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# Assassin in the Palace! watch

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1. (Original post by Axel Johann)
Also, can you reserve Plagio's place for the next game? He also missed it ;-;
2. (Original post by BookBird)
Also, can you reserve Plagio's place for the next game? He also missed it ;-;
Plagioclase right? the mod? If so, yes I will reserve a place for him
3. We need to elect a leader if we were to use that strategy, and the leader picks who to lynch each time. However there is a 1/12 chance that the leader will be the assassin if we were to pick a leader at random, and if the leader is the assassin we automatically lose.

Here is the way the strategy works.
We pick a leader COMPLETELY at random out of the lot of us. It may be a guard, it may be the king, it may be the assassin!
Each round, the leader picks who to lynch, and EVERYONE follows suit. The leader will not pick himself to lynch, or the king, if he is a guard. If he as the assassin, we are completely screwed.
The chance the Assassin has of killing the king with his dagger if he dies and there are N non assassins still remaining is

So the probability of us LOSING will be
1/12 -> Assassin gets elected immediately (We lose)
1/12 -> King Gets Elected as leader
-> 1/11 -> Assassin dies when there are N people remaining, where N ranges from 1-11 (so there are 11 values of N, and by symmetry each value is equally likely to occur)
----------------------------------------------------------------
10/12 -> Guard gets Elected
-> 1/10 -> Assassin dies when there are N people remaining, where N ranges from 2-11 (so there are 10 values of N, and by symmetry each value is equally likely to occur)

So the probability of us losing with this strategy will be approximately 0.2745
4. So many strategies discussed lols

Some of the players haven't said anything on the thread yet so it'll get more interesting once they get involved. Anyway, everyone looking forward to the King's so-called Sunday feast?

(Plenty of dat Mountain Dew and Doritos as well fingers crossed the King's into that shizz) 🍗🍖🍕
5. Erm, King?

King: Yes Guard?

I will protect you from the assassins! (Joined yesterday)

King: good because I need guards to protect me because there are assassins everywhere!-to kill me!

Thank You BobShakesphere for being my guard!

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6. (Original post by MathQ123)
I have a feeling that he is actually the assassin because with his strategy the guards are more likely to get lynched so it's going to be easier for the assassin to find the King.

Edit: he also said that we should vote for the King as well so there's going to be fewer option for the assasin to choose from after the vote is done, if that makes sense
Ah, but maybe you are the assassin and are trying to trick us by laying the blame on someone else. You seemed keen to say you would sacrifice yourself for the King, but is this all a ploy? Equally, I could be trying to trick you.

7. Anybody have a strategy that beats 0.2745? I reckon that is probably our best bet if we dont want to play mindgames
8. imsoanonymous123
upon further research on the interwebz I found that the 'quick-lynch no discussion' seems to be the best technique
someone votes to lynch and we say nothing but all vote for that person - no discussion
and no discussion of who and why we should/shouldn't lynch them because that gives clues!!
it's not an elected leader who votes them off, it could be any of us voting but as soon as one person has a vote on them that's it they're lynched
that apparently gives us the best odds - can't calculate because dumb soz x'D

pros: quick, efficient win
cons: it's all silent, no discussion so people argue that it makes the game boring

sounds pretty good to me though what do y'all think ?
9. (Original post by z33)
imsoanonymous123
upon further research on the interwebz I found that the 'quick-lynch no discussion' seems to be the best technique
someone votes to lynch and we say nothing but all vote for that person - no discussion
and no discussion of who and why we should/shouldn't lynch them because that gives clues!!
it's not an elected leader who votes them off, it could be any of us voting but as soon as one person has a vote on them that's it they're lynched
that apparently gives us the best odds - can't calculate because dumb soz x'D

pros: quick, efficient win
cons: it's all silent, no discussion so people argue that it makes the game boring

sounds pretty good to me though what do y'all think ?
I didn't search anything on the internet, I just thought about what to do and what strategy gives the best chance of winning.
10. (Original post by imsoanonymous123)
I didn't search anything on the internet, I just thought about what to do and what strategy gives the best chance of winning.
okay... but I did and I was just sharing what I'd found
and apparently that gives us the best chances but we could do your thing if you wanted...
11. (Original post by z33)
okay... but I did and I was just sharing what I'd found
Whoops, I'm blind, I thought you quoted me and were mocking what I was saying
the strategy you found is essentially what I was saying except the other strategy doesn't have an elected leader. The problem is that if we don't have an elected leader we essentially give the assassin 2 stabs at the king, first, if he votes to lynch the king we cannot all vote to lynch the king- we must modify our behavior. And this will give away what we are doing.
12. Axel Johann can you please clarify what happens if some members end up with the same number of votes in the group? Does someone out of the people with the same number of votes get lynched completely at random?
13. (Original post by imsoanonymous123)
Whoops, I'm blind, I thought you quoted me and were mocking what I was saying
the strategy you found is essentially what I was saying except the other strategy doesn't have an elected leader. The problem is that if we don't have an elected leader we essentially give the assassin 2 stabs at the king, first, if he votes to lynch the king we cannot all vote to lynch the king- we must modify our behavior. And this will give away what we are doing.
oh right x'D no I quoted you cos you asked if any of us found another technique
yeah but even with your technique the leader would never vote to lynch the king which will eventually give it away too
and like you said - if the assassin was elected then we're screwed
so it's basically the same

idk the logic behind it but from what I've seen the 'quicklynch dont discuss' thing works - because we're using our size to our advantage since we outnumber the assassin 11:1
adding the no discussion part will prevent the assassin's chance of picking the king from increasing - i couldn't find a way to completely eliminate the possibility of the assassin winning but this makes it harder since it's completely random and no other info is being given so they have to make complete guesses

