- May 8, 2013
I was under the impression that only 16 people were in this game. That is how I came to my previous calculation 16/4 = 4 wolves. Did someone join the game after that?If my reasoning is correct, we need to get a wolf lynched tonight. If there's still four wolves alive tomorrow, and they play their cards correctly, it becomes mathematically impossible for the village to win. Which, oddly enough, seems to argue in favor of lynching as many random people as possible in the hopes that one of them is a wolf.
Given that we do lynch a wolf tonight, how many more villagers can we afford to lynch?
0: Tomorrow, we'd have six villagers and three wolves. Definitely winnable, at least if we can figure out who they are.
1: Five villagers and three wolves tomorrow. Winnable.
2: Four villagers and three wolves. Winnable if we lynch two of those wolves tomorrow, and the last one the next day.
3: Three and three. Only winnable if the wolves mess up.
I propose that we lynch exactly three people today. That gives us our best shot at eliminating one wolf (which is critical), while still permitting a town victory, even if the wolves don't cooperate. Anyone who tries to thwart this plan will garner themselves a bucketload of wolfpoints in my eyes.
Here's a list of the currently living players:
... uhh, that's twelve people. If four of those are wolves, then there are eight villagers left, not seven. @Robijnvogel, check your math.
- Someone Else 37
A solo mislynch tonight would put us at six and four tomorrow. Might still be winnable, but we'd definitely need to lynch a wolf tomorrow, and with only six villagers, we have a much smaller margin of error. And probably not much more information to go on.
Let's see... if we lynch three people at random tonight, each lynch has approximately a 1 in 3 chance of hitting a wolf. More specifically, the first lynch has a 4 in 12 chance; if that hits a villager, the second lynch would have a 4 in 11 chance of hitting a wolf, and if that fails, the third lynch would have a 4 in 10 chance.
4/12 + 8/12 * (4/11 + 7/11 * (4/10)) = 0.75454545...
4/12 + 8/12 * (4/11 + 7/11 * (4/10 + 6/10 * (4/9))) = 0.858585...
If my math is correct, we'd have a 75% chance of hitting a wolf by lynching three people at random. 86% by lynching four. We can do better than that, but only if we get input from *everyone*, so any wolves trying to get villagers lynched would be drowned out.
... On the other hand, *I* don't have much idea on who looks wolfy, so maybe it would be best to choose unfortunate victims at random. Any ideas on a wholly impartial random number generator that doesn't rely on anyone who might be a dirty wolf messing with things?
I think that your calculations are correct, however you fail to include that the villagers know with 100% certainty that they aren't wolves themselves. I think this improves our chances a little bit. Also, if the wolves know of our plan, I think they could easily misguide us into killing three citizens. (Maybe even killing a fourth while they're at it.)
I'll do some calculating, I guess.