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[ehunt]

This keeps coming up, and I keep forgetting to post about it when I'm not playing a mafia game (I feel a little weird posting mafia theory while playing a mafia game). Anyway, why an odd population is more pro-town than an even population with one extra townie.

Counting by "how many mislynches can town afford?" is a very useful way to think clearly about some theory issues - my friend explained it to me.

Suppose there are an odd number of people. I am going to say 7 town and 2 mafia, but the principle is always the same. Then town has a starting mislynch number of 2. If town no-lynches, there will be 6 town and 2 mafia the next day, which has a mislynch number of 1. Clearly no-lynch is a mistake. The town may as well have picked someone to lynch at random. It would have the same effect on the mislynch number, and give a free shot at scum.

On the other hand, suppose we started with 8 town and 2 mafia. The mislynch number is still 2. Voting no-lynch strictly decreases the probability of a mislynch from 8/10 to 7/9. Therefore, a no-lynch vote is good.

[Tables]

If you know that there will be exactly one night kill, this is useful. However, power roles (especially in RMM games, but they're a whole other class) can really scupper this logic. Firstly a doc save can suddenly increase your mislynch number (or well keep it the same as the previous day if you had a mislynch then). Secondly a vigilante, or Killer, can make it much harder to apply.

It definitely should be applied however in the lategame. With 4 or 6 people left and no indication of a doctor/Vig/Killer being alive, then a no lynch is definitely the right choice. This can lead to happily ever after scenarios, though, where both town and mafia don't want to kill (if there's a cop alive that isn't the case), but that's a whole other issue.