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Considering the fact that the +2 increase to a creature's Armor Class from the Haste spell is reasonably a result of the creature being "sped up" and thus having faster reflexes and dodging attacks better, similar to the AC increase from a creature's Dexterity modifier, would it be fair to say that this bonus should also apply to the illusory duplicates of the same creature resulting from a Mirror Image spell?

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No. Strictly speaking, haste does not improve the AC of your duplicates from mirror image.

Mirror image specifies:

A duplicate’s AC equals 10 + your Dexterity modifier

Haste increases your AC directly by adding a +2 bonus to it. It also grants advantage on Dexterity checks but it does not change your Dexterity modifier.

Since the duplicates from mirror image always calculate their AC based on 10 + dex mod, haste has no effect on the duplicates.

Note also that worn armor and other spells or effects that might affect your AC do not impact your duplicates' AC values.

That's not to say that it doesn't make logical sense to apply it in that way, but doing so would be a house-rule and is not covered by the rules as presented.

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No.

Mirror image states,

A duplicate’s AC equals 10 + your Dexterity modifier.

Haste only does the following:

Until the spell ends, the target’s speed is doubled, it gains a +2 bonus to AC, it has advantage on Dexterity saving throws, and it gains an additional action on each of its turns.

It does not change your dexterity modifier, so it does not change the duplicate's AC.

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