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I am trying to design a game where there are X citizens + 1 saboteur. Unfortunately for the saboteur he does not know that he is it. All the citizens know that one of them is replaced, and they all have a "guess" as to who the saboteur is, but they can't be sure if their guess is correct of if they are themself the saboteur.

I want every person to know that it is either a specific player or themselves. Everyone's "guess" for the saboteur is correct, except for the saboteur, whose guess is another player at random.

My initial thought was to deal out role cards, and have everyone reveal their cards to everyone else but not look at their own card. This unfortunately does not work. The saboteur would just not see any saboteur cards and know he is it.

Is there any way to set this up without using a moderator?

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Neat idea, but I don't see how it's possible. If you are a citizen, then you said you will know who it is. Thus, the saboteur will know he is the saboteur because unlike a citizen, he wasn't told who the saboteur was. –  GendoIkari Jun 28 '13 at 17:10
    
The saboteur thus has some other citizen told to him. Everyone just knows its that guy, or you –  Andrey Jun 28 '13 at 18:38
    
Ah ok. I like it! –  GendoIkari Jun 28 '13 at 21:17
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@user1873 Disagree. Perhaps it needs re-wording, but I believe the real goal is "I want every person to be able to know that the saboteur is either himself or one other player, but no player can be sure whether he himself is the saboteur." –  Gregor Jun 29 '13 at 15:13
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@Andrey I'm going to edit your question a bit for clarity. Please do rollback or modify if any of my assumptions are incorrect. –  Gregor Jun 29 '13 at 19:34
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6 Answers 6

up vote 12 down vote accepted

Working Solution:

For n players, you need two identical decks of cards, each with cards numbered 1 to n-1. Keep the first deck ordered from 1 at the bottom, to n-1 at the top, and add a random card from the second deck to the top of the first deck. Set the rest of the second deck aside. Each player will get a single card from the first deck, telling them the relative position of the (alleged) saboteur. For example, if you get a 2 that means the saboteur is the 2nd person to your left (or yourself). Because the cards are ordered, all the cards from the first deck will point to the same person. The one card from the other deck points to another player at random.

To distribute the cards, the order must be maintained but the starting point can be anywhere in the deck. So, the deck is "shuffled" by repeatedly cutting it, which preserves the order but randomizes the start. If the cards are dealt clockwise (to the left), then the relative positions will be also be clockwise.

Characteristics: Everyone has equal probability of being the saboteur, and the civilian the saboteur is mistakenly suspicious of is chosen with equal probability. Equipment is relatively simple, you only need 2*(n-1) cards where n is the maximum number of players. Two decks of playing cards with the same backs could be used in a pinch. (With a bit of preparation, a single deck could be used. Separate out A through n-1 in two suits, and pick one of each rank at random to separate the two "decks".) The only drawback I see is that mis-shuffling will mess things up, but if players are careful it shouldn't be a problem.

For a worked example of this scheme see TTTPPP's answer.


I'll save my previous solution attempts below, none work completely as the one above does.

Almost Solution: Lots of ranked cards

Have many more uniquely ranked cards than players, e.g. cards numbered 1 to 100. Every player is dealt one card, and whoever has the lowest number is the saboteur. Players reveal their cards, as you suggest, to everyone but themselves (maybe Indian Poker-style, card on forehead). It generalizes: need more than one saboteur? Use the two lowest cards. Need a unknowing "citizen leader"? Whoever has the highest card.

You could even do it with a regular deck of playing cards. Just determine a rank order (make sure everyone knows if Aces are high or low) and a suit order to breaks ties in rank (such as Clubs, Spades, Hearts, Diamonds, as in Sheepshead--which is where I got this idea).

Pros: Everyone has a guess to who the saboteur is. Everyone except the saboteur is right about their guess. It can be implemented with standard supplies.

Cons: The non-saboteurs can't be 100% sure that they aren't the saboteur--but I really don't see a way around this. It requires a large number of cards that probably won't have another use in the game. During the reveal, there's a danger of people accidentally giving it away by asking questions clarifying the ranking of cards/staring/asking another player to confirm who they think the saboteur is.

