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Subject: Setup Problem to Solve for Unique Social Deduction Game rss

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Jon Perry
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Hi everybody,

I have a game I've been working on for over a year. It's really fun and unique when it works, but setting it up is tricky. I have some passable setup methods, but each of them has problems. I'm wondering if one of the board game geniuses around here can come up with a better way.

The goal is to invert the usual traitor paradigm. Instead of one person betraying the group, the group is betraying one person. And instead of doubting your friends, you doubt your own identity. The current theme I'm using is inspired by the replicants in Blade Runner, and the scene where the android doesn't realize she is as android.

So here is an example of the ideal result I want:

--Imagine a four player game where the players are numbered I-IV.
--Players I, II, and IV get dealt a card telling them that III is the replicant.
--Player III, on the other hand, gets dealt a fake card telling them that II is the replicant.

In other words, the experience of playing the game is that there's someone you think is the replicant, but there's a 1/4 chance that the replicant is in fact, you. In order to figure out whether or not you're the replicant, you have to keep an eye on how the other players act toward you.

Anyway, this setup turns out to be extremely difficult to create.

So far the solutions I have are:

(a) Use an app. Pass a phone around before the game starts that tells everybody whom they should suspect. This will do a perfect job, but involves mandatory app integration which is not ideal. (As a side question, how do people feel about the marketability of an app-integrated 15-20min social deduction game?)

(b) Have 12 different decks in different bags (Spyfall style) that represent the 12 different possible ways a 4p game could go. Each deck contains 4 cards, one for each player. The backs of the cards specify which player that card goes to. This is essential to ensure no one gets their own number.

The problem with this solution is that it's component heavy. Which would be okay maybe if the game was only 4p, but I'd like the game to handle 3p, 5p, 6p as well. In that case you'd need an exorbitant number of decks, since it's not even clear you could re-use the same decks across player counts.

(c) All the cards in the game's main deck are numbered in the top left corner. The range is about 1-40. Before the game starts you deal a card from the main deck to each player to use as their ID card. Players DO NOT look at their own ID card, but rather put it in a card stand facing AWAY from them, Hanabi-style. The player with the highest numbered card is the replicant. So you look around the table and see the highest number. That person is the replicant, unless of course you yourself have a higher number.

This is the least fiddly option and the primary one I've been testing with. The problem is it's uneven. Some deals are better than others. Some games are good and exciting, and some less so. The biggest problem is that when a person looks around and sees only low numbers, they have a very strong prior probability that they are the replicant, which isn't ideal, since I'd rather people deduced things based upon in-game social cues and player decisions, rather than an artifact of setup.

---

Thanks in advance for any thoughts! The more I think about the problem, the more I think that the app route may simply be the best way, but I thought I'd check to see if any of you can find a way to solve this with physical components.

-Jon Perry
Quibble Games

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Jeremy Lennert
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I think that using an app would be reasonable.

(And obviously, players could substitute a referee instead.)
 
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Jeff Warrender
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I think this works:

Say it's a 5p game. There would be two sets of four cards. Each set has the following cards:

"It's the person on your left"
"It's the person two to your left"
"It's the person three to your left"
"It's the person four to your left"

Arrange one set in order. Randomize the other, take the top card (keeping it face-down of course), and place it on the top of the ordered pile.

Then, "cycle-shuffle" this deck of five cards. I.e., rearrange without randomizing. You would move the bottom card to the top, then repeat, over and over again, a bunch of times, until everyone has lost track of which card is the top one. (Perhaps several players each cycle the cards a few times under the table, but don't disclose how many times they each cycled)

Then, deal out the cards clockwise around the table.

So, for example, players are A-E. The 'extra' card from the randomized pile is 'it's 2 to your left'. So say after cycle-shuffling we got this deal:

A - 3 to your left
B - 4 to your left
C - 2 to your left
D - to your left
E - 2 to your left

So C is the android, but C thinks that A is the android.
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Harv Veerman
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The above is brilliant in its simplicity.
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Jon Perry
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Wow, this sounds really promising! I think you've solved it! Or at least I'm not seeing a flaw yet.

