TWG XXXVI SOS Brigade Member Sign Ups: The Melancholy of Haruhi Suzumiya

[Bird]

Being all ninja MG again.

From a mathematical standpoint only, this game is HEAVILY towards the mafia side. If the game is played out randomly the formula for the wolves chances of winning is equal to the number of wolves divided by the square root of other players.

So..
1 wolf.. 4 humans
2 wolves.. 8 humans
3 wolves.. 36 humans
4 wolves.. 64 humans

You can see how it would quickly grow.

I realise that this is if people did random votes and didn't put thought into the game. But it would also happen with perfect players because they would have to do random votes as well. If you do the math on this game. 3/sqrt(9) = 1. By random votes the wolves would win every time. So, there should either be card flipping or a change in the wolves/humans ratio.

(Note that the probability gets thrown out of whack when you throw seers and guardians in.)

Anyways. That's my input. I did put a vote for cardflipping yes as well (which is a surprise to myself). As much as I'd like to play, I'm incredibly busy right now and my internet hasn't been reliable lately.

Bump.

MG, do you mind telling me how you came to the conclusion that that formula was correct? Let's think of a hypothetical game with 1 wolf and 5 humans. Your formula says that the wolf should have a 44% chance of winning if the humans lynch randomly. However, that isn't really the case!

There are three outcomes for this game.

1: Wolf is lynched day 1 (5 players alive). Probability = 1/5 - Human Victory
2: Human is lynched day 1 (5 players alive), Wolf is lynched day 2 (3 players alive). Probability = 4/5 * 1/3 = 4/15 - Human Victory
3: Human is lynched day 1 (5 players alive), Human is lynched day 2 (3 players alive). Probability = 4/5 * 2/3 = 8/15 - Wolf Victory

So with random lynches, wolves will win 8/15 of the time (53%) rather than the formula's 44%.

Also, take that game you mentioned where there's 9 humans and 3 wolves. The formula says the wolves would have a 100% chance of winning, but that can't be right since there are random outcomes where the humans may lynch all the wolves. Isn't it a possibility (a remote one) that the wolves would be killed on days 1, 2, and 3? If you compute the probabilities for all 12 outcomes of that game, you'll see that there's actually an 83.5% chance that the wolves would win if everybody voted randomly.

I'm not just posting this to prove you wrong or anything, I'm just really curious as to how you got that formula!