# Werewolf Statistics

Here are the results of some simulations I ran. I used the simplest possible setup: Given N players (including the moderator), and X werewolves, and assuming that lynchings are always completely at random, what are the chances that the humans will win?

Remember, these values are not representative of actual games. They assume that all the humans are entirely stupid -- werewolves always kill humans, but humans lynch entirely at random, and the seer never pays attention to his visions. In actual games, the humans' chances will be higher. How much higher is unknown. I expect that humans' advantage (over chance) is stronger in longer games, since they have more time to gather information and the seer has more visions.

The first notable result is that games with an even number of players (including the moderator) really suck for the humans. For example, it takes a 16-player even game to gives the humans the same chance as a 11-player odd game, but a 13-player odd game is considerably better than both. (These are two-wolf games I'm talking about.) This is probably because an even game always ends with a nighttime murder, and an extra murder is always to the advantage of the wolves; whereas an extra daytime lynching could help either side.

The main reason I did simulation was to estimate when to add a third wolf. If we figure that 9 or 11 players is ideal for a two-wolf game, and we assume that these probabilities actually means anything (heh heh), then an ideal game has a human-win chance of 0.23 to 0.29. (Again, for completely stupid humans.) So a three-wolf game is best if there are 17 or 19 players. And a four-wolf game might be best with 27 players -- but that's stretching the simulation way too far, since a 27-player game would be incredibly long and the humans would gather a huge relative advantage.

And you might be able to play a one-wolf game with six players, but again, the even/odd difference makes that prediction rather shaky.

Try it and see.

```(one wolf)
3 players: humans win 0
4 players: humans win 0
5 players: humans win 0.334
6 players: humans win 0.250
7 players: humans win 0.466
8 players: humans win 0.374
9 players: humans win 0.544
10 players: humans win 0.453
11 players: humans win 0.593
12 players: humans win 0.508
13 players: humans win 0.630
14 players: humans win 0.548
15 players: humans win 0.659
16 players: humans win 0.580
17 players: humans win 0.682
18 players: humans win 0.607
19 players: humans win 0.700
20 players: humans win 0.629
21 players: humans win 0.716

(two wolves)
5 players: humans win 0
6 players: humans win 0
7 players: humans win 0.133
8 players: humans win 0.083
9 players: humans win 0.229
10 players: humans win 0.157
11 players: humans win 0.299
12 players: humans win 0.215
13 players: humans win 0.352
14 players: humans win 0.264
15 players: humans win 0.395
16 players: humans win 0.305
17 players: humans win 0.430
18 players: humans win 0.339
19 players: humans win 0.460
20 players: humans win 0.370
21 players: humans win 0.485

(three wolves)
7 players: humans win 0
8 players: humans win 0
9 players: humans win 0.057
10 players: humans win 0.031
11 players: humans win 0.115
12 players: humans win 0.069
13 players: humans win 0.164
14 players: humans win 0.106
15 players: humans win 0.207
16 players: humans win 0.140
17 players: humans win 0.245
18 players: humans win 0.170
19 players: humans win 0.278
20 players: humans win 0.199
21 players: humans win 0.306

(four wolves)
9 players: humans win 0
10 players: humans win 0
11 players: humans win 0.025
12 players: humans win 0.012
13 players: humans win 0.058
14 players: humans win 0.031
15 players: humans win 0.090
16 players: humans win 0.052
17 players: humans win 0.122
18 players: humans win 0.074
19 players: humans win 0.151
20 players: humans win 0.096
21 players: humans win 0.178
22 players: humans win 0.116
23 players: humans win 0.202
24 players: humans win 0.136
25 players: humans win 0.225
26 players: humans win 0.154
27 players: humans win 0.245
```

Last updated August 14, 1997