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Alchemist's Fire is a kind of Adventuring Gear which you can throw to deal 1D4 points of Damage to a creature and set it on-fire, dealing 1D4 damage at the start of each of its turns. From Roll20 (and the SRD):

Make a ranged Attack against a creature or object, treating the alchemist's fire as an improvised weapon. On a hit, the target takes 1d4 fire damage at the start of each of its turns. A creature can end this damage by using its action to make a DC 10 Dexterity check to extinguish the flames.

Using a Crafting Skill, what would happen if a Character took a regular arrow and attached a vial of Alchemist's Fire to it, say with sinew, then a Rogue fired it from a bow?

Could the Rogue then use this to Assassinate and Sneak Attack a Target? Would a Critical from the Assassinate effect (Surprised Target) also apply to the Fire Damage, or would that be exempt?

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Yes, you get assassinate and sneak attack.

No, the critical would not apply to the fire damage.

Let us assume the DM allows you to craft this contraption, possibly giving it a -2 to hit or something of the sorts due to its unwieldy nature.

PHB, page 96, Sneak Attack:

Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

Sneak attack is applied on any attack roll with advantage as long as it is a ranged or finesse weapon. A bow is a ranged weapon.

PHB, page 97, Assassinate:

You have advantage on attack rolls against any creature that hasn't taken a turn in the combat yet. In addition,any hit you score against a creature that is surprised is a critical hit.

We have our advantage and critical against a surprised creature that hasn't taken their turn yet.

PHB, page 196, Critical Hits:

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... If the attack involves other damage dice, such as from the rogue's Sneak Attack feature, you roll those dice twice as well.

The key phrases here is when you score a critical hit. You would roll double the damage dice for the hit on the turn you hit the creature (including double the sneak attack damage), but at start of each of that creature's turns you would roll the 1d4 fire damage separately without doubling it.

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  • \$\begingroup\$ Now, how would damage from this be calculated? The same as the damage for the bow, or would I add the 1D4 Fire Damage on hit to the damage from the Bow? \$\endgroup\$ – SeraphsWrath Feb 18 '18 at 18:38
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    \$\begingroup\$ the 1d4 on its turn from being on fire wouldn't change but I don't think you answer whether the 1d4 of fire from the initial hit would double. \$\endgroup\$ – Tadhg McDonald-Jensen Feb 18 '18 at 19:05
  • \$\begingroup\$ I personally would not add 1d4 fire damage on the initial hit. If you refer to Alchemist's Fire you would see that even when you hit a creature with the bottle initially they take no damage. It's the lingering burning over time at the reagent burns their skin which deals the damage. Feel free to rule otherwise, but it would significantly buff the contraption and should be accounted for in crafting DC or time to craft. \$\endgroup\$ – Zac Francis Feb 24 '18 at 14:47

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