I'm sorry for the long wait, I've been home for a while - but as you can see below, I was writing something big. I felt it needed clarification and changes, and I needed a break from all that GMing. Surely you can forgive me? D:
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I've given the whole School of Hocus Pocus some serious thought on the way home, and I'm redefining it right now. So, no to the Mathamancy space warping abilities - because they will not have them anymore, as you will see in a moment. I get the feeling that was put in there for a lack of anything better to do with them and the feeling that 'people could do mathematics on their own anyway'. Yes, this is technically going into Fanon here, but looking at all the information already given in the comic, I'm pretty sure I'm about as close as we're going to get right now.
HOCUS POCUS ERRATAHocus Pocus is the School of magic that in other settings would be called Divination. It deals with the Life of all Erfworlders, thus it being aligned to that element. The school is concerned with one thing only - the Future.
Each Discipline of Hocus Pocus is concerned with a different part of the Future, though.
I'm going to put up a diagram here of the School and how it works. It will make more sense as you read through here.
Findamancy <----> Predictamancy <----> Mathamancy.
Being part of the same school, they bleed together to a certain extent.
Findamancers, aligned with the Erf axis, concern themselves with Places, and the People on it. Findmancers can locate cities, terrain types, people, and beasts. The discipline bleeds into Predictamancy, and more experienced Findamancers can locate things that will be important to you - Inform you of where enemies could be found, from sides that you have not met or allies might harbor plans against you, or tell you where might something that could alter the Fate of your side might lie - but only in a general, directional sense that works on geographic terms. They are wholly separate from the Discipline of Mathamancy, and cannot touch statistical data. They cannot find "how likely" something is to occur, or provide anything relating to cause and effect. So you can ask them "Where should I go to better further my victory against my enemy, Egyptalon?" and they would answer "To the northwest" (Viola, there is a volcano to the northwest or perhaps an Artifact or Magic item), or you could ask them "Where can I someone who find might hinder my plans for prosperity?" and they would answer "To the east" (and whoop, there is another side you haven't heard of.) Keep in mind they are NOT Predictamancers though, and their grasp of Fate is tenuous at best. This will not tell you where enemies ARE, but where they MIGHT be. The Findamancer could direct you to a new side haven't met -and anything could happen with them-, but if you already know all of them and are allied the Findamancer will only point to the one MOST LIKELY to become an enemy, and be completely wrong in practice. It should be taken with a grain of salt, because if you think about it, immediately attacking them based on that information will make it a self-fulfilling prophesy.

Of course, if you ask them that when you're at war with someone, guess where they're going to point? And you just wasted some of their juice on that pointless question.
Mathamancers, aligned with the Numbers axis, concern themselves with Statistics. In most cases this goes hand in hand with combat. Not only can they tell you if you are likely to win a battle, but HOW likely you are to win it. They are not Parson's magic bracer artifact though, so they will not give you instantly start giving you an X% chance but rather an intuition based on learning that same point. Only high level Mathamancers can spout percentages, and they can't do it endlessly like Parson's Bracer - it takes juice. Mathamancy bleeds into Predictamancy, as we have already seen in the comic. Questions like "What is the chance that doing X will be profitable to me?" will get an answer of increasing clarity based on the level of the Mathamancer. They cannot locate objects or concepts, just give you the likelihood that the stated effect will occur ("How likely is it that going west is going to help me in this war?"). When relaying actual combat statistics though, Mathamancers follow the same basic rule as computers - Garbage in, Garbage out. They can only produce results on what is already known. If you don't know they secretly have a caster linked to an Arkentool wielder sitting in their Tower, your information from the calculation is not going reflect that. Don't try to work your way around that by asking tricky questions either. Asking what the possibility that your previous calculation was wrong would still give you statistical information, maybe 25% chance at best. I mean, what are the chances that a Royal is going to hire an Arkentool wielder during the war between the two sides, have him link with a Turnamancer using the Arkendish (a process that is likely to have exorbitant rates considering Charlie), and then your massive army of Dwagons is going to enter that casters hex and fart around without attacking for long enough for said Turnamancer to cast a super End Turn spell? ... Whoops.