It also enables people to make some educated guesses--if no one else has a particularly low card, you might get suspicious that you're the saboteur. My guess is people will overthink this and it will actually throw people off more often than it will give a good hint, which might end up making things more exciting.

Other Brainstorming: Cards numbered from 1 to n+1

This has a slightly different result, but it might be on to something so I'm recording it here in case it inspires someone else: If you have n players, have n+1 cards labeled from 1 to n+1. Deal each player one card, with the remaining card remaining hidden (call it the hole card). The saboteur is whoever holds the card one above the hole card, with the 1 card considered one above the n+1 card. As above, everyone reveals their card to all but themselves. Let's say we have n=5 players, so 6 cards, and the 3 card is the hole card. The two people adjacent to the hole card (including the saboteur, who is 1 above the hole card) see a "big hole", so they know that their card is either 1 above or 1 below the hole card, so they know they have a 50% probability of being the saboteur, and that whoever is above the big hole is the only other possibility. The people who are not adjacent the hole card see two small holes, so they can also narrow the saboteur down to two possibilities, but they know for sure that they themselves are not the saboteur.

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I was thinking something like this. Biggest problem is that if the 1 comes out, the cat is out of the bag. My idea was that if the 1 is out, then 100 beats it. If the 1 and the 100 are out the 99 beats it, and so on –  Andrey Jun 28 '13 at 20:40
    
Hmmm. That might make using playing cards better. If 1 is out, then odds are still low that 100 is out too. With cards, you could say if Aces are out, then Kings are low... I'll keep thinking about it. Feels like there ought to be a workaround. –  Gregor Jun 28 '13 at 21:05
    
I think it's fine if a 1 comes out... then the other players know for a fact who the saboteur is, but the saboteur still doesn't know that it's him. The only way the sab. would know for sure is if all the other players have the highest possible numbers. –  GendoIkari Jun 28 '13 at 21:19
    
@GendoIkari it's not totally clear in the question, but I think Andrey wants everyone to have some possibility that they are the saboteur, but to have a single other person they think could also be the saboteur. (I didn't realize this until the comment above.) –  Gregor Jun 28 '13 at 22:45
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Hi shujaa, I don't have a problem creating one 'best' answer, consisting of the best ideas from all the answers, but it would be nice if you could at least add a reference to my answer below (assuming that's where the latest edit is taken from). Thanks! –  tttppp Jul 1 '13 at 8:08
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Take two decks of cards with the numbers 1 to n-1 on them. The first deck should be in order, 1 at the bottom and n-1 at the top. The second deck should be shuffled. Put one card at random from the second deck face down on top of the first deck. Pass the created deck around the table, with people cutting and restacking it, so that the cards remain in the same order, but no one knows which card is at the top. Deal one card to each player around the table in a clockwise direction.

The chosen player is the one with the random card from the second deck. Each player holds a card with some number x on it, and knows that either they have been chosen, or it is the player x places clockwise around the table.

Worked example for ten players (all cards are face down, top of deck is at the left)

Initial decks
First Deck: 9,8,7,6,5,4,3,2,1
Second Deck: 4,2,5,1,9,6,7,3,8

Add random card to first deck
First Deck: 5,9,8,7,6,5,4,3,2,1

Cut several times
First Deck: 5,4,3,2,1,5,9,8,7,6

Deal to players A to J
A5 B4 C3 D2 E1 F5 G9 H8 I7 J6

By looking at their card, most players know that either they have been selected, or that player F has been selected. F knows that either they have been selected, or player A has.

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Enthusiastic +1 for coming up with this idea first, and enthusiastic thanks for working together on creating a great, comprehensive answer! –  Gregor Jul 3 '13 at 17:19
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Maybe you can change the game such that there are multiple saboteur roles(except less likely to come up), and then just not deal all of the role cards.

