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Does the magical bonus of armor and a shield stack?

For example, would a PC with a +2 armor and a +2 shield be able to stack both bonuses?

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Yes

In D&D5 everything with a plus/minus stacks with every other thing with a plus/minus.

Things that set a value do not stack with other things that set a value but do stack with things that give a plus. For example, the Mage Armor spell sets your AC to 13 + DEX bonus; it does not stack with a draconic sorcerer's natural armor which also sets your AC to 13 + DEX bonus, however, either will stack with the Shield spell which adds +5 to your AC.

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  • \$\begingroup\$ Bonuses from the same source don't stack, though. You can't get extra AC from dual-wielding shields. \$\endgroup\$
    – nick012000
    May 20 at 1:18
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Yes.

Normal armour stacks with a normal shield, and there's nothing in the rules to suggest that this is different for magic items. It even allows you to wield/wear multiple of the same item, for example three rings of protection, granting you a total bonus of +3 to AC.

The only mention of multiple items with the same effect is the "multiple items of the same kind" section on page 141 of the DMG. This section states that you should use logic to decide whether a character can wear more than one of a given item. There's nothing in the book that suggests that multiple rings of protection cannot be worn at the same time (or even multiple cloaks of protection, for that matter), so if that's the case, there's no reason why you shouldn't be able to get the magic bonus from a magical armour and magical shield.

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    \$\begingroup\$ @Xanderh I don't think you can wear multiple of the same item: "Additionally, a creature can't attune to more than one copy of an item. For example, a creature can't attune to more than one ring of protection at a time." DMG P 138. \$\endgroup\$
    – Seyres
    Jun 20 '15 at 1:11
  • \$\begingroup\$ That is correct for attunement. So, for rings of protection etc, you can't. But for cloaks that don't require attunement, you can wear a couple. Not that it'll make much of a difference. \$\endgroup\$
    – xanderh
    Jun 20 '15 at 8:25
  • \$\begingroup\$ @xanderh Did 5e do away with the restriction of one item per slot, then? \$\endgroup\$ Nov 19 '15 at 22:32
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    \$\begingroup\$ @DanHenderson Yeah, no hard restrictions. The DMG does state that you can only benefit from two items from the same "slot" if it would make sense that you could wear them both. Two suits of armour wouldn't work (a lenient DM might allow a chain shirt and plate armour), and two pairs of boots or gloves wouldn't either, as paired items only work when you wear both. But 5e doesn't have actual magic item slots. \$\endgroup\$
    – xanderh
    Nov 20 '15 at 0:06
  • \$\begingroup\$ @xanderh The DMG was given an errata that prohibits multiples of the same magic item: “ Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items.” \$\endgroup\$ May 20 at 10:09

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