Predictamancers, aligned with the Fate Axis, and concern themselves with just that - Fate, the future itself. Their discipline bleeds into both Mathamancy and Findamancy, but they can neither point you in a definitive direction nor give accurate account of the chance that something will happen. They can view murkily into the Numbers axis and tell you in a broad manner how likely something is to happen (unlikely (0%-35%), unpredictable (36%-65%), or likely (66%-100%).) or distantly into the Erf axis and tell you if you are going in the right direction for what you wish to find (For instance you might be heading east, but what you are looking for is NOT east, but to the northeast. However, you can only reach that place by first going east, perhaps because there are mountains or a sea in the way). Their real specialty, however, is seeing into the misty veil that is fate itself. Aside from the axillary uses mentioned earlier for Predictamancers, they have no real use in the day to day affairs of a side. They function in a different, special manner. All unused Juice at the end of a turn is expended as if it had been spent (giving XP too), and that Juice is put into a special Pool of Fate. Your Pool of Fate is a hidden value from you, the player, but it accumulates over time. There are specific criteria that, if you have enough Juice in your Pool of Fate when it occurs, cause a Revelation to occur. A Revelation is a special event where your Predictamancer receives a vision of the future. These visions are never concrete and specific, but they provide instantaneous information that no other Hocus Pocus school can without a lot of work and spent juice poking around. Some examples of Revelations:
-An enemy (non-allied) army is nearing one of your cities.
-One of your Allies has turned on you.
-The coming battle will change the fate of the world.
-An Arkentool exists in the world.
-Someone has found an Arkentool.
I've compiled a list of spells for Hocus Pocus again. Some of it is the same, some of it is new, some is changed or gone.
Hocus PocusFindamacy
Terrain Direction: Gives the direction of the closest hex of chosen terrain. 5 juice.
Locate Terrain: As Terrain Direction, but also gives number of hexes away. 10 juice. Usable by level 3+ Findamancers.
See Terrain: As Terrain Direction, but pinpoints exact location. 20 juice. Usable by level 5+ Findamancers.
Unit Direction: As Terrain Direction, but finds a target unit. Can be fooled by veils. 20 juice.
Locate Unit: As Unit Direction, but also gives number of hexes away. 40 juice. Usable by level 3+ Findamancers.
Find Unit: As Unit Direction, but pinpoints the unit's exact location. Usable by level 5+ Findamancers.
City Direction: As Unit Direction, but finds target city (name of city required, unless it is a capital, in which case name of side required). 20 juice. Usable by level 10 Hocus Pokers.
Locate City: As City Direction, but also gives number of hexes away. 40 juice. Usable by level 3+ Findamancers
Find City: As City Direction, but pinpoints exact location. 80 juice. Usable by level 5+ Findamancer
Threat: Finds hex of closest non-allied units. 50 juice.
Dowsing: Finds the direction towards a desired destination or concept. 30+ Juice depending on difficulty of question and accuracy provided. Is based on Findamancer level and remaining juice - exhausted Findmancers will give you vague directions, even if they are Master-class. Subject to moderation to determine.
Neighbor: Finds hex of closest non-allied city. 80 juice.
Predicatamancy
Predictamancy is special. Unused Juice goes into the Pool of Fate as if spent when the turn ends, where it may cause a Revelation.
Weal or Woe: Gives vague prediction of whether a stated eventuality will occur (unlikely (0%-35%), unpredictable (36%-65%), or likely (66%+).). 40 Juice.
Pathfinder: Determines if a unit or stack that has moved this turn is heading in the right direction to reach a destination. 40 Juice.
Mathamancy
Battle Calculator: Gives percent chance of victory in an engagement, based on known information. Detail of percentage prediction is based on Mathamancer level (Level 1+ (very unlikely (0%-17%), Unlikely(18%-35%), Maybe not (36%-50%), Maybe so (51%-65%), Likely (66%-83%) Very likely (84%+), Level 3+ (Actual percent rounded to nearest 10), Level 5+ (Exact pecent )). 10 juice.
Analytical Speculation: Provides probable chance that a stated eventuality will occur. Up to GM to determine this, but it should be drawn from how the world as a whole tends to work (garbage in, garbage out), not what is actually happening this moment. Ergo, if your ally has been a faithful ally for many turns, the chance will be low that he will do so, even if he just has a turn ago. Granted, as more time passes and he plots against you, the scale of chance will slowly slide more towards certainty, because the world is changing - they talk to you less, some units just 'happen' to disappear near his cities, so on. Questions that directly pertain to your side are more likely to yield useful information. 40 Juice.
As a final note, I would like to point out this - all spell lists (ALL of them) are given possibilities, not the be all and end all of magic use. If you can think of an interesting use for your casters Discipline, ask a GM. The worst that can happen is they will decline the idea or set a Juice cost that requires Thinkamancy to perform.
Be creative, my friends! Break the game with lateral thinking - Wake up some volcanoes.
Phew. That was a lot of writing. I'm ready to go back to GMing
