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Does the AC bonus from Bracers of Defense stack with the AC calculation from the mage armor spell?

I'm asking this because there is some contention behind the ruling of this combo, between two designers. In 2016, Mike Mearls states that they do not.

However, in 2017, Jeremy Crawford says the opposite. Twice, in fact.

I also question whether donning the Bracers of Defense counts as putting on armor, as the mage armor spell stipulates that donning armor will dismiss the spell. In my opinion, it does not, as the bracers are classified as a Wondrous Item, not as an armor piece, despite actually being a piece of armor. For reference, here are the item/spell quotes:

Bracers of Defense:

While wearing these bracers, you gain a +2 bonus to AC if you are wearing no armor and using no shield.

Mage armor:

You touch a willing creature who isn't wearing armor, and a protective magical force surrounds it until the spell ends. The target's base AC becomes 13 + its Dexterity modifier. The spell ends it if the target dons armor or if you dismiss the spell as an action.

How should our DM rule this, RAW?

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Yes, they do stack

Jeremy Crawford is the official rules arbiter for 5e, not Mike Mearls. Even so, the response by Mearls that you linked misunderstands what the Bracers of Defense do. Mearls' response:

don't believe so. AC buffs only if they are expressed as a bonus (+2 to AC), rather than a formula or number (AC 13 or AC 12 + Dex)

As the replies to his tweet point out, the description of the Bracers of Defense says "you gain a +2 bonus to AC"; they don't provide a different AC calculation, so the two do stack.

Bracers aren't armor

First of all, to point out the obvious: if bracers were considered armor, the Bracers of Defense would never provide any benefit because they'd disqualify their wearer from gaining their own benefit.

Secondly, bracers in general are not considered armor. The only things considered armor (besides the "natural armor" of some creatures) is the list of items on the Armor and Shields tables, or an item that is otherwise listed as being armor. Shields are not armor, and neither are wondrous items.

The Bracers of Defense are listed as a wondrous item. Wondrous items are their own separate category, as Jeremy Crawford confirms here (in response to a question about whether druids can use the Bracers of Defense):

A magic item has a category, such as armor, weapon, or wondrous item. A druid’s taboo against metal armor would extend to magic items in the armor category only.

(In fact, the "wondrous item" classification is specifically applied to magic items that are neither weapons nor armor. Any magical equipment that doesn't fit into either of those two categories is listed as a wondrous item.)

Bonuses always stack unless they're from duplicates

As Jeremy Crawford points out here:

Bonuses stack unless they are from the same game feature (spell, class feature, magic item, etc.).

Does that mean you can get a bonus to AC from either a magic shield or magic armor? and not both?

I was referring to more than one of the same magic item, not magic items in general.

Multiple bonuses to AC from different Magic Items (cloak of protection, +1 shield, etc), would they stack or not?

Bonuses stack unless they're from duplicates of something (2+ castings of the same spell, 2+ copies of the same magic item, etc.).

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The effects stack.

The Bracers are not armor. Armor is a specific subset of items, and the Bracers, as you note, are a Wondrous Item rather than any of the items that appear in the list of armor.

Also note that the Bracers don't work if you are wearing armor; if they counted as armor then they would be nonfunctional as they would invalidate their own effect.

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