Can Prince safely claim Day 1? With 16 players alive, it is guaranteed that there is either a Knight, Physician, Court Wizard, friendly Alchemist in the game who can protect him.
Advantages:
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Protective classes don’t waste their time trying to find the Prince. They also don’t accidentally save evil classes.
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Investigative classes don’t waste time using a night to accidentally find the Prince. They can have a smaller list of suspicious players to investigate.
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Prince won’t be accidentally voted up to trial and executed by an Evil King.
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Prince can safely receive whisper claims from suspicious people (or everybody, why the hell not)
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The Prince won’t die randomly the first night.
Disadvantages:
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You have to trust that protective classes believe you or otherwise don’t screw up somehow.
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The Prince is subject to dangerous day abilities like Chilling Touch or Nightshade.
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Prince can die at night if there is an Unseen Enforcer or Sage.
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Possessors can Puppet Strings a BD player into you, potentially causing two BD deaths in one night (However, he may also target evil classes as well – this might be a good strategy to get the MM killed Night 1 every now and then.)
Dangers at night?: There are not a whole lot of threats during the beginning of the game. Even Empowered Reaper attacks or Possessor jumps still die to the Knight. Once a Knight dies, I’d expect NKs to try a shot at the Prince as they won’t immediately lose if they’re wrong when a Knight is guarding. However, there can be two Knights in a game, so even this fact might scare off NKs. Even if 2 Knights are dead, there is still the Ice Ward from the CW or Physicians and friendly Alchemists wanting to prove themselves. There are a lot of barriers to go through before an evil class can get to the Prince. This isn’t even accounting for the King’s guards which can also help prove his allegiance.
I’m not sure where I lean on the Day 1 claim. I’m inclined to think it is advantageous right now because it causes protective classes to be immediately useful Night 1 instead of playing whack-a-mole for a few days before finding a confirmed BD. Even if the Prince is poisoned, there are still a lot of class slots open for Physicians and Alchemists. Every now and then evils will try to kill the Prince claim anyway and fail, too. The real dangers are the Marshall, Sage and Enforcer.