What are the rolls to determine whether alchemists fire catches a building on fire, and what would the skill check be to extinguish said fire?
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Unattended objects generally do not get a save against things affecting them, so throwing alchemist fire at a wooden wall or thatch room would instantly set it ablaze.
Extinguishing the fire would depends on the size of the building and how long it has been burning, but I would set the 1st round DC at the same as extinguishing yourself if you are hit with alchemist fire.
"If desired, the target can use a full-round action to attempt to extinguish the flames before taking this additional damage. Extinguishing the flames requires a DC 15 Reflex save."
I would say for a wooden structure the DC would increase by 5 each round and the fire spreads another 5 feet out from the splash zone. Hope this helps.
It helps greatly, thank you.
I think I may house rule this into a skill challenge, and give them a certain number of rounds to collectively come up with a number of successes and add in the potential of the fire spreading.