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P Santos
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In the absence of any verifiable or observable information, like at the start of the game when proposing a team for the first Quest, if you are the team leader, always include yourself in the team you are proposing. This is the optimal strategy.

Consider a 5-player game. If you are Good (a loyal servant of King Arthur), randomly selecting the 2 players to go on the first quest has only a 30% probability of picking out two Goods (10% probability of selecting two Evils (minions of Mordred) and 60% of selecting one Good and one Evil).

If you are Good, proposing yourself as one of the two, and selecting the other team member any other way (no better than randomly, in the absence of any verifiable info yet) there is a 50% probability that the other one selected is also Good. Hence, the conditional probability that both members selected are Good is 50% (given that the included team leader is good).

If you are Good, and you exclude yourself from the proposed team, there is only 16% probability that both team members are Good.

So, from the point of view of the Good, to maximize your chances of having two Goods in the team, as team leader put yourself as one of two team members (50% probability of having both Goods, versus 30% randomly choosing, and 16% when you exclude yourself). Same conclusion for a 6-player game. Probabilities of having both Good in team for first quest: 40% when randomly choosing, 60% when including yourself when you are Good, only 30% when excluding yourself if you are Good).

If you are Evil, deviating from this strategy would out yourself as Evil because no Good would choose an action (in the absence of any new verifiable info, no Oberon) that would lower the chance of his team of having both Goods in the first quest. Hence, best option for Evil is to mimick the strategy of Good - nominate yourself in the team of you are the team leader..

If you are Merlin, it would be detrimental to the Good side if you deviate from this strategy. The Goods might suspect you as Evil if you take a course of action that reduces your team's chance of getting two Goods in the team. But from the point of view of Evil, who knows everyone's allegiances, you would out yourself as Merlin.

Hence, regardless whether you are Good or Evil, the optimal strategy, at the start of the game in the absence of additional verifiable info, is to nominate yourself in the proposed team, if you are the team leader.
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Putting yourself in the mission is the default choice. However, if there is something that is always done, it causes you to lose flexibility - both as a way to gain information and as a way for a spy to play the game. So, sometimes you would want to choose two other players and not yourself (for 5p) into a 2-member team. If you manage to get two spies into that and neither submits a fail, you have gained a successful mission, and if both submit fails, you have won the game. If you reveal one fail, that gains information too.
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I think the leader should put themselves on the team 99% of the time. There may be some edge cases here or there where it may be beneficial not to do so.

Even if you put two evils on a team without you, it can be very suspicious that you managed to pick two evils - a possible Merlin giveaway. Absent unusual circumstances, the leader will always place themselves on the team.
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MyParadox wrote:
Even if you put two evils on a team without you, it can be very suspicious that you managed to pick two evils - a possible Merlin giveaway.

If you are not Merlin, that is perfect for you. And if you are, how does the Assassin know it was not just an (un)lucky pick? The key is to deviate from "the norm" often enough whatever role you have.
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P Santos
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Putting yourself on the team, when you are the leader (Leader Put Self, or LPS), in the absence of any additional/new verifiable info, is the optimal move. Deviating from this significantly increases your team's chances of losing. If you are Evil, you will out yourself; if you are Good, it reduces your team's chances of putting two Goods on the team, thus, increasing the chances that at least one Evil will be included and, the quest eventually failing rather than succeeding. Again, it's very important to remember that LPS is strictly optimal only when the players don't have any new/additional verifiable info, like at the start of the game, (when no team voting has been done) and the only info the players have is the game setup info (# of Goods, Evils, roles,etc) and the probabilities. Once voting results are available, that's already new info, and must be taken into account, which may or may not make LPS optimal anymore. Be wary though of considering any claims as 'new info' at the start of the game, as those are not verifiable and may be dismissed as simply 'red herrings' (depends on group though).

For the purposes of discussion, let's assume a 5-player competent game, no special roles, for the ease of calculating the probabilities and game analysis.

