Wouldn't it be less risky if the cop revealed himself now and just asked to protect him every night? That way it would be harder for mafia to find the doctor, because the probability decreases.
I mean now have 2/8* (25%) probability to lose an important townie role at night. If mafia and the doctor knew who is the cop, there would be no sense for mafia to kill cop at night as he would be defended, so the probability to find the doc decreases to 1/7** (14%).
* 2 important town roles (doc and cop); 8 townies in total.
** 1 doc; 7 remaining townies, considering cop is not targeted at night.
I mean now have 2/8* (25%) probability to lose an important townie role at night. If mafia and the doctor knew who is the cop, there would be no sense for mafia to kill cop at night as he would be defended, so the probability to find the doc decreases to 1/7** (14%).
* 2 important town roles (doc and cop); 8 townies in total.
** 1 doc; 7 remaining townies, considering cop is not targeted at night.

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