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The spell Melf's Acid Arrow does 4d4 on hit and 2d4 next turn (I'm ignoring what happens for a miss). If you roll a 20 for your spell attack roll, you double the 4d4 to 8d4.

What about the 2d4 next turn? Does that get doubled too or does that just stay at 2d4 because it occurs on the next turn?

I know that How does extra damage work for critical hits? covers additional kinds of damage during a critical hit, but this is the same substance that did critical damage, continuing its damage in a later round.

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    \$\begingroup\$ @SevenSidedDie I am skeptical that the two questions are identical. The linked question deals with damage as part of the same attack and this one is about subsequent damage effects on the next round. I admit they could be related but don't think they are identical as I even found specific information from Crawford about additional damage. Also, the answer I was about to post will not fit into the other one. \$\endgroup\$ – Slagmoth Nov 27 '17 at 16:25
  • \$\begingroup\$ The other is about both: damage that is + to an attack, and damage that is cause by successful attack but happens later (e.g. poison). That covers this I think. \$\endgroup\$ – SevenSidedDie Nov 27 '17 at 16:28
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    \$\begingroup\$ Poison damage happens on the same round and is resolved with the same attack, is it not? Unlike previous editions where it would deal damage again after 1 minute. \$\endgroup\$ – Slagmoth Nov 27 '17 at 16:31
  • \$\begingroup\$ I see what you're getting at: that the additional damage is in a different round is the distinction here. I'm pretty sure that difference doesn't change the answer, but that would be judging the close by the answers rather than by the question, which is the wrong way around. Okay! (I'm also going to give the question a small edit to mention the other question and point at that difference overtly, for the benefit of future readers.) \$\endgroup\$ – SevenSidedDie Nov 27 '17 at 17:17
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    \$\begingroup\$ @SevenSidedDie I'm happy with what you've added, that does indeed reflect the purpose of my question. Thanks! \$\endgroup\$ – NathanS Nov 28 '17 at 8:42
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There seems to be intent that it is not doubled, as evidenced by the Green Flame Blade question below:

In a tweet Crawford specifically answers a question about the subsequent damage on Green Flame Blade.

Question:

If you critically hit with the attack part of Green Flame Blade, and are greater than level 5, do you roll extra dmg against the 2nd target?

Answer from Crawford:

The splash damage of green-flame blade isn't affected by the attack critting. Think of the attack as process X & the splash damage as Y

This leads me to believe that the only part of a spell attack that is doubled is the part that is dealt as part of the actual attack roll. As the subsequent round's damage would be the 'Y' in this instance.

I went through the podcasts and couldn't find anything else, mostly the spells section dealt with targeting in the one from Jan 17, 2017.

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    \$\begingroup\$ Yeah I agree, this translates to the 2d4 perfectly. Deleted my answer since it has been prove false. \$\endgroup\$ – Miatog Nov 28 '17 at 13:46
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It gets doubled

The rule for critical hits is:

When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together.

The 2d4 are part of “the attack’s damage dice” so they get rolled twice.

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