For a new project that I’m working on finalizing in time for the holidays, I’ve been looking into the ideal odds for a game of mafia/werewolf. Turns out, the odds of the werewolves winning is equal to the number of werewolves divided by the square root of the total number of players. Thanks, Wikipedia!
So, if you want to take a look at the Google spreadsheet I devised to figure out what the best numbers would be, here’s the link. Enjoy – and have fun lying to your friends before murdering them!
It may or may not have something to do with this little guy here...
The longer explanation, if you care
Since the ideal would be that the werewolves and the villagers have an equal chance of winning (or that either side has a 50% chance of winning), sometimes, the ideal number of werewolves is going to involve cutting some of your friends in half. And while the game is all about ripping friends to pieces, it’s best to save that for during the game – so you have to round. But the question is whether to round up or round down.
Ultimately, I decided the best course of action was to calculate the odds of the werewolves winning if you rounded up and if you rounded down. Then, I figured out which one was closer to a 50% chance of winning and go with that.
However, the mere math overlooks a much bigger issue: how good people are at the game. The math simply assumes that each day, the people are guessing randomly – and that at night, the werewolves are randomly eliminating villagers. In any good game, this just isn’t the case. (One of my friend, every time I’m a werewolf, looks at me and says, “Yeah. It’s Doug. He’s doing his tell.” The worst part is he won’t tell me was my damn tell is. Some friend…)
So, while the math may lead you to ideal games mathematically, it won’t lead you to perfect games that come right down to the wire every time. However, given that you assume that the werewolves can pick off the people who seem better at it – and that some of the villagers are better at reading players, this advantage probably about averages out.
But then you have special roles – and I’m not even going to try to figure out how those various roles affect the math. All I’ll say about that is this: in cases where the odds are in the werewolves’ favor, a special role or two would give the villagers a bit more of a chance – but calculating most of these mathematically would be really, really difficult.
And, so that you don’t have to scroll up to the top, here’s that link again.