I'm going to test it first, obviously, but assuming this method works well, you are going to get a very big thank you in the game's credits.


jwarrend wrote:
I think this works:

Say it's a 5p game. There would be two sets of four cards. Each set has the following cards:

"It's the person on your left"
"It's the person two to your left"
"It's the person three to your left"
"It's the person four to your left"

Arrange one set in order. Randomize the other, take the top card (keeping it face-down of course), and place it on the top of the ordered pile.

Then, "cycle-shuffle" this deck of five cards. I.e., rearrange without randomizing. You would move the bottom card to the top, then repeat, over and over again, a bunch of times, until everyone has lost track of which card is the top one. (Perhaps several players each cycle the cards a few times under the table, but don't disclose how many times they each cycled)

Then, deal out the cards clockwise around the table.

So, for example, players are A-E. The 'extra' card from the randomized pile is 'it's 2 to your left'. So say after cycle-shuffling we got this deal:

A - 3 to your left
B - 4 to your left
C - 2 to your left
D - to your left
E - 2 to your left

So C is the android, but C thinks that A is the android.
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Todd Jordan
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Give this idea a shot if you like it. I'll use a trump card deck as an example but you'll still need to rob cards from another deck(s). In a four player game, First make 4 sets of three cards identical cards (true replicants). Kings, Queens, Jacks, Aces. Then give each set 3 more cards one of each fraction that set is not. One example set 3 kings, 1 jack, 1 queen, 1 ace. Place those added 3 cards on the top of each set. (One of these cards will become the false replicant). Place each set (of all 6 cards) in to each of their own card sleve. Shuffle the sleeves under the table. Choose one sleve and remove all cards,
Don't look at them. Take the top 3 cards off the set shuffle them and place one back into the set. Discard the other 2 but keep them hidden. Shuffle the set and deal cards. Now you have no one able to calculate based on probability and you've got a fully blind game setup. Hope it works good luck.


 
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Carel Teijgeler
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jwarrend wrote:
I think this works:

Say it's a 5p game. There would be two sets of four cards. Each set has the following cards:

"It's the person on your left"
"It's the person two to your left"
"It's the person three to your left"
"It's the person four to your left"

Arrange one set in order. Randomize the other, take the top card (keeping it face-down of course), and place it on the top of the ordered pile.

Then, "cycle-shuffle" this deck of five cards. I.e., rearrange without randomizing. You would move the bottom card to the top, then repeat, over and over again, a bunch of times, until everyone has lost track of which card is the top one. (Perhaps several players each cycle the cards a few times under the table, but don't disclose how many times they each cycled)

Then, deal out the cards clockwise around the table.

So, for example, players are A-E. The 'extra' card from the randomized pile is 'it's 2 to your left'. So say after cycle-shuffling we got this deal:

A - 3 to your left
B - 4 to your left
C - 2 to your left
D - to your left
E - 2 to your left

So C is the android, but C thinks that A is the android.

A really neat solution.

But does have to be cards? A blind counter drawing would not requiring the shuffling, methinks.
 
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Jeremy Lennert
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jwarrend wrote:
Then, "cycle-shuffle" this deck of five cards. I.e., rearrange without randomizing. You would move the bottom card to the top, then repeat, over and over again, a bunch of times, until everyone has lost track of which card is the top one. (Perhaps several players each cycle the cards a few times under the table, but don't disclose how many times they each cycled)

This is a clever solution, but I question whether it's possible to "cycle-shuffle" well enough to foil someone who is trying to keep track. I suppose you could do it in turns so that no single person can watch the entire shuffle process...

anijunk wrote:
But does have to be cards? A blind counter drawing would not requiring the shuffling, methinks.

How would you ensure that they stayed in the correct relative order? The whole crux of this plan is that you don't know where the cycle starts but you know that all the cards are in the exact right order after the start.
 
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Harv Veerman
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Antistone wrote:
This is a clever solution, but I question whether it's possible to "cycle-shuffle" well enough to foil someone who is trying to keep track. I suppose you could do it in turns so that no single person can watch the entire shuffle process...


