AbOrigineMundi

When playing the game of werewolf, it can be useful to predict the number of rounds the game will take. A round is defined as a night plus a day. In each round, both parties play once.

We assume that

• players die because of werewolf bite or hanging (no other characters can kill players)
• werewolves kill one villager every night
• villagers hang one suspect every day
• there is no information: the villagers hang a random suspect every day, they do not have actual information about who the werewolves are.

Stated differently, the vanilla rules apply and no turns are lost. (Interestingly, there is a situation in which both parties might think it is better not to kill a fellow citizen during that round.)

Types of endings

Basically, there are four types of endings, two common and two uncommon ones:

Common endings

• slow daytime massacre: werewolves and villagers keep murdering each other unt
  

  The expected number of playing rounds, depending on the number of villagers and the number of werewolves.

  il werewolves and villagers are about the same number. This type of game takes longest to play.

• slow werewolf extinction: werewolves and villagers keep murdering each other until the last of the werewolves has been found. This type of game takes long to play.

Uncommon endings

• quick daytime massacre: only when the initial number of werewolves is big compared to the total number of players (around 50%). Unusual in normal play, since this does not make for a fun game: the werewolves will always win such games.
• quick werewolf extinction: after a few rounds, werewolves have been found. If the assumption of “no information” is valid, this type of game ending is not common.

Rule of thumb: for any “normal” number of players (8 to 30) with a sensible number of werewolves (there should be far less werewolves than villagers), calculate the expected number of rounds as follows:

• If there is one werewolf, divide the number of villagers by 3 and add 1.
• If there is more than one werewolf, divide the number of villagers by 2.