I believe a doctor claim right away is awesome sauce, and is officially the D1 ashersky plan.
Why? Glad you asked...
1) It reduces the lynch pool. Each town player is looking for 4/12 bad guys today. Already nice odds. Each town player that isn't the doctor gets to instead look at 4/11 players, which is better. The doctor gains nothing and is still looking at 4/12, but the overall chances have gone up.
2) If we have multiple doctor claims, we catch scum.
3) There is WIFOM for the night kill, no matter what scum!liopoil says. It is impossible for either team to know if the other will shoot the doc. They cancel each others' kills. I'd give good odds that the Doctor lives, and possibly saves someone else.
4) The doctor is a weak PR here. Doctors are weak anyway, and no difference here. Let's go worst case: VT lynch today. We go into N1 with 2 kills, each of which have 10 possible kill targets. The doctor needs to choose 1/11 to protect. He has two chances to protect, though. I don't know how to include the odd possibility of both scum teams and doctor all targeting the same person and resulting in a death. No matter what, the doctor can only stop one kill anyway.
So, I think the doctor claiming works well.
Hmm.
1) If the Doctor is run up to L-1, he will claim. He won't get lynched. And we have the benefit of his almost-wagon to help us decide where the lynch SHOULD fall.
2) Yes. But that's not going to happen Day 1. Scum won't counterclaim Doctor unless they can win the game by doing so. I.e., in the late game where, if town mislynches, they lose. Otherwise, they're just trading 1 scumplayer for the Doctor - and in a game where there are two small scumteams (like here), that's a losing proposition for scum.
3) I agree with this point. ash, do you think the Doctor has a
better chance of living through the night if he claims? Note, however, that this WIFOM falls apart mid-game once one scumteam is eradicated; the Doctor will die immediately after that happens.
4) Unless I am misreading the rules, the doctor's protection does NOT transmute a mafia crosskill into a death. I.e., if the doctor and both mafia teams all target the same player, that player does NOT die at night. Separate point: the doctor is more useful later in the game when he has a higher chance of successfully blocking a kill (because there are fewer targets for him to choose from).
So I am not convinced that the best plan is for the doctor to claim right away.