A person can cycle-shuffle 1, 2, 3 or more cards at a time without changeing the order. How do you keep track. If you hear me shuffle two times, you still don't know how many cards I cycle-shuffled, right?
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Jon Perry
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So this is basically a more card efficient version of my solution (b).

It's actually a very good efficiency improvement, but it still does require a fair amount of cards:

To handle up to 4 players you'd need 24 cards.
To handle up to 5 players you'd need 40 cards.
To handle up to 6 players you'd need 60 cards.

With small sized cards it'd be doable but I think it's probably more unwieldy than the alternate solution suggested above.


Azuremirror wrote:
Give this idea a shot if you like it. I'll use a trump card deck as an example but you'll still need to rob cards from another deck(s). In a four player game, First make 4 sets of three cards identical cards (true replicants). Kings, Queens, Jacks, Aces. Then give each set 3 more cards one of each fraction that set is not. One example set 3 kings, 1 jack, 1 queen, 1 ace. Place those added 3 cards on the top of each set. (One of these cards will become the false replicant). Place each set (of all 6 cards) in to each of their own card sleve. Shuffle the sleeves under the table. Choose one sleve and remove all cards,
Don't look at them. Take the top 3 cards off the set shuffle them and place one back into the set. Discard the other 2 but keep them hidden. Shuffle the set and deal cards. Now you have no one able to calculate based on probability and you've got a fully blind game setup. Hope it works good luck.


 
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Jeremy Lennert
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Mad Math wrote:
Antistone wrote:
This is a clever solution, but I question whether it's possible to "cycle-shuffle" well enough to foil someone who is trying to keep track. I suppose you could do it in turns so that no single person can watch the entire shuffle process...


A person can cycle-shuffle 1, 2, 3 or more cards at a time without changeing the order. How do you keep track. If you hear me shuffle two times, you still don't know how many cards I cycle-shuffled, right?

If I can only listen to you, then no, I probably can't tell.

If I can watch, or if I am the person doing the shuffling, I think I can probably count whether the smaller pile of the cut has 1, 2, or even 3 cards in it. And I can probably add mod 5 in my head faster than you can shuffle without risking getting the cards out of order.
 
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patrick mullen
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You have 4 square shaped cards. On each of their 4 sides is a number. Arrange 4 of cards such that they all have the same orientation (the "1" is pointed "up" on all of them). Rotate all of the cards to a random orientation (but keeping the fact that they all have the same orientation). Roll a d6 and divide by 2 and rotate the top card that many times to the right. Shuffle the cards (without changing orientation) and deal them out such that each player when they look at the card will see it from the correct orientation.

Fiddliest part is keeping the orientation correct when handing them out. Perhaps after the orientations are decided they could be put in sleeves that only reveal the correct number.

This method could be adapted for different shapes as well, with pentagon for 5 players, hexagon for 6 etc.
 
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The Chaz
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Antistone wrote:
jwarrend wrote:
Then, "cycle-shuffle" this deck of five cards. I.e., rearrange without randomizing. You would move the bottom card to the top, then repeat, over and over again, a bunch of times, until everyone has lost track of which card is the top one. (Perhaps several players each cycle the cards a few times under the table, but don't disclose how many times they each cycled)

This is a clever solution, but I question whether it's possible to "cycle-shuffle" well enough to foil someone who is trying to keep track. I suppose you could do it in turns so that no single person can watch the entire shuffle process...


I do it under the table. Then you do it under the table. This is discussed in the quote!


If a player is trying to gain meta knowledge of the state of the deck by listening/watching, they can leave the group immediately. Of course, it sounds like you are that player!

I like the solution.
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Jon Perry
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The problem with this is it doesn't solve the issue that 75℅ of the time someone will get their own number.


saluk wrote:
You have 4 square shaped cards. On each of their 4 sides is a number. Arrange 4 of cards such that they all have the same orientation (the "1" is pointed "up" on all of them). Rotate all of the cards to a random orientation (but keeping the fact that they all have the same orientation). Roll a d6 and divide by 2 and rotate the top card that many times to the right. Shuffle the cards (without changing orientation) and deal them out such that each player when they look at the card will see it from the correct orientation.