I'd link the forums I've searched (cos this exact game has been played before) but then the assassin can access them too
14. (Original post by imsoanonymous123)
Axel Johann can you please clarify what happens if some members end up with the same number of votes in the group? Does someone out of the people with the same number of votes get lynched completely at random?
I asked that too - he said we all die if all of us have equal number of votes
15. (Original post by z33)
yeah but even with your technique the leader would never vote to lynch the king which will eventually give it away too
well - the leader would have not voted to lynch any of the other N members alive so it doesn't give it away. He has not voted to lynch all of the alive players. From the Assassin's perspective, all the other N players have not been voted by the leader yet, and any player that has been voted on has been eliminated anyway. From the Assassin's perspective, everything is symmetrical more or less.

and like you said - if the assassin was elected then we're screwed
so it's basically the same
No it's not the same . I've done some maths and your strategy and the probability of losing with it is 0.3824

idk the logic behind it but from what I've seen the 'quicklynch dont discuss' thing works - because we're using our size to our advantage since we outnumber the assassin 11:1
adding the no discussion part will prevent the assassin's chance of picking the king from increasing - i couldn't find a way to completely eliminate the possibility of the assassin winning but this makes it harder since it's completely random and no other info is being given so they have to make complete guesses

I'd link the forums I've searched (cos this exact game has been played before) but then the assassin can access them too
16. Here is the table for Z33's "Random Lyncher each round" strategy that I used to compute the probability of losing

17. (Original post by Gribby2)
Ah, but maybe you are the assassin and are trying to trick us by laying the blame on someone else. You seemed keen to say you would sacrifice yourself for the King, but is this all a ploy? Equally, I could be trying to trick you.

Anyone could be the assassin but if I was the assasin I wouldn't have said all that because it makes everyone more likely to vote to lynch me. Why would the assassin do that, especially at the start when he/she has no clue who the King is?
18. (Original post by imsoanonymous123)
well - the leader would have not voted to lynch any of the other N members alive so it doesn't give it away. He has not voted to lynch all of the alive players. From the Assassin's perspective, all the other N players have not been voted by the leader yet, and any player that has been voted on has been eliminated anyway. From the Assassin's perspective, everything is symmetrical more or less.

No it's not the same . I've done some maths and your strategy and the probability of losing with it is 0.3824
ah right so all lynching a player would do is increase the probability of the assassin guessing any other player equally
and if we don't give any clues etc. that probability should stay constant for every player
i think i understand

(Original post by imsoanonymous123)
Here is the table for Z33's "Random Lyncher each round" strategy that I used to compute the probability of losing

daym! that's the difference a leader makes?!
can't argue with the maths your strategy has the lowest probability of losing so far so... I'd say let's go with that then :3
19. (Original post by z33)
ah right so all lynching a player would do is increase the probability of the assassin guessing any other player equally
and if we don't give any clues etc. that probability should stay constant for every player
i think i understand

daym! that's the difference a leader makes?!
can't argue with the maths your strategy has the lowest probability of losing so far so... I'd say let's go with that then :3
Hm actually thinking about it, the leader strategy doesn't completely preserve symmetry - so I think my calculations could be incorrect again! If there are for example, just 3 people left and the Assassin and the Assassin gets lynched - he knows that one of the two people left must be the Leader/King but that doesn't imply the following cases are equally likely:
The Leader is the king and the other guy is some random guard
The Leader is a guard and the other guy is the king

So his chances may be better than just a 50/50 blind guess

.. may have to check my maths again but not now.
20. (Original post by imsoanonymous123)
Hm actually thinking about it, the leader strategy doesn't completely preserve symmetry - so I think my calculations could be incorrect again! If there are for example, just 3 people left and the Assassin and the Assassin gets lynched - he knows that one of the two people left must be the Leader/King but that doesn't imply the following cases are equally likely:
The Leader is the king and the other guy is some random guard
The Leader is a guard and the other guy is the king

So his chances may be better than just a 50/50 blind guess

.. may have to check my maths again but not now.
#2maths4me
what about MathQ123 's technique? http://www.thestudentroom.co.uk/show...&postcount=108
but then again there's still that chance of the king getting 2 votes and having to change our methods again UGH
MAH BRAInz

Axel Johann is there anyway we could get a 'no-lynch' to happen?

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Updated: February 23, 2016
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