Arcane Tradition
Notes from the Nails: been a while since we’ve done a wizard, eh? No prizes for guessing the inspiration here!
School of Arithmetick
Arithmeticians are particularly learnèd wizards who use numerical techniques to analyze natural phenomena and execute pinpoint magical attacks. Their skill with numbers extends into the metaphysical realm, warping the laws of probability and enabling them to achieve incredible efficiency in everything they do.
Mathematical Savant
When you choose this school at 2nd level, your arithmetical studies have begun to pay dividends. You have advantage on any Intelligence check made to perform mathematical calculations or solve numerical puzzles.
Stable Effect
Also at 2nd level, whenever you roll a d20, you can replace the d20 with 3d6. If the roll would be subject to a critical success or critical failure, these events only occur if all three dice land on 6 or 1 respectively.
Factorize Spells
At 6th level, you can perform calculations to modify your spells. As an action on your turn, you can factorize a spell that you are able to cast that normally targets one creature and does not have a range of self or touch.
When you take this action, you must select one statistic from the following list: HP, Strength, Dexterity, Constitution, Intelligence, Wisdom, or Charisma. Also choose 3, 4, or Prime. Then, examine the final two digits of the statistic you chose for every valid target within the spell’s range, including yourself and any friendly, neutral, or hostile creatures in range. A creature becomes a target of the spell if its statistic is a multiple of the number you picked; or if its statistic is a prime number and you chose Prime. You do not have to see the target or have a line of effect to it when you factorize a spell.
After you have factorized a spell, you must use your action on your next turn to cast the spell (if you are unable to cast the spell, such as by being incapacitated, the factorization is wasted). It then affects all of the targets that were selected on the previous turn (even if they have since moved out of range). However, a factorized spell’s power is attenuated: if creatures can make a saving throw to resist the spell’s effects, they have advantage on the save, and if a spell would restore hit points or grant temporary hit points, the number of hit points is halved.
Accrual
By 10th level, you are able to use minor magical charms to accrue tiny amounts of power with every step you take. For every 10 minutes you spend walking, you regain 1 hit point, and earn 1 copper piece and 1 point of XP.
Advanced Numerology
At 14th level, you have complete mastery of all things arithmetical. If, when making an ability check or saving throw, you beat the target DC by 10 or more, you can conserve some of the success, adding a 1d4 bonus to the next ability check or saving throw you make. Whenever you reduce a creature to 0 hit points, any excess damage you did beyond what was necessary to reduce them to 0 is also conserved; you can add half of the excess to the next damage roll you make. If you reduce more than one creature to 0 hit points simultaneously, you can store the excess from only one of the creatures of your choice.
Both of these bonuses can be stored for up to 1 minute, after which they disappear.
Sidebar: Prime Numbers
As a quick reference, the prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Changelog:
11/3/19: Factorize Spells: CR/Level removed from statistics