Fiddliest part is keeping the orientation correct when handing them out. Perhaps after the orientations are decided they could be put in sleeves that only reveal the correct number.

This method could be adapted for different shapes as well, with pentagon for 5 players, hexagon for 6 etc.
 
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Jeremy Lennert
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The Chaz wrote:
If a player is trying to gain meta knowledge of the state of the deck by listening/watching, they can leave the group immediately. Of course, it sounds like you are that player!

I am continuously baffled at the number of people who respond to the point "this makes cheating easier than I would like" with the sentiments

1) "I don't play with cheaters"
and/or
2) "sounds like YOU must be a cheater"


Regarding #1, no one intentionally plays with cheaters, but anyone could be playing with a cheater by accident. If you play non-solitaire games and think that couldn't happen to you, then (a) you are probably deluded, and (b) even if you're right, could you show a bit of sympathy for the rest of the world?

Particularly in the case of "taking advantage of information you're not supposed to have", it is sometimes pretty difficult not to cheat. If someone accidentally shows their hand in a card game, a reasonable person doesn't say "don't worry, everyone will just choose to play exactly as if they hadn't seen your hand (and anyone who doesn't is a cheater and will be banned from the game)". If you "hide" information in an easily-trackable fashion, you are actually asking quite a lot from players when you want them to fail to notice.


Regarding #2: when someone suggests that you improve your security, that is NOT evidence that they intend to break in. In fact, it's probably evidence of the opposite. (People with bad intentions don't want your security to improve!)

When someone points out flaws in your security, and you respond by questioning their intentions, then at best you are shooting the messenger, and the community as a whole suffers for it (we get fewer messages in the future).

If this were about something serious (like bank security, rather than board games), I would suspect you of intentionally defrauding your customers by convincing them your security is better than it is. (The field of security research is, unfortunately, littered with examples of this.) Even if you are not doing this, you are making it easier for the crooks of the world to do this in the future by normalizing the practice of vilifying whistle-blowers.


I do not routinely suspect fellow players of cheating. I'm even the designer of a published board game that self-admittedly does not work if people try to cheat.

I still think it's a good idea to point out when a design makes it easy to cheat and ask if there's a way to change that.
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Jon Perry
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Given the genre of my game (social deduction that prioritizes experience over cut throat competition) I think the level of cheating potential that exists in the proposed solution is tolerable.

In general, I do support the idea that game designers should actively try to minimize cheating opportunities in games as best they can. So I think it's worthwhile raising the issue.

However, since you can never reduce the chance of cheating to 0% in a tabletop game, you have to settle somewhere, and this seems like a decent settling point for my purposes.

If anything, I'm more concerned that this whole cycle shuffling idea is one more thing I have to explain in the rulebook to an already pretty bizarre game.

Since they're not mutually exclusive, I'll probably include the app solution as well.
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Martin Windischer
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Another solution with easier handling:
There are 12 cards, with all possible combinations. Not in plain text but under a red pattern - Something like this:



One of the cards is drawn randomly, and every player now may look at his opponent (for every player there is a specific location on the card).
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MartinWin wrote:
One of the cards is drawn randomly, and every player now may look at his opponent (for every player there is a specific location on the card).

So if I'm player #4 in a 6-player game, I pick up the shared filter and need to make sure that I read the center-right section of the card without accidentally reading the top-right, bottom-right, or center-left sections?

Or do you have 6 different filters that each reveal only one of the six sections on the card? Someone was asking about that last month in this thread and no one seemed to know how to do it.
 
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Jon Perry
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MartinWin wrote:
Another solution with easier handling:
There are 12 cards, with all possible combinations. Not in plain text but under a red pattern - Something like this:



One of the cards is drawn randomly, and every player now may look at his opponent (for every player there is a specific location on the card).


Let me just make sure I understand this.

So a card might have 3, 3, 3, 2 written on it, one numeral in each corner.

Then we put the card in the middle of the table and we each use the glasses to look at a different corner of the card?

