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The Resistance: Avalon» Forums » Strategy

Subject: Avalon "solution"? rss

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Mike Williams
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Nerdy yes, but is there a mathematical solution to Avalon?

If all communication must be public (no 'under the table' note passing, private texting, etc.), is there a guaranteed way for the good guys to win 3 quests without revealing information about who Merlin is?

This appears to be a convoluted solution for when playing without Mordred:
http://boardgames.stackexchange.com/questions/20476/solution...

Is there a similar solution for when playing with Mordred?

When I've played, we didn't even use pencil and paper (the game owner said "we're not playing Clue!"). So this is more an intellectual curiosity thing. However, it ruins the game a bit for me to know that a cell phone app could easily "solve" the game.

I guess we'll play with Mordred more often now!
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Des Lee
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I hope that's just an intellectual exercise. Because the theoretical method described in the link actually sounds like the least fun way to play ANY game ever.
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Pasi Ojala
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The number of cases you can 'solve' is reduced significantly when minions know how to play, i.e. choose when to float missions and vote like they are servants. And the other way around: servants look more Merlin than Merlin himself by just chance and keeping up with their guess (and it can backfire spectacularly).

(Edit: I see the suggested "solution" is not for you to win a game of Avalon, it is for the good team to win Avalon by using secret communication. It ceases to be a game, because the role you are dealt determines if you win or lose. But it also goes against the assumption and agreement of most groups that communication is above-the-board. I'm not interested enough to even read the thing fully through.)
 
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Mike Williams
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Des Lee,
Yes, just a curious intellectual exercise. Playing like that, everyone would get together, enter some stuff on some phone app I assume, and press go. Totally pointless as far as entertainment goes.

However, trying to actually come up with the mathematical solution, for some reason I find that entertaining. A fun puzzle if you will.


Pasi Ojala,
I think you missed the point. It looks like there is a mathematical solution (when not using Mordred at least). So there is no need to base results on guesses of how you interpret someone is acting.

Of course I would never advocate someone actually playing this way.
I've never even played with the aid of pencil and paper, although I think I would like to try that at some point to see if recording votes and stuff actually helps.
 
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jack elfrink
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losfp wrote:
I hope that's just an intellectual exercise. Because the theoretical method described in the link actually sounds like the least fun way to play ANY game ever.
More specifically, double key encrypted messages kind of stretches the definition of "public" communication.

Heck, I played with a group once where two of the players knew American Sign Language and we had to 'house rule' that they could only communicate to each other in English during the game. Technically they would have only communicated publicly with one another. Every single other person at in the game could fully see everything they would have signed to each other.

 
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user4735 wrote:
So there is no need to base results on guesses of how you interpret someone is acting.

I was not referring to acting-acting, just what your votes for teams and mission results are. You can sometimes deduct from mission results who must be clean, and sometimes spies paint themselves in a corner by failing missions with specific players, but otherwise you can usually only see things like "at least one of A and B is a spy, or C is a spy", and the game is over before you have fully solved who the spies must be.

When you add voting, any off-team approve vote is a suspect, but by itself is not enough to deduct the spies.

 
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Mike Williams
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I'm curious to hear more about the Sign Language. How were they using it to help each other? I guess if they were both evil, they could openly discuss ideas on who Merlin is.

Other than that, I'm not sure what help it would be. If your friend claimed to be Merlin, would you believe him anyway? Seems mostly like just another channel to deceive and bluff over
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Bobby Ramsey
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I consider encryption as a breach of only allowing public discussion. To me, it violates the rules, but I understand other groups play differently. As such, I have a few issues with your "proof".

It appears like there will be some disparity in sizes between the cyphertext sent by the non-Merlin good guys, and by that of Merlin. Merlin is packing lots of info in his message. The bad guys know the teams, so they know which good guy's cyphertext is WAY BIGGER.

My main issue, however, is one of semantics. This "proof" assumes that decrypting without authorization is impossible. That assertion may be statistically impossible, but not "theoretically impossible" which the term "proof" implies. Theoretically, a brute-force attack will eventually decrypt. Practically, it just takes a while.
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Jeff Wood
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Looks heavily flawed.

One: public communication only, recall. Not private messages, that's clearly outside the rules

Two: you can not reveal your card during play, not its text or picture, again per the rules. The 'proof' requires that Merlin ignore that fully.

Three: this 'proof' assumes that Team Evil won't out the first Team Good message they receive as a 'spy', outing that key. This ends up with smart Team Evil play with most of the keys known to all, and Merlin identified if he tries to finger anyone.

Well, that's my read on it.
 
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John
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Cinnibar wrote:

Two: you can not reveal your card during play, not its text or picture, again per the rules. The 'proof' requires that Merlin ignore that fully.

