I totally agree that it was a great experience! Having played Werewolf before, it has never been as much fun as this time, probably due to playing with other LessWrongians. I liked that we had very long and detailed discussions, trying to decide on the most optimal strategy, bluffing on several levels-- and it was very interesting to see how minor less rational thoughts could affect our decisions very substantially! Like that time when I was playing werewolf, I decided to maul Thomas during my last night, thinking that I knew I was dead the next day anyway but at least I would have some revenge. I should have thought a bit longer and mauled James instead - he would have passed the sheriff badge to me!
I definitely learned a lot about myself during this game - how I analyse things when pressed for time; how emotions affect my rationality; how hard I find it to bluff in a game more complex than poker...
I would strongly recommend other meetup groups try playing this game!
Douglas explained that for the villagers it is always best to lynch someone because otherwise the next day you'll just be in the exact same position with one less villagers' vote against the same number of werewolves' votes. This seems definitely true, but oddly counter-intuitive given that you're more likely to lynch a villager by mistake, the more of them you have.
That reasoning sounds like a bias against inactivity to me. The comparison is between being down 1 villager for sure, or being down {2 villagers, 1 villager 1 werewolf}. That has to be justified on the grounds that killing a werewolf gets you more than killing a villager costs you. Consider your first game, and assume that the players have no information the first round (i.e. you have a day before a night). Lynching someone at random gives them a 1/6th chance of winning, and a 5/6th chance of being at 3 villagers and 1 werewolf day 2; not lynching someone at random puts them at 4 villagers and 1 werewolf day 2. Whether or not that's a good idea depends on the relative chances of villagers winning with 4 villagers and 3 villagers against 1 werewolf. (If villagers have p(win)=.5 with 4, and anything more than p(win)=.4 with 3, then they should go for the random kill. The worse the villager's chances, the more they should be winning to kill randoms- assuming there's only one werewolf.)
If the village never lynches, the game is closed on werewolf victory.
There's also a social dynamic at play. Particularly in larger games, the village tends to split into factions. The wolf wants to encourage this, but doesn't want one faction to defeat the other too quickly. So the wolf wants to plausibly switch sides frequently. When there's no lynch, switching sides has less consequence. The more decisions with consequence that must be made, the more lies the werewolf must tell and more inconsistencies the wolf must reveal.
If the village never lynches, the game is closed on werewolf victory.
Sure. I expect it's a solid strategy for the villagers to lynch if there's any evidence to single someone out, and possibly even in the absence of such evidence (I can't model tells and suspicion well enough to do the relevant math). But that needs to be grounded in "we're better off lynching than not," not "we have to do something!" There are probably scenarios where inactivity is a better option.
There are probably scenarios where inactivity is a better option.
If the wolf or wolves can form a nucleus for that something and there are no other credible options, inactivity is better. The wolves also vote as a secret bloc - if they're good, they can determine the outcome of a "do something" vote (although if they're not as good as the village, this reveals them pretty severely).
(This is my experience with the game, not a worked solution or anything.)
If a majority of players agree that a random player needs to be lynched, this is possible. Everyone picks a number from 1 to N, where N is the number of living players, and you add the numbers mod N and then lynch the corresponding player. This is robust against colluding wolves: even if exactly one person picks a random number, the sum will be random.
Of course, I don't see this strategy being adopted, because it arguably takes the fun out of playing.
I explicitly prevent my players from introducing 'true' sources of randomness like coin flips ('true randomness' in that all parties can see and agree it was random), or from recording information with pen and paper. The key to challenging and enjoyable mafia is embracing the 'social reality' concept: no fact or claim can be free from ulterior motives, no truth can be clearly untwisted.
I guess then the challenge of randomization is whether players can do modular arithmetic with large primes in their head.
The additional factor one has to take into account is the odds of gaining information, and the likely effect of that information gain upon improving your chances of killing werewolves at future lynchings.
One reason I suggested Werewolf/Mafia was the write up of having at go at Paranoid Debating by the London Meetup. I thought, if we wanted to have a go at Paranoid Debating at a future meeting, it would be good for people to have tried Werewolf first, to get an idea of the general tactics of spotting defectors, before mixing in the Aumann Game.
It would be interesting, some time, to do another game of Werewolf, where people kept a private systematic record of the probabilities they assign each day, so at the end of the game they can reverse calculate via Baysian reasoning, what their actual estimates of evidence presented during each day were, that the evidence updated their prior estimates by the amount it did.
There is already a post related to this meetup but it concerns a discussion which took place after I had left so I will write about the games of Werewolf. Please post your thoughts too and correct any inaccuracies.
Thoughts:
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Games:
1 GM: {Douglas}, Villagers: {Ramana, Jon, Jonathan, Alexey, Ai}, Werewolf: {Thomas}
Jon mauled. No-one lynched. Jonathan mauled. Thomas lynched. Villagers win.
2 (Seer added) GM: {Douglas}, Villagers: {James, Jonathan, Alexey}, Werewolves: {Thomas, Ai}, Seer {Ramana}
Ramana mauled. Jonathan made Sheriff. No-one lynched. Alexey mauled. Ai lynched. Jonathan mauled. James lynched. Werewolves win.
3 (Sheriff's deputy and wills added) GM: {Douglas}, Villagers: {James, Jonathan, Ai}, Werewolves: {Ramana, Alexey}, Seer: {Thomas}
Jonathan mauled. James made Sheriff. Ramana lynched. Thomas mauled. Alexey lynched. Villagers win.
4 GM: {Thomas}, Villagers: {Douglas, Jonathan, Alexey}, Werewolves {James, Ai}; Seer {Ramana}.
Ramana mauled. Alexey made Sheriff. Douglas lynched. Alexey mauled. Sheriff passed to Ai. Jonathan lynched. Werewolves win.
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This post was partly motivated by this comment in the google group:
So, I'd observe that
"we tried a social meeting, we played werewolf [also called Mafia], it went well/badly etc."
is far more useful data to the community that
"we failed to call taboo on a contentious term, and thus displayed massive confusion"
From a community building perspective, the former is useful and the latter is not. From an informational perspective, the first is null and the latter is a net negative, in that it looks like it might contain content but does not.