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I know from this question that each PC rolls his or her saving throw against the cloudkill spell's poison at the start of each of his or her turns.
When calculating the damage a PC is dealt, is a new posion damage roll (5d8) made for each Constitution saving throw? Or, is one roll made when the spell would deal damage, then subsequently halved or not depending on the saving throw's success or failure?
When a creature enters the spell’s area for the first time on a turn or starts its turn there, that creature must make a Constitution saving throw. The creature takes 5d8 poison damage on a failed save, or half as much damage on a successful one. (SRD. 125)
There are two ways the effect can be triggered, either a creature:
And, when a creature does trigger the effect, they immediately:
The amount of damage is decided after the saving throw has been made by the creature and not before. So, it relates specifically to the creature that has triggered it, and made the saving throw, not any other creatures.
This is in direct contrast to 'Instantaneous' effect spells, which are not triggered by the target and deal damage once to multiple targets simultaeneously (ie. Burning Hands).
For evidence of this ruling, that you may consider authoratative, see this Crawford tweet on applying damage from other concentration spells which deal damage repeatedly.
But if you find this too labour intensive, with your DM's permission you could choose to take the average instead, or roll once and keep applying the same figure.
Beware, if rolling and keeping that figure, that the damage will be more extreme. A bad roll would nerf the spell for its whole duration, while a good roll that was applied consistently could seem overpowered. This could result in more metagaming - either from players knowing how much damage they'll take from a DMs spell in advance, or players deciding to drop concentration early, if they rolled poorly on damage, for their own spell.
A comprimise option, to save labour in crowded encounters, that avoids some of these issues, might be to roll damage once per round and apply that figure as necessary.
Roll each time
You can think of the dealing damage part as an instantaneous effect of the Cloudkill each turn. Each time the Cloudkill deals damage it is a separate saving throw and should be a separate damage roll.
Even without a saving throw, as seen on witch bolt (requires only a hit when cast and nothing else on consecutive turns), even if essentially the same spell separate instances of damages should be rolled each time.
Yes.
Whenever a creature enters the area for the first time or starts it turn in the area it makes a Constitution saving throw. Hence you would roll the damage then as well (half damage on successful save).