Merlin just claims Merlin & says who the other good guys are. That's allowed (though a terrible idea if you're not allowing some form of private communication). It's debatable whether the method proposed is public or not, but for the purposes of the solution I'm happy to accept it is public (for an actual game on the other hand I wouldn't).
 
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Mike Williams
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Just to be clear, this is just a puzzle. I would never attempt to play this way of course.

Cinnibar wrote:
One: public communication only, recall. Not private messages, that's clearly outside the rules

All messages, even key exchange, is public and available for anyone to inspect. In fact, this is necessary for the setup.

But yes, I agree this goes against the spirit of public communication. So one could just reject it on that grounds.

I just find it fascinating that there may be a solution despite no one having any reason to trust any individual. Imagine these were real countries at war, even if completely private messages could be sent, they could just lie to you over the private communication channel. It's quite amazing to me that concrete information can be gained by passing around messages publicly that everyone can see.

It seems that the assymetry that allows this is Merlin, and the majority of players being good. For example, I can't think of a way this would help a Resistance game with no special characters. (But maybe that means I'm just not creative enough... might still be possible.)

Cinnibar wrote:
Three: this 'proof' assumes that Team Evil won't out the first Team Good message they receive as a 'spy', outing that key. This ends up with smart Team Evil play with most of the keys known to all, and Merlin identified if he tries to finger anyone.


I didn't understand this objection. Team Evil already knows who all the good guys are, and is never given any good guy's pass phrase (only derived individual keys for communication). So there is nothing to "out", and they can't deduce who merlin is. (Unless, as someone mentioned earlier in the thread, they had enough time to brute force the pass phrase or something.)



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Pasi Ojala
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user4735 wrote:
All messages, even key exchange, is public

All messages are public, but their actual content is not public. There is a fairly significant difference.
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Mike Williams
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a1bert wrote:
All messages are public, but their content is not public. There is a fairly significant difference.

I of course agree this goes against the spirit of public communication. So one could just reject it on that grounds.

Since evil characters all know each other, any comment they make during a normal game is not truly public if we require "public" to mean everyone gets the same "content" from the message. To the other evil characters, the messages are interpreted through the extra context which the evil players have and the good players don't.

In some sense, the messages after key exchange is just maximizing disparity of the 'context' in which public messages are interpreted. Most players only get the information that a message was stated of a certain size.

As Bobby Ramsey pointed out, if one is not careful (padding out the messages with nonsense words or something), this information alone is still enough 'context' for the bad guys to figure out who Merlin is. An interesting observation Bobby!
 
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a1bert wrote:
user4735 wrote:
All messages, even key exchange, is public

All messages are public, but their content is not public. There is a fairly significant difference.

If it could be done with message contents public that'd make this solution slightly less interesting (and probably make Avalon significantly less interesting). As that's almost certainly impossible then this solution is still interesting (though admittedly not to everyone). The fact that you could break the game by doing something that could be classed as public communication is interesting (e.g. it could be done in a play by forum game with all communication in forum posts) though it has no impact on what anyone would do when playing Avalon (which is good).
 
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Pasi Ojala
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zabdiel wrote:
If it could be done with message contents public

I think I was a bit too vague. Using public-key cryptography what bytes are sent (the message as transferred symbols) are public, but only the receiver can interpret the content (the message as transferred information). This is what I was talking about. So, yes, everyone can see all information transferred, but can still not interpret the information that is not intended for them.
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a1bert wrote:
I think I was a bit too vague.

No I think I understood what you were getting at - I think we agree that this would not be considered public communication by anyone playing the game, but if the OP wants to consider it public for the purposes of a mathematical solution then I'm fine with that. He's obviously not claiming that Resistance/Avalon is solved in the sense that if a certain strategy is employed in a normal game then one side will always win (I'm sure I've read threads where people claimed that). Using public-key cryptography for analysis of the game is certainly an interesting thing to consider.
 
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zabdiel wrote:
Cinnibar wrote:

Two: you can not reveal your card during play, not its text or picture, again per the rules. The 'proof' requires that Merlin ignore that fully.

Merlin just claims Merlin & says who the other good guys are. That's allowed (though a terrible idea if you're not allowing some form of private communication). It's debatable whether the method proposed is public or not, but for the purposes of the solution I'm happy to accept it is public (for an actual game on the other hand I wouldn't).
not so! I very often claim Merlin when I am, and just straight up claim the right spies. I very rarely get killed, because WIFOM.
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John
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I should have know you'd say that

Don't you frequently claim Merlin regardless of whether you are?
 
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Clyde W
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Well, yes. Doesn't everyone? It ain't Avalon unless you're saying WIFOMy things the entire time.
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Clyde W
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I must admit, I didn't read the OP's stuff, despite understanding PKE.

Regardless, OP, what if I'm PoRry, but really good at reading evil in the hearts of mine enemies, and in my message, I claim Murray and name the spies?
 
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John
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Just noticed the hover text for your avatar
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