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Numbers, Part 1
The following lists probabilities for the town winning in different setups. All are basic games, with Mafia and Townies only, starting with Night and assuming random lynchings and night kills. The numbers probably do not reflect what the actual outcome would be if real games were played, as they don't account for the Mafia giving themselves away through bad logic. Only games with probabilities between 30% and 70% are included (except for 5 players, where 25% is the closest to 50%). Note that the probability for the Town drops when there are an odd number of players to start with.
| # of Players | # of Mafia | Town win % | ||
|---|---|---|---|---|
| 4 | 1 | 33.33% | ||
| 5 | 1 | 25% | ||
| 6 | 1 | 46.67% | ||
| 7 | 1 | 37.5% | ||
| 8 | 1 | 54.29% | ||
| 9 | 1 | 45.31% | ||
| 10 | 1 | 59.37% | ||
| 11 | 1 | 50.78% | ||
| # of Players | # of Mafia | Town win % | # of Mafia | Town win % |
| 12 | 1 | 63.06% | 2 | 35.21% |
| 13 | 1 | 54.88% | ||
| 14 | 1 | 65.9% | 2 | 39.49% |
| 15 | 1 | 58.11% | 2 | 30.5% |
| 16 | 1 | 68.17% | 2 | 43.01% |
| 17 | 1 | 60.72% | 2 | 33.95% |
| 18 | 2 | 45.97% | ||
| 19 | 1 | 62.91% | 2 | 39.52% |
| 20 | 2 | 48.51% | 3 | 30.66% |
| 21 | 1 | 64.76% | 2 | 50.71% |
| 22 | 2 | 50.71% | 3 | 33.21% |
| 23 | 1 | 66.36% | 2 | 41.82% |
| 24 | 2 | 52.65% | 3 | 35.49% |
This table assumes (for some reason) that the moderator is also a player. In a game with 2 town and 1 scum, the probability of a town win is 33.33%. With this revision, it is also easier for town to win if the number of players at the beginning is even.
See also ...and they all lived happily ever after.