Deviating from LPS, in the absence of additional verifiable info, does not help you get better info and only increases the probability that quest will eventually fail (1/6 chance of getting clean team if you exclude yourself [non-LPS], vs 50% via LPS), which hurts Good. With non-LPS, in a 2-member team, you have 4/6 probability of an Evil-Good combo and 1/6 of having two Evils, or 5/6 (84%) that quest will eventually fail. Regardless of how many Evils are in the 1st quest, it will likely succeed (esp in 5 or 6-player game) as the competent Evils will not out themselves and lose the game outright. You won't gain any meaningful different info than had you just randomly selected the team members. The second quest, though, would likely have 1 fail (higher prob of only one Evil, compared to having 2 Evils), a situation no different had you randomly selected the team members. How about the probability of having the desired 2-Evil who will double fail and out themselves in Q2? More like wishful thinking. The probability of having 2 Evils for Q2 given that Q1's team leader used a non-LPS is only 39% (someone verify my probs), meaning the group is more likely to get a single Evil than double Evil, which doesn't really help as far as getting that 'special' info you want to uncover. But even if by unlikely chance, the Q2 team had double Evils, a competent Evil group using the Assassin-always-fail technique would eliminate the double fail possibility (in 5 or 6 player group), again giving the Good no meaningful insight. What’s clear is deviating from LPS reduces Goods' chances of succeeding a quest in the absence of any new/additional verifiable info. Aiming for the possibility of double fail is so remote that Good would more often lose games by systematically reducing its chances of quests succeeding. This is not enough to justify non-LPS to aim for the double-fail homerun win, which could happen once in a blue moon.

a1bert wrote:
If you are not Merlin, that is perfect for you.


Doing this (non-LPS) is actually very bad for Good. Let's keep in mind that succeeding three quests is a necessary condition for Good to win, but not a sufficient condition (Merlin not assassinated). In other words, protecting Merlin would be useless if three quests would fail. If Good uses non-LPS, he is reducing Good's chances of landing a clean team (from 50% to 16%), not gain any meaningful insight but increase the chances that the quest will eventually fail, which is to advantage of Evil. As Evil, you would be happy to see that Good is making it harder for quests to succeed, you'd likely score three failed quests, and you won't have to worry about assassinating Merlin. Thus, non-LPS is detrimental if you are Good.

a1bert wrote:
And if you are, how does the Assassin know it was not just an (un)lucky pick? The key is to deviate from "the norm" often enough whatever role you have.


Using non-LPS when you are Good (not Merlin) has only 1/6 probability of being "lucky" selecting the two Evils (in 5-player game). In other words, there is a 5/6 chance that it was not due to luck, ie. you are Merlin, again in the absence of any new/additional verifiable info, like at the start of the game. As Evil, I'd be happy to take that chance (5/6) that you are Merlin. If by some unlikely chance that Good managed to succeed 3 quests when they have been systematically reducing their chances of succeeding and I would have to pick Merlin, I'd rely on the 5/6 odds that you are Merlin. Five out of 6 will win me the game, 1 in 6 lose it. I'd gladly take that odds than the 'paltry' 1/3 chance of randomly selecting Merlin (in a 5-player game, or 25% in a 6-player game). By relying on probability alone, as Evil, I would win 5 times more often than you would as Good. So, clearly non-LPS is bad if you are Merlin.

The reason why LPS is optimal is because deviating from this is detrimental to your team (again, in the absence of additional/new verifiable info). It cannot be exploited by Evil.

Since LPS is optimal if you are Good, then a competent Good will always use LPS. If you don't use LPS, then you are harming the Good team's chances of winning and so would likely be labeled as Evil. Being labeled Evil is detrimental for both cases when you are Good or when you are Evil. Evil will out himself if he uses non-LPS. Can't Evil exploit this? No, he cannot 'play' the field given competent Good players. If Evil nominates two other players (exludes himself), whether both Good or both Evil, in the hopes of 'metagaming', it won't work. The competent Goods don't have to fall for the Evil's bluff or whatever he has to say. But what will be clear is since he used non-LPS he must be Evil and thus, outed himself in the process. A tremendous advantage for the Good, with one Evil already outed at the start of the game. So, non-LPS even if you are Evil is really a mistake.