If so, then this method reduces the number of cards needed from 48 to 12 (and adds a cool toy factor) but it ultimately doesn't work, because it fails to solve the problem of someone getting their own number 75% of the time.

EDIT: I guess you could fix that problem by marking (in a non-encoded way) which corner each player is supposed to look at.
 
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jonperry wrote:
If so, then this method reduces the number of cards needed from 48 to 12 (and adds a cool toy factor) but it ultimately doesn't work, because it fails to solve the problem of someone getting their own number 75% of the time.

Presumably the corners are labeled so that player #1 always looks in corner #1, etc.
 
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Antistone wrote:
So if I'm player #4 in a 6-player game, I pick up the shared filter and need to make sure that I read the center-right section of the card without accidentally reading the top-right, bottom-right, or center-left sections?

Or do you have 6 different filters that each reveal only one of the six sections on the card? Someone was asking about that last month in this thread and no one seemed to know how to do it.


If you want, you can make different filters which consists of a normal card with a little hole in it, this hole is covered with the filter.
On every card the position is different, so the player just has to put his private decoder card on top of the other card to see his number.

But I don't think that's necessary, if the filter is small enough it should work without that.

Antistone wrote:
Presumably the corners are labeled so that player #1 always looks in corner #1, etc.

Yes, this is what I thought.

On the other hand, if the game should work for different counts of player, this method isn't really efficient as you need different cards for every player count. In this case Jeffs method seems better to me.
 
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patrick mullen
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jonperry wrote:
The problem with this is it doesn't solve the issue that 75℅ of the time someone will get their own number.


saluk wrote:
You have 4 square shaped cards. On each of their 4 sides is a number. Arrange 4 of cards such that they all have the same orientation (the "1" is pointed "up" on all of them). Rotate all of the cards to a random orientation (but keeping the fact that they all have the same orientation). Roll a d6 and divide by 2 and rotate the top card that many times to the right. Shuffle the cards (without changing orientation) and deal them out such that each player when they look at the card will see it from the correct orientation.

Fiddliest part is keeping the orientation correct when handing them out. Perhaps after the orientations are decided they could be put in sleeves that only reveal the correct number.

This method could be adapted for different shapes as well, with pentagon for 5 players, hexagon for 6 etc.


*Ooof* I thought I had a good one.

This thought experiment is a good example of why quantum entanglement is cool but probably can't be used for super-lightspeed communication.

Here's another VERY off the wall one I thought of:

In a 4 player game, there is a deck of 12 cards in the center. They either say "replicant" or "not replicant" (more than 1 of each). There is also a deck or counters with the numbers 0-4 for each player.

Player 1 draws a "not replicant" and passes the number 0 to the left. Player 2 draws "replicant" and passes the number 1 to the left - the last player who went is the replicant.
Player 3 receives the number 1 and knows who the replicant is. But he draws a card anyway and passes a number 1 regardless.
Player 4 receives the number 1 and knows who the replicant is. He draws a card anyway... but randomly selects - let's say a 2 - to pass to player 1.

Player 1 goes again, THINKING that the replicant was player 2. If he draws "replicant" he will pass a 4, "not replicant" he will pass a zero.
Player 2 goes, but already got that number in the first round. Players 2, 3, and 4, all already got a number. So when they receive their number, they set it aside because it's not accurate. They again pass the correct number (1). When it gets to player 1 again (who thinks it's player 2) he will draw and pass a 2 again.

Continue until the replicant deck is empty.

The fun part for me here is that rather than just being given the information by the system, you are given the information by someone who might have been lying to you.

The downside is I could see players easily doing something wrong, passing the wrong number by accident etc. Also I may have made another mistake somewhere, let me know This is a really fun design challenge to think about.
 
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saluk wrote:
This thought experiment is a good example of why quantum entanglement is cool but probably can't be used for super-lightspeed communication.

How so?

saluk wrote:
Here's another VERY off the wall one I thought of:

In a 4 player game, there is a deck of 12 cards in the center. They either say "replicant" or "not replicant" (more than 1 of each). There is also a deck or counters with the numbers 0-4 for each player.
<snip>

I had some trouble following this explanation. When player 4 passes a "2" counter to player 1, why does player 1 follow up by passing either a "0" or "4", and why does it depend on what card player 1 draws the second time?


