### Arcane Tradition: Arithmancy <!-- If your game isn't very serious, this subclass should absolutely be called "mathmagician". //--> Fluff about the weave and math and shit #### Calculation Savant Beginning when you select this school at 2nd level, you learn to mentally optimize your method of copying a spell before using any materials. When calculating the cost to copy a spell into your spellbook, you may interpret the cost in gold as a base-9 number rather than base-10. This does not reduce the time it takes to copy the spell into your spellbook. <!-- This is between a 10 and 20 percent decrease in spell cost depending on the level, with an added bit that forces you to learn how to convert base 9 to base 10. It's not nearly as significant a decrease as halving the cost as with the phb subclasses, but it is much more versatile. //--> #### Computational Casting Starting at 2nd level when you choose this school, you learn how to carefully plan your spells to increase their effects while minimizing the use of your arcane power. You have a pool of d6's equal to twice your wizard level called a variable pool. As an action on your turn, you can begin casting a Wizard spell of 1st level or higher you have prepared and have spell slots for. When you do, your turn ends, and you must maintain concentration until the beginning of your next turn as if you were concentrating on a spell. Then, consult the following table: | Spell Slot Level | Target Numbers | |:---:|:-----------:| | 1st | 3, 5, 7 | | 2nd | 11, 13, 17 | | 3rd | 19, 23, 29 | | 4th | 31, 37, 41 | | 5th | 43, 47, 53 | | 6th | 59, 61, 67 | | 7th | 71, 73, 79 | | 8th | 83, 89, 97 | | 9th | 101, 103, 107 | At any time between now and the start of your next turn, you may roll dice from your variable pool. Write one or more equations that uses every result of the rolled dice as well as addition, subtraction, division (drop remainders), and multiplication and simplifies to a unique<!--unique so you can't make ten different equations that are slightly different and all simplify to the same number.//--> target number for the spell level. You may choose to roll more dice from your pool at any time, but once a die is rolled, it must be used in your equation. As long as you have maintained concentration, you may cast the spell at the start of your next turn as a bonus action.<!-- The bonus action is intentional here for the not casting 2 levelled spells in a turn rule. //--> When you do, you may choose one of the additional effects for the spell for each prime constant you found an equation for using the dice rolled from your variable pool. * *Surge.* The spell's level is increased by 1, up to your maximum spell slot level. This does not use a higher level spell slot. * *Spin.* The spell bounces, hitting an area that would normally be impossible. Choose a point in the spell's range. The spell is cast from that point rather than from you, and requires line of sight from that point. * *Pierce.* Roll a variable die. If the spell requires a saving throw, one target of your choice has a penalty on that saving throw equal to the result. ___ > ##### No Calculators! > This subclass is intended to be used without calculators or scripts to solve its math questions. If you aren't interested in doing math while you play Dungeons and Dragons, this probably isn't the subclass for you. * *Blast.* The spell uses raw magical energy rather than its traditional effect. Any damage the spell deals is Force damage rather than its usual type. One creature of your choice that takes damage from the spell is knocked prone. <!--This was originally just force damage, but the knockdown was added to bring it up to the level of other spells.//--> * *Insist.* The spell rebounds if it misses. Once if you miss an attack roll with the spell, you can make the attack again against the same target with disadvantage. <!--This has a lot of synergy with lucky.//--> * *Safeguard.* The spell becomes more difficult to break. The spell's level is increased by 2 for the purposes of being affected by the *Counterspell* spell. You regain all expended dice from your variable pool whenever you take a long rest. <!-- This is the meat of the subclass, and is largely based around the (somewhat infamous) pathfinder feat Sacred Geometry. While that feat does some things well, it also has a lot of issues, so I made a pros/cons list to avoid making the same mistakes the pathfinder designers did. *Pros* * The math puzzle generated is random. The other math feat from pathfinder (arithmancy) makes the mistake of allowing the player to pre-solve the math puzzle it presents for each spell, meaning it's basically a flat boost in play sessions. * It has some drawback to use (increased casting time), so you need to make a deliberate choice to use the feat. *Cons* *It scales too well with knowledge(engineering) ranks. The likelyhood of it generating a solveable puzzle is fairly low even for 1st level spells with only the required ranks of knowledge(engineering), while at higher levels, higher level spells are guaranteed to have a solution. *The spell can outright fail, wasting spell slots and actions. This is a balancing point for the feat, but it can kinda suck at low level to waste a spell slot doing nothing when combined with the above point. *Metamagic is sorcerer's domain in 5e, so we won't be using metamagic effects here; people don't like the UA onomancer for a reason. Computational casting should do things that are distinct enough from metamagic to retain the sorcerer's identity. Note: I basically ended up going back on this because I couldn't think of meaningful ways to impact spellcasting that weren't metamagic-like and also weren't strict DC buffs or similar (which would be kinda broken.) Surge fits this bill, but is limited in the spell level not being above your highest level slot, so I think it's probably ok balance-wise. *It eats game time. Because the calculation is supposed to be performed on your turn, other players have to wait for you. Computational casting will avoid this by having you start the casting action on your turn, and then make you finish the calculation by the time your next turn starts. //--> #### Logical Spells Starting at 6th level, you learn to use your mathematical skills to ensure the consistency of your spells. After you roll damage for a spell but before the outcome of the roll is determined, you may choose to replace any number of the dice rolled with variable dice. Spend one variable die for each die replaced and roll the variable dice. You must use the new result. #### Rejuvenated Equations At 10th level, you've learned how to power through difficult equations even when mentally exhausted. When you roll initiative and have less dice in your variable pool than your intelligence modifier, you regain variable dice up to your intelligence modifier. <!--Yeah, this comes pretty early compared to similar abilities, but honestly, those abilities are godawful capstones and some of the most disappointing design decisions in 5e. //--> #### Calculating Mind Beginning At 14th level, you've learned there are numbers larger than 6.<!--I should really change this but I think it's funny cause I'm a mongoloid. I'll probably make a second version of this document that's less serious so I can say things like "Mathmagician" with a straight face..//--> Whenever you roll a variable die, you can choose to roll a d8 rather than a d6. \pagebreak ##### Example for Computational Casting: Computational casting is an ability with a lot of moving parts, so lets go through an example. Henry is a 7th level Arithmancer. On his turn, he decides to start casting Fireball using a third level spell slot with computational casting. His turn then ends. He has until the start of his next turn to make equations for all three target numbers: 11, 13, and 17. First, he's going to need to roll at least three of his variable dice. He gets a 5, a 2, and a 4. This can't be used to make any of the target numbers, so he rolls another die: a 3. Henry comes up with the equation (5 · 3) + (2 · 4) = 23. Henry still has some time before his turn starts, so he tries to make another equation for one of the other numbers. After some computation, he comes up with ((3+4) · 2) + 5 = 19. Just as he finishes his math, it's his turn. He starts his turn by using a bonus action to cast the fireball he's been preparing. Because he found two equations, he chooses two effects: Surge and Blast, and casts Fireball at 4th level dealing force damage.