Thus,LPS is strictly optimal, in the absence of any new/additional info. Once new info comes in, we cannot safely say that LPS is still strictly optimal.
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Pasi Ojala
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A player's responsibility is not to help the Good team to win, but win themselves. Optimizing the chances of the Good team instead of the individual player's chances to win ultimately means that you win by the random deal of the loyalty cards. What's the point in playing then?

It might be the optimal strategy for the Good team, because they are a majority, but not for an individual player.

This becomes more obvious in ONUWW, where it is not the goal of a player to help villagers win, but win the game for themselves.
 
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John
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Despite what I said above I do still think this is a good argument:
a1bert wrote:
However, if there is something that is always done, it causes you to lose flexibility - both as a way to gain information and as a way for a spy to play the game.


I don't know if I'm being totally illogical. Maybe I'm a spy

Edit - I seem to have deleted or failed to post the previous post that I thought I'd posted...
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Simon Kamber
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Id like to challenge an assumption behind the analysis: The goal of the first mission is not to succeed, the goal of the first mission. Is to gain as much information as possible. Viewed in that light, a proposal including a spy is not necessarily a poor outcome, if the circumstances are valuable (for instance if the voting pattern was interesting).
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Simon Kamber
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a1bert wrote:


It might be the optimal strategy for the Good team, because they are a majority, but not for an individual player.win, but win the game for themselves.


However, the fact that the good team has the majority means that the (revealed) rationales should reflect their interests. That is the core dynamic of the game.

Publicly declaring your intention to give the spies a chance (because you might be one) is not, and should not be, a good strategy.
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What I said was something like Simon's posts (but probably more wordy).

Must summary of the OP's argument was:

1. The optimal strategy for good is to aim to succeed the first mission

2. The optimal strategy for achieving this aim is to include yourself on the first mission.

3. Anyone who doesn't do what they think is in the best interests of good is probably a spy

4. Being suspected of being a spy is likely to lead to you losing the game.

If we ignore meta-game arguments, incompetence and people not trying to win then 2 & 3 are clearly true. 4 is true unless you are a spy and gain something else (persuading a good player to believe something incorrect) but that's unlikely to happen with M1 mission proposals.

Whether the optimal strategy for good is to aim to succeed the first mission is debatable. I'd say the best outcome of M1 is that the mission succeeds with a clean team* but since that isn't that likely to occur then maybe focusing solely on that isn't the best plan.

* I'm excluding double fail here.
 
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Eugene Wong
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The goal of the first mission could be whatever a player wants, but the best goal should be to gather as much power and information as possible.

A player can plan to position the leadership token for the next round. He can also try to win a point for the team. He can use his votes to provide information.
 
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zabdiel wrote:
Whether the optimal strategy for good is to aim to succeed the first mission is debatable. I'd say the best outcome of M1 is that the mission succeeds with a clean team*

Of course, you don't know that a successful M1 was clean (except if you're a minion or Merlin - unless Mordred is used, and he should in 5p). You gain no information.

While in base Resistance failing M1 in a 5-player game makes spy win more probable, the same cannot be said about Avalon that easily.
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a1bert wrote:
Of course, you don't know that a successful M1 was clean

Agreed. Perhaps I shouldn't have made the distinction, I'm not sure if matters. You may gain information later though and at the end of the game you'll know.

a1bert wrote:
While in base Resistance failing M1 in a 5-player game makes spy win more probable, the same cannot be said about Avalon that easily.

Fair enough. I don't think I've played enough Avalon to know. Actually I don't know how many games I've played as they are all logged under The Resistance: Hidden Agenda & Hostile Intent. Presumably the reason fails early may be better in Avalon is that they make it easier for Merlin to give clues?
 
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David Williams
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I think the importance of voting is being glossed over in the mathematical analysis - people seem to be forgetting a team has to be voted through. The implicit assumption being the Leader will vote for their own team to go. In fact it's a perfectly viable option to nominate a team you think is risky, then vote against it.

In this way there's a good chance the other 2 Good players will also vote against it (because they aren't on it) and the only players to vote for it will be the players nominated, or an evil player who knows their partner is on the team.

Voting your own team down is not an uncommon occurrence for us, and can catch people out - especially if alcohol is involved!

