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So here’s a fun scenario that’s going to play out Saturday: A magician with a rat familiar is going to visit the Silvery Eel. What do you think happens to the rat? Does it fall under the gnagana’s sway? I have some devious ideas, but I don’t want to screw over a 1st-level PC too badly.
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I guess how far away it gets and if it strays too far from them?
Would the other rats steal it? Maybe. They might be just as likely to kill it. It's not of their brood.
I had a necromancer send an undead cat into the walls and it got killed. They might have had a rat as well.
Those aren't a familiar and not really of interest to gnagana. Being dead and all.
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I would imagine that the connection to the sorcerer would protect the rat from the gnagana's influence, possibly even allow for the sorcerer to glean information if the daemon tries to control it (if they need hints basically), but that would also make the familiar a target for the gnagana's rats so it might be in danger of assassination.
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What I ended up going with was increasing skittishness in the rat familiar. When the magician first arrived at The Silvery Eel, the rat seemed a little agitated. Its anxiety became more pronounced as the party delved deeper. When they finally confronted the gnagana, the familiar failed a morale check and fled, depriving the magician of its bonus hit points. It did eventually return after the gnagana had been destroyed, because I didn’t want to screw a 1st-level PC too badly.