I really, really need to go to sleep right now, but I 1) wanted to get this posted before I forget, and 2) am only having intermittent success with this hotel’s wifi, so…
During one of the Berlin Werewolf sessions, we had a slight disagreement over the wisdom of a particular strategy. In this particular game, the wolves didn’t kill anyone on the first night, and the village as a whole had to decide whether to lynch someone the first day. My argument was that lynching someone semi-randomly (based solely on activity during the lynching discussion) before the first murder would result in a higher probability of losing one of the special roles (we had both healer and seer) than waiting until the second day to lynch someone - i.e., we might kill the seer, leaving us with no way to get some valuable information.
On the looooong flight back to DC from Frankfurt, I ran a few numbers and came up with the following (all numbers assume 14 villagers, 1 seer, 1 healer, and 4 wolves, for 20 total players):
Where the first two deaths are a lynching followed by a murder (i.e., our situation), you get
- 1 wolf dying 20% of the time (1 in 5 chance of lynching one randomly on the first day)
- a virtual certainty of killing at least one dead villager, and a 63% chance of 2 dying
- a 10% chance of the seer dying
- a 5% chance of the healer being lynched, and another 5% chance of no murder in the night (if the healer isn’t lynched, it’s assumed she heals herself until given reason to do otherwise)
- An 0.5% chance of BOTH the healer and seer dying
So in that scenario, you run a 15% risk of losing the healer or the seer before either’s had the chance to do anything to help the village.
In the case where there IS a kill on the first night, or there is no lynching on the first day after a peaceful night, you get:
- An 88% chance a villager is killed
- A 6% chance the seer is killed
- A 6% chance of no murder (assuming self-healing, again)
So in this case, you’ve only got a 6% chance of losing a special-role villager before they can use their ability.
Obviously, there’s more to the story - a no-kill night this early in the game exposes the identity of the healer to the wolves (but not the other villagers), which can have dramatic effects later in the game. Also, after the first night kill all of this goes out the window, since you generally get much more information (reactions upon waking or hearing who the victim was, speculation as to why the victim was chosen, etc.) - these stats only apply when the lynchee and the murderee are both ‘random’, in that there’s been little or no reason in the game so far to choose them.