Personally I suspect that if everyone treated this game as a purely mathematical exercise and executed perfect logic, keeping quiet and giving nothing away, then it would be pure luck. That's why the social aspect is so important - some people are good liars, others take accusations so badly it makes them look like liars. The skill after a couple of games is untangling that aspect and taking advantage of it.
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Eugene Wong
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Proposing a team without the leader can catch spies only so often. Spies can make such proposals, too, to appear rebelish.

It's a good trick to have, though, to use on players, who haven't thought of it before.
 
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Rob Rundle
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After 400 games played, I can see only one occasion where it is worthwhile to propose a team without yourself on it.

When ALL the following circumstances apply:

a) You are good, but perhaps not generally trusted by the remainder of the good guys (perhaps because you were on a failed mission), AND

b) Good guys just need to succeed the current mission to win the game (subject to any assassinations, of course), AND

c) The previous mission and the current mission require the same number of people (so no need to add anyone), AND

d) The previous mission (without you) was successful when any sane baddie would have failed it, so is overwhelmingly likely to be 100% good*.

So you just pick the successful mission team, instead of - as you would in other circumstances - putting yourself on the team.

I have seen Merlin pick a team without himself a few times when the circumstances were not as above, but it was a bad move every time. Usually it didn't get voted up, but if he was fifth pick and it went without a vote, disaster inevitably ensued. Either it failed (because he picked Mordred) or else he got assassinated afterwards.

I suppose a spy might do this for other reasons, but they all shriek SPY so you would just out yourself. I tried to think of a reason a spy might propose a mission without him/herself and not be either immediately branded a spy or lead to a win for the good team, but failed.

*Once in a while this action fails dramatically, because a spy WAS on the successful mission, and should really have failed it but didn't. Evil chuckles and probable win for the bad guys ensue.
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I have't played nearly that much, only with inexperienced players (which includes myself) and only with alcohol involved. So people are likely to be reasoning fallaciously at least some of the time.

The situation I recall was to choose a team of 2, pretending it's for reasons along the lines of those outlined above (people say they don't trust you anyway, or have said they think the 2 you choose are OK, or give no reasoning at all, perhaps pretend you don't care and have no idea what to do) then vote against it. If another player votes for it who was not on the team, that team will probably go (unless one of those chosen votes against it, which they might if they don't trust their chosen partner) but if the mission fails then then it seems likely the outsider is a spy who knew the other spy was chosen for the team. You now know 1 spy with relative certainty and 2 people are under strong suspicion.

The social aspect means this situation can often out the spies because they think they have won; "Aha the idiot chose a team with the spy on it, now all I do is vote for it and we can win!" but that backfires because you didn't expect both the leader and one of the chosen players to reject their own team.
 
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Max DuBoff
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Orion3T wrote:
I have't played nearly that much, only with inexperienced players (which includes myself) and only with alcohol involved. So people are likely to be reasoning fallaciously at least some of the time.

The situation I recall was to choose a team of 2, pretending it's for reasons along the lines of those outlined above (people say they don't trust you anyway, or have said they think the 2 you choose are OK, or give no reasoning at all, perhaps pretend you don't care and have no idea what to do) then vote against it. If another player votes for it who was not on the team, that team will probably go (unless one of those chosen votes against it, which they might if they don't trust their chosen partner) but if the mission fails then then it seems likely the outsider is a spy who knew the other spy was chosen for the team. You now know 1 spy with relative certainty and 2 people are under strong suspicion.

The social aspect means this situation can often out the spies because they think they have won; "Aha the idiot chose a team with the spy on it, now all I do is vote for it and we can win!" but that backfires because you didn't expect both the leader and one of the chosen players to reject their own team.


Yeah, that's still relatively basic reasoning. The meta only gets more complicated from there...
 
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MD1616 wrote:
Orion3T wrote:
I have't played nearly that much, only with inexperienced players (which includes myself) and only with alcohol involved. So people are likely to be reasoning fallaciously at least some of the time.

