability a number of times per day equal to your Intelligence modifier (minimum 1).
Reserve Training	—	The arithmetician may select a Reserve feat as a bonus feat. The arithmetician must still meet all prerequisites for this bonus feat
Restless Scholar (Su)	6th	The arithmetician can go without eating or drinking for a number of days equal to his Intelligence modifier before he must make Constitution checks to avoid nonlethal damage. Additionally, he can spend 8 hours studying his spells instead of sleeping. This confers the same benefit as an 8 hour rest, but he is awake the entire time.
Rod Mastery (Su)	—	Whenever the arithmetician uses a rod, he calculates the DC for any spell it contains using his Intelligence modifier (minimum 0) instead of the minimum modifier needed to cast a spell of that level.
Rod Wielder (Su)	—	The arithmetician adds his Intelligence bonus (minimum 0) on caster level checks made to overcome spell resistance when using a spell contained within a rod.
Round Reality (Su)	12th	You gain the ability to manipulate the numerical structure of reality, changing figures to the nearest value. As an immediate action, you may choose any single numerical value within range (60 feet) and round it up or down to the first significant figure, allowing you to alter a numerical value—such as a measurement, or the price of an item— (e.g., increasing a 16-foot jump distance to 20 feet, or reducing a 450 gp potion’s price to 400 gp). You must choose to round either up or down, and the number must remain positive after rounding. This ability cannot create or destroy matter, and cannot be used to produce impossible, paradoxical, or non-numeric effects. If the result of the rounding would negatively affect a creature (e.g., reducing the gold they receive, increasing their internal body temperature, or modifying an effect they control), the target gets a save of an appropriate type as determined by the DM (e.g., If one is warping the value of a potion that costs 450 gp to make it 400, a will save for the financial damage, or a fortitude save if you are targeting someones internal body temperature) You may use this ability three times per day.
Sacrificial Numbers (Su)	12th	If the arithmetician’s hit points would fall below 0, he may sacrifice one of his summoned creatures as an immediate action. If he does so, the summoned creature instantly dies, and the arithmetician is reduced to 0 hit points instead. He may do this once per day.
Speed Calculus (Ex)	—	As a standard action, once per day, the arithmetician can replace one of his memorized spells with a new one. The new spell gains the benefits of the arithmeticians discount if it is replacing one that was already discounted.
Speed of Thought (Ex)	—	The arithmetician can no longer be surprised, and always act during a surprise round. In addition, the arithmetician may dismiss any spell he has cast as a free action.
Spell Lore (Ex)	—	The arithmetician adds his level to all Spellcraft checks made to identify a spell being cast. (This is most often useful when attempting to counterspell.)
Spell Sage (Ex)	—	When the arithmetician attempts a Use Magic Device check to cast a spell from a materia, he gains a +4 competence bonus to the check.
Surecast (Su)	Combat Casting feat	The arithmetician exercises caution when in danger, casting his spells with more care. While in a threatened square, he may choose to spend a full-round action to cast a spell, with a casting time of standard action or less. Doing so allows him to cast the spell without needing to cast defensively.
Think on It (Ex)	—	One per day, the arithmetician can re-attempt any previously failed Knowledge check. On this attempt, he adds a +5 competence bonus on the check. At 10th level, this bonus increases to +10.
Tranquil Mind (Ex)	—	The arithmetician gets a bonus on all concentration checks equal to your constitution modifier.
Wand Mastery (Su)	—	Whenever the arithmetician uses a wand, he calculates the DC for any spell it contains using his Intelligence modifier, instead of the minimum modifier needed to cast a spell of that level.
Metamagic Talents		Talents marked with an asterisk (*) add effects to a black mage’s spellcasting ability. Only one of these talents can be applied to an individual spell and the decision must be made before the spell is cast.
Empowered Magic (Su)	—	The arithmetician can cast one spell per day as if it were modified by the Empower Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Extended Magic (Su)	—	The arithmetician can cast two spells per day as if they were modified by the Extend Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Maximized Magic (Su)	12th	The arithmetician can cast one spell per day as if it were modified by the Maximize Spell feat. This does not increase the MP cost or the level of the spell.
Quickened Magic (Su)	12th	The arithmetician can cast one spell per day as if it were modified by the Quicken Spell feat. This does not increase the MP cost or the level of the spell.
Reach Magic (Su)	—	The arithmetician can cast two spells per day as if they were modified by the Reach Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Selective Magic (Su)	—	The arithmetician can cast two spells per day as if they were modified by the Selective Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Silent Magic (Su)	—	The arithmetician can cast two spells per day as if they were modified by the Silent Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Still Magic (Su)	—	The arithmetician can cast two spells per day as if they were modified by the Still Spell metamagic feat. This does not increase the MP cost or the level of the spell.
Spellcasting ability*		Talents marked with an asterisk (*) add effects to an arithmetician’s spellcasting ability. Only one of these talents can be applied to an individual spell and the decision must be made before the spell is cast.
Creative Destruction (Su)*	—	The arithmetician has learned how to use destructive energy to empower himself. When he casts a spell with flexible spellcasting that deals damage, he gains a number of temporary hit points equal to the total number of dice used to determine the damage caused by the spell. Temporary hit points gained from this talent disappear after 1 hour.
Defensive Feedback (Su)*	—	Rather than dissipate damaging energy, the arithmetician can redirect some of it back to its source. When an enhancing spell the arithmetician casts prevents damage (with damage reduction or energy resistance), if the attacking creature is within 30 feet of the protected creature, the foe takes 1d6 points of damage (of the same damage type that was prevented) for every 10 points of damage prevented.
Exhaustive Barrier (Su)*	—	Whenever the arithmetician casts a spell he may allow excess energy from the spell to leak out in all directions to repel attacks and protect himself from harm. He gains a deflection bonus to AC equal to the spell’s Spell Exhaustion rating until the start of his next turn.
Improved Enhancements (Ex)*	—	When the arithmetician casts an enhancement spell, it’s highly effective on the first round. During the first round that the enhancement spell was cast, the effects are doubled. He may use this ability three times per day.