I disagree. On the first day, if everybody just randomly votes, there is a 7/9 chance that a town member would get lynched. I do not want to vote randomly for this reason. If I see someone acting scummy, I will vote for them. If not, I would rather wait one night to get some vital cop information (assuming we have one) and analyze the night kill. On day two, I would rather be 1 townie down than 2 townies down.
I dont think relying on roles is a very good idea. Scumhunting is a key part, and a mislynch would give us loads of info, so a no-lynch vote is not a very good idea.
I am not relying on the cop role. I was just saying that it would be a huge benefit to wait a day and get a cop result if there was one. I am a very logical and mathmatical person, so when I read day one, I see this:
there is a 2/3 chance there is a cop in this game. and 2/9 of the players are mafia if we lynch on day 1, and we get the 2/9 chance to lynch mafia, meaning that in the next night, there will be an 1/12 chance of a cop getting the mafia. But there is a 7/9 chance we will lynch town, and if that happens, there is a 1/6 chance that the guard will get scum. In total, if we randomly vote on day one, there is a 1/54 chance that both mafia will be lynched/discovered by cop. 7/18 chance of getting 1 mafia lynched/discovered by cop. And a 16/27 chance of getting a town lynched and no mafia discovered by cop.
In percentages, if we randomly vote day one, (and assuming the mafia kill night 1 and don't kill the cop)there is a:
2% chance of lynching a mafioso day one, and the town cop finding the other one (one townie killed, 2 mafioso killed)
13% chance of a mafia getting lynched and the cop finding a townie night 1 (one mafia killed, 1 townie killed)
16% chance that a townie is lynched day one, and the cop finds a mafioso during the night (2 townies killed, one mafioso killed)
69% chance a townie is lynched and the cop finds a townie during the night (2 townies killed)
Note: this includes the 2/3 chance of a cop being in the game, I tread an absent cop the same as a cop finding a townie since for this purpose, they are the same
(please correct me if you see any mathematical errors)
the odds are stacked against us for finding a mafia to lynch. I would rather minimize our casualties day one, then ruthlessly attack the mafia every day afterwards.