The situation I recall was to choose a team of 2, pretending it's for reasons along the lines of those outlined above (people say they don't trust you anyway, or have said they think the 2 you choose are OK, or give no reasoning at all, perhaps pretend you don't care and have no idea what to do) then vote against it. If another player votes for it who was not on the team, that team will probably go (unless one of those chosen votes against it, which they might if they don't trust their chosen partner) but if the mission fails then then it seems likely the outsider is a spy who knew the other spy was chosen for the team. You now know 1 spy with relative certainty and 2 people are under strong suspicion.

The social aspect means this situation can often out the spies because they think they have won; "Aha the idiot chose a team with the spy on it, now all I do is vote for it and we can win!" but that backfires because you didn't expect both the leader and one of the chosen players to reject their own team.


Yeah, that's still relatively basic reasoning. The meta only gets more complicated from there...


Spies should quickly learn (for at least the first couple of missions) not to vote for teams with other spies on, just as good guys should quickly learn not to vote for teams they are not on themselves. Both involve serious risks to their own team's chances of success. And voting against the team that you are on (because you don't trust one or more of the other people selected) is so normal for my group that I sometimes forget that not everyone would think of doing this! I was once accused of being a spy when I voted for a proposed team on mission 1 that I had chosen including myself - because no-one else for the entire round voted for anything!
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Robrun wrote:
just as good guys should quickly learn not to vote for teams they are not on themselves.

A good guy must vote for a team that they are not on twice, or spies win by 5 failed team suggestions. (If the good guy is known to do that on hammer, spies can vote no to hammer.)

But I have only played 240 games face-to-face, so maybe I haven't arrived to the so-called optimal strategy yet. whistle

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Rob Rundle
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a1bert wrote:
Robrun wrote:
just as good guys should quickly learn not to vote for teams they are not on themselves.

A good guy must vote for a team that they are not on twice, or spies win by 5 failed team suggestions. (If the good guy is known to do that on hammer, spies can vote no to hammer.)

But I have only played 240 games face-to-face, so maybe I haven't arrived to the so-called optimal strategy yet. whistle



Of course - if you play the rules as written, but we never take a vote on the fifth pick's choices - we regard it as pointless, though I know some people disagree - so I tend to forget about that.
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Robrun wrote:
MD1616 wrote:
Orion3T wrote:
I have't played nearly that much, only with inexperienced players (which includes myself) and only with alcohol involved. So people are likely to be reasoning fallaciously at least some of the time.

The situation I recall was to choose a team of 2, pretending it's for reasons along the lines of those outlined above (people say they don't trust you anyway, or have said they think the 2 you choose are OK, or give no reasoning at all, perhaps pretend you don't care and have no idea what to do) then vote against it. If another player votes for it who was not on the team, that team will probably go (unless one of those chosen votes against it, which they might if they don't trust their chosen partner) but if the mission fails then then it seems likely the outsider is a spy who knew the other spy was chosen for the team. You now know 1 spy with relative certainty and 2 people are under strong suspicion.

The social aspect means this situation can often out the spies because they think they have won; "Aha the idiot chose a team with the spy on it, now all I do is vote for it and we can win!" but that backfires because you didn't expect both the leader and one of the chosen players to reject their own team.


Yeah, that's still relatively basic reasoning. The meta only gets more complicated from there...


Spies should quickly learn (for at least the first couple of missions) not to vote for teams with other spies on, just as good guys should quickly learn not to vote for teams they are not on themselves. Both involve serious risks to their own team's chances of success. And voting against the team that you are on (because you don't trust one or more of the other people selected) is so normal for my group that I sometimes forget that not everyone would think of doing this! I was once accused of being a spy when I voted for a proposed team on mission 1 that I had chosen including myself - because no-one else for the entire round voted for anything!


This is obviously too simplistic but has some good rules of thumb. Predictability is the enemy; in a group where spies tend to accuse each other, saying you have a great read on another spy can be awesome. And I also often vote down my own teams based on hammer considerations and the general order, but upvoting something you're not on is indeed often necessary.
 
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Robrun wrote:
a1bert wrote:
Robrun wrote:
just as good guys should quickly learn not to vote for teams they are not on themselves.

A good guy must vote for a team that they are not on twice, or spies win by 5 failed team suggestions. (If the good guy is known to do that on hammer, spies can vote no to hammer.)