It might also be interesting to see how the game plays out when there are no saboteurs

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That sounds workable: with N players, have (at most N-1) citizen cards and (at least 2) saboteur cards, so that at least one card will go unused. Of course, if you can see 2 (or whatever) saboteur cards, you can still conclusively prove that you're not a saboteur. Perhaps with N players, you have N citizen and N saboteur cards? Can the game still work with far more saboteurs than citizens? –  Paul Marshall Jun 28 '13 at 17:20
    
@PaulMarshall you can just change the number of saboteur cards every game so that people can't just make that assumption –  Sam I am Jun 28 '13 at 18:23
    
But somebody's going to know the number of saboteur cards: the person who created the set of cards to deal out. Of course, to be fair, that person could not play... but now you have a moderator, and OP is trying to avoid that. –  Paul Marshall Jun 28 '13 at 20:48
    
@PaulMarshall Having a variable number of evil is easy. good cards = to players+ X evil cards. Shuffle cards. Deal 1 to each player. Do not reveal the ones not used. –  Andrey Jun 28 '13 at 21:16
    
But the guy who does the shuffling knows exactly how many evil cards there are. Even if he doesn't reveal the number of unused cards to the other players at the table, he'll know: he has to gather the correct number of good cards and evil cards to create the deck he's going to shuffle. So one player is going to have special knowledge about the game that nobody else has. –  Paul Marshall Jun 28 '13 at 23:08
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Eventually, the saboteur must learn that he is the saboteur, otherwise he won't be able to sabotage anything (unless the game is entirely predetermined, in which case it isn't actually a game, like snakes and ladders).

But you can delay his learning of his role. Let's say that each player has certain actions they can take (maybe they have cards to play). You can set it up so only the saboteur has cards that are sabotage cards, and that he doesn't see them until a few turns in. This can be accomplished with something like:

  • Cards are separated into two piles: a large 'good' pile and a small 'bad' pile.
  • Cards are separated further into piles for each player. Only one of the piles will have any bad cards (and may optionally contain a few good cards).
  • A person who did not do the separations above proceeds to randomize the position of each pile. In this way, no player knows which pile is the bad pile.
  • A few good cards are then put on the top of each pile. This will delay the revelation of who the bad player is until a few turns in (at which point, he may well have the best 'good' setup, only to learn he has to destroy it!! Mwahahaha!!)

Now perhaps you're not using cards, but you might be able to do something similar to this, or use it as inspiration for a cool mechanic.

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In the game as planned, the last action of the game will be to decide to do the sabotage or not. If you are a citizen and you do it you just loose. If you are the saboteur you win alone. If you do not and are the saboteur you loose. if you do not and the saboteur does not, you win. I am not yet sure about the middle:) –  Andrey Jun 28 '13 at 18:37
    
@Andrey So... the entire win/lose condition hinges on the saboteur trying to guess or deduce that they are the saboteur, and make the correct decision for the last action? –  Jefromi Jun 28 '13 at 19:15
    
Yes, this would be about as deep as 1 night werewolf –  Andrey Jun 28 '13 at 19:51
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Have the deal deck include 2 or 3 saboteurs, but be 2 or three cards larger than the number of players. Therefore, if he doesn't see a saboteur, he knows he's it, but seeing one doesn't let him off the hook.

Or, Deal 2 cards to each player. Each shows them to everyone else without looking. Then, after the process, everyone randomly picks one of their two, and discards face down the other. Everyone knows who might be the saboteur except the saboteur. Works best if there are multiple saboteur cards.

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You'd need something else to make the game interesting, but as far as I understand it you could probably just draw 5 citizen cards and 1 saboteur card and put them face down in front of each person, so nobody knows who anybody is. Then they have to try to decide if they want to do the sabotage not knowing if they are a citizen or a saboteur. If they decide to do it, they look at their card and if they're the saboteur, they win. If they're a citizen, they reveal their identity to the group and are out. That way each unsuccessful attempt increases everyone else's probabilities of being the saboteur.

You could also do something like Mafia where everyone has to try to vote on who they think the saboteur is. Or something like that.

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Sounds pointless of no one knows –  Andrey Jun 28 '13 at 20:54
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