Here's an algorithm that might or might not be what you intended and comes close to solving the original problem:

Shuffle 1 card saying "replicant" and 3 cards saying "not replicant".

Players take turns drawing a card and then passing a numbered counter to their left. If a player draws the "replicant" card, it means the player to their right is the replicant.

If you are passed a "0" counter (or are going first) and you draw a "not replicant" card, then you don't know the identity of the replicant, so you pass a "0".

If you are passed a "0" counter (or are going first) and you draw a "replicant" card, then the player to your right is the replicant. Pass a counter with his player number (e.g. if player 3 draws the replicant card, he passes a "2" counter).

If you are passed any other counter, then the replicant card has already been drawn, and the counter tells you who the replicant is. Ignore your card draw and pass the same number to the next player...

...unless you are about to pass a player their own number (which would tell them that they are the replicant), in which case you pass a counter for a different player.

You go 2 full circles around the table (everyone draws a card only the first time, but passes a counter both times). If you received a non-zero counter on the first cycle, then ignore the second counter you receive and pass any counter you like the second time (since it will also be ignored).

Net result:

- Everyone passes "0" until someone draws the replicant card
- Then, everyone passes the number of the replicant until play cycles back to the true replicant
- The true replicant is passed a fake number
- None of the counters passed after that point matter, since they will all be ignored by the receiving player

When you're done, the following are guaranteed:

1. There is exactly 1 replicant at the table
2. Seating order does not affect your prior probability of being the replicant
3. Everyone except the replicant received a card or counter indicating the replicant's identity
4. The replicant received a card or counter falsely indicating someone else

However, I see a couple of problems:

5. The player to the replicant's left can be 100% sure that they are not the replicant, because they drew the actual card that started the whole chain.

6. Everyone else can be 100% sure that the player to their right is NOT the replicant (since they didn't draw the "replicant" card). That is, when you give a fake number to the replicant, you can't give your own number.

7. If someone passes you a zero, then you know that everyone who went before you drew "not replicant" cards.

For instance, if player 1 draws a "not replicant" card and passes a 0 to player 2, then player 2 knows that player 4 cannot end up being the replicant. If player 2 turns out to be the replicant, player 1 can't pass him a "4" token, because that would give the game away; he'll need to pass a 3 token.

If player 2 also draws a "not replicant" card and passes a 0 to player 3, then player 3 also draws a "not replicant" card, then player 3 immediately knows that he's the replicant (he'll receive some counter in the second rotation, but he'll know it's a lie because he didn't receive it on the first rotation).

You can mitigate this problem by increasing the number of cards. For instance, if you play with 12 cards (instead of 4) and go 4 cycles around the table (instead of 2), then player 3 can't be sure that he's the replicant, because the card could have been drawn in the second cycle rather than the first. But this takes longer, and if the replicant card happens to be one of the last 3 in the deck, you're still leaking information. (And you can't abort that game and start over, because then you're reducing the effective deck size to whatever point you abort at, which means you leak information if the replicant card is drawn in any of the 3 slots before that point.)
 
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patrick mullen
United States
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I thought I mentioned starting out with 12 and cycling through several times - I did in fact make a mistake in the description of the algorithm in my head with player 4. The fake number player 4 passes (or any player who passes a fake number) can be the zero until the second to the last round.

Yeah the worst part is you know the player to your right isn't.

In any case players would have to be extremely honest or good luck!
 
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Dave Platt
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I've never played one of these games so feel free to tell me if I'm missing the point.

Would it really matter if someone got their own card? The game sows doubt about your own identity so would this not just thicken the plot? And if so, then you would only need a pack of 36 cards. 6 of each, saying player 1 is the replicant, player 2 is the replicant and so on. Sort into 6 like packs swop one card from each, then move the packs around, turn away whilst someone else moves the packs around, repeat and repeat again maybe. Someone chooses a pack to play which is shuffled and dealt one card to each player. The other packs are put away.

Someone tell me if I'm missing something really obvious.
 
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