But I have only played 240 games face-to-face, so maybe I haven't arrived to the so-called optimal strategy yet. whistle



Of course - if you play the rules as written, but we never take a vote on the fifth pick's choices - we regard it as pointless, though I know some people disagree - so I tend to forget about that.


Still, always letting the vote come down to the hammer is definitely put resistance strategy, so you have to vote for teams you are not on from time to time.
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Rob Rundle
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Dulkal wrote:
Robrun wrote:
a1bert wrote:
Robrun wrote:
just as good guys should quickly learn not to vote for teams they are not on themselves.

A good guy must vote for a team that they are not on twice, or spies win by 5 failed team suggestions. (If the good guy is known to do that on hammer, spies can vote no to hammer.)

But I have only played 240 games face-to-face, so maybe I haven't arrived to the so-called optimal strategy yet. whistle



Of course - if you play the rules as written, but we never take a vote on the fifth pick's choices - we regard it as pointless, though I know some people disagree - so I tend to forget about that.


Still, always letting the vote come down to the hammer is definitely put resistance strategy, so you have to vote for teams you are not on from time to time.


Only once you know what you're doing. For new players, it's a bad, bad idea for the first two or three missions.
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MD1616 wrote:
Orion3T wrote:
I have't played nearly that much, only with inexperienced players (which includes myself) and only with alcohol involved. So people are likely to be reasoning fallaciously at least some of the time.

The situation I recall was to choose a team of 2, pretending it's for reasons along the lines of those outlined above (people say they don't trust you anyway, or have said they think the 2 you choose are OK, or give no reasoning at all, perhaps pretend you don't care and have no idea what to do) then vote against it. If another player votes for it who was not on the team, that team will probably go (unless one of those chosen votes against it, which they might if they don't trust their chosen partner) but if the mission fails then then it seems likely the outsider is a spy who knew the other spy was chosen for the team. You now know 1 spy with relative certainty and 2 people are under strong suspicion.

The social aspect means this situation can often out the spies because they think they have won; "Aha the idiot chose a team with the spy on it, now all I do is vote for it and we can win!" but that backfires because you didn't expect both the leader and one of the chosen players to reject their own team.


Yeah, that's still relatively basic reasoning. The meta only gets more complicated from there...


I'm sure you didn't mean that as an insult, lol.

I imagine you mean that most groups (assuming they learn entirely by playing and not reading forums etc) will go through this sort of process, discovering this sort of play after a few plays as they try to out-guess each other and probably not taking a huge number of games to do so (in our case less than half a dozen plays, so I'd agree!).

The initial assumption of many players new to the game is that the leader takes a (hopefully educated) guess on who to send, and it makes sense to play the odds by picking yourself as you know you are good - or if evil, you will pretend to be good anyway. Which is exactly what I think the OP is getting at.

However if other players employ the same reasoning without being led (and potentially misled) by social aspects of the game, then a 2-player team will never be passed; the leader and player chosen will pass the team, the other 3 will reject it. This will happen 4 times then on the last team everyone will vote to pass it (because only spies would even consider rejecting it and would out themselves instantly if they did) and thus nobody will learn anything.

So to me, if such seemingly 'obvious' logic is employed then the game becomes a guessing game with no skill at all. Hence my earlier comment about the necessity of the social aspect. This is really why my son caught me out with his 'basic' play - he had utterly convinced me that he genuinely thought the players he chose were the safest team he could choose which might pass the vote, so the natural assumption was that he would pass it himself. There may also have been an element that some players had declared they would reject any team with him on it - which set him up to make his best guess at a team he thought would pass.

I also believe, but cannot remember for certain, that if that mission failed then Evil would win. So even if I had considered that he might reject it it seemed worth the risk as there was a fair chance those going on the mission would both accept it as well. I think as it turned out one of the team members rejected their own selection as well.

Point being, I'm simplifying the situation somewhat but this is a fairly good example of why you can't assume players will follow rules like that proposed in the OP, and why you shouldn't always follow them yourself either.

TBH I think we're agreed on everything, I just felt the discussion up to my first post had somewhat overlooked the voting aspect of the game.
 
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