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At 18th Level, Wizards of all Schools gain the "Spell Mastery" feature:

At 18th level, you have achieved such mastery over certain Spells that you can cast them at will. Choose a 1st-level wizard spell and a 2nd-level wizard spell that are in your Spellbook. You can cast those Spells at their lowest level without expending a spell slot when you have them prepared.

Meanwhile, at 2nd level, an Abjuration Wizard gains the "Arcane Ward" feature:

When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell’s magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has hit points equal to twice your w izard level + your Intelligence modifier. Whenever you take damage, the ward takes the damage instead. If this damage reduces the ward to 0 hit points, you take any remaining damage. While the ward has 0 hit points, it can’t absorb damage, but its magic remains. Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell.

Provided a player character picked the Wizard as his class and the Abjuration School of Magic: If he was to select Shield (1st-level abjuration) as the 1st-level spell for his Spell Mastery feature, could that Wizard in theory recharge the ward with 2HP/Turn for free, all day? Also, would this imply that, provided he had the time between fights (At most 2.3 minutes, 23 rounds with Lv20 and +5 INT) he could heal the ward up to full by casting shield at the start of every round out of combat?

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Yes it is viable but not with Shield.

Your best bet would to use Mage Armor, since it is a single action spell as opposed to the reaction of Shield that has specifics on when you are allowed to cast it (emphasis mine).

Casting Time: 1 reaction, which you take when you are hit by an attack or targeted by the magic missile spell

So unless you actually have someone hit you repeatedly you can't cast this spell all that often per PHB 196. At least by RAW.

A reaction is an instant response to a trigger of some kind...

This section goes on to say that the opportunity attack is one such instance of a reaction but you can't take it unless something would trigger that as detailed in all the descriptions of reactions. This why when you ready an action you are required to specify a trigger.

Mage Armor could be used as often as necessary to regenerate the ward, unless there is errata somewhere that changes the wording to slots as opposed to level. One thing to note is that spells with verbal components could be overheard and thus could give away position or spoil the element of surprise, so choose when to do this with care.

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  • \$\begingroup\$ Shield still works, it's just a lot more specific. If you have a lvl 18 wizard friend who took magic missile as his first level specialised spell, you can both spam these spells at one another and recharge your ward. \$\endgroup\$ – Valthek Jan 3 '18 at 7:25
  • \$\begingroup\$ Do this with a Deep Gnome from SCAG and take the Deep Gnome feat and you can have this feature at 4th level instead of 18th. They can cast non-detection at will, with no material components, as part of the feat... \$\endgroup\$ – Carey Sauerbrun Jan 3 '18 at 19:02
  • \$\begingroup\$ @CareySauerbrun Whereas this is true the query was specifically about the synergy between the two class features. I will keep this in mind though. \$\endgroup\$ – Slagmoth Jan 3 '18 at 19:15
  • \$\begingroup\$ @Slagmoth that's why I put it in a comment instead of an answer. It's not an answer to the question, but it adds to the information available. Since the question was asked in the manner it was, I made an assumption that the person was not familiar with this either. \$\endgroup\$ – Carey Sauerbrun Jan 3 '18 at 19:20

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