Blood Mage

Arcane Transfusion

At 2nd level, you have learned on how to draw out the essence of magic from your own blood. Your blood can replace the Verbal, Symatic and Material Components. By reducing your Maximum Hit Points by half you can remove either a Verbal or Symatic Component to the next spell you cast within 1 minute. This Max Health reduction cannot exeed 25 Hit Points on each use. If it would, it reduces your Max Hit Points by 25 instead. By reducing your Maximum Hit Points, you can use your blood in place of Material Components. By spending 1 Maximum Hit Point You reduce the Material Gold requirement by 2 Gold Pieces. If you reduce the amount to 0, you remove the Material Component altogether for that spell. You must begin casting that spell within the next 1 minute or the effect is lost. You recover your Maximum Hit Points when you finish a Long Rest.  You cannot use this feature if you have 1 Maximum Hit Point. 

In addition, when you gain a level in this class, you gain an additional 1 hit Point upon leveling. This works retroactively for the previous level in this class. 

Blood Sacrifice

Also at 2nd level, you can reduce your Maximum Hit Points by 5 to target a creature within 60ft of you. They recover 1d6+ Constitution Modifier hit points. For each 5 additional Maximum Hit Points you spend, you increase the pool of dice by 1d6.

Blood Infusion

Starting at 6th level, you can transfer your blood into the actions you take. When you would make an Ability Check, Saving Throw, Attack Roll or Damage Roll, you can reduce your Maximum Hit Points up to an amount equal to your Constitution Modifier. When you do, add that amount to the roll. 

Blood Clot

Beginning at 10th level, the blood you channel helps ward off harm. While your Maximum Hit Points are reduced by one of your Blood Mage features, you gain resistence to Necrotic damage and while you are not wearing armor, you add your  Constitution Modifier to your Armor Class. 

In addition, your Arcane Transfusion becomes stronger. When removing a Verbal or Somatic Component, the Max that it can be reduced is set to 15 instead of 25 and the gold value of your blood increases from 2 gold to 10 gold. Lastly, the amount of hit points you gain at each level increases from 1 to 2 and works retroactively for each of your Wizard levels.

Bound In Blood

At 14th level, you have connected with your blood magic at a stronger level. When you take a Short Rest, your Maximum Hit Points reduced by your features are recovered to their normal Maximum amount. In addition, you can reduce your Maximum Hit Points tohave the ability to cast spells you dont have prepared. By reducing your Maximum Hit Points by 3 per Spell Level, you can choose a spell that you dont have prepared and temporarily prepare that spell. That spell remains prepared for a number of hours equal to your Constitution Modifier. 

Mathemagician 

Mathematical Studies 

When you choose this subclass at 2nd level, you become proficient in Investigation and you can make Investigation checks that use numbers or require calculations as a Bonus Action.

Mathematical Analysis 

Starting at 2nd level, you gain the ability to analyze and calculate probabilities, allowing you to gain insights into your opponents and the battlefield. You can use an Action to make an Intelligence (Investigation) check contested by their Deception check. On a failure, you cannot use it on this creature again for 24 hours. On a success, you gain one of the following insights:

• You learn the number and die level of hit die of a creature within 60 feet of you.
• You learn the AC of a creature within 60 feet of you.
• You learn the saving throw bonuses of a creature within 60 feet of you.

You can use this feature a number of times equal to your Intelligence modifier (minimum of once), and you regain all uses of this feature after finishing a long rest.

Geometric Patterns  

At 6th level, you have unraveled the ability to change your Area of Effect spells. When you cast a spell that targets an area with a radius of 5ft or more, you can apply your Geometric Patterns to it instead. You choose a number of 5ft cubes equal to your Intelligence Modifier + twice the spells level (min. 3). These become the new area of effects for your spell. They must still stay within the spells range, each one must connect to at least one other one horizontally or vertically and be within your line of sight. All other rules of the spell happen as normal. If the area of effect can be moved, it all moves in the same pattern as it normally would.

Equation Casting

At 10th level, you can use complex equations to cast spells. When you prepare your spells each day, you can choose to prepare a number of equation spells equal to your Intelligence modifier. These spells do not count against your total number of prepared spells. You can only prepare these spells for spell levels of which you can cast. Equation spells can be found at the end of this class.

Probability Manipulation 

At 14th level, you gain the ability to manipulate probability. As a Reaction, you can roll a d20. You can choose to add or subtract a number from the roll equal to your Intelligence modifier + proficiency bonus. This ability can be used to influence any d20 roll made within 60 feet of you, including ability checks, attack rolls, and saving throws. The target must be willing or unaware of your manipulation. This ability cannot be used to influence rolls made by deities or other entities with divine power. When you do this, you can choose to use your roll or allow the targeted creature to make their own roll.

You can do this a number of times equal to your Intelligence modifier. You regain all expended uses on a Long Rest.