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Subject: Hidden Identity Changing Problem rss

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Stefan Lopuszanski
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Game Design Challenge:

Solve this design problem. Game is a secret identity deduction game where players are divided into 2 team and the game is played over two phases (think Battlestar: Galactica). In the first phase people are somehow divided secretly into two groups ("Good" and "Evil"). For the second phase some of the "Evil" people remain "Evil" while some might become "Good." Likewise, some "Good" might become "Evil." What team you are on in the first half somehow influences the probability of what team you'll be on in the future (an "Evil" player in the first half is more likely to stay "Evil" than a "Good" person is to become "Evil").

Specific example to solve: For a 5 player game the group is randomly divided such that 1 to 3 of the 5 people (or 0 to 3 if you want) are on the "Evil" team. When the second phase occurs however there are always exactly 2 people on the "Evil" team (such that it is possible if the "Evil" team has 3 people one of them becomes "Good"). This could also mean a "Good" player becomes "Evil" (in the case that 1 [or 0] were "Evil" in the first half). This must be done such that no one knows the team each player is on and each player knows only their own identity. What do you do to achieve this?

Note: Requiring a digital device is not allowed as that makes it too easy to solve and has a huge burden on players. Also, this solution does not need to be scalable for number of players outside of 5, but bonus points if you can make it that way.

Any thoughts?
 
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Andrés Santiago Pérez-Bergquist
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Presumably, you also do not want players to know during the first half of the game what role they will have in the second half (or otherwise they would likely play according to their final role instead of their current role). If this is not the case, you can deal cards that specify the role during the first half and then during second half. (e.g. Good/Good, Evil/Good, Good/Evil, Evil/Evil)

To keep the second half role hidden, you could go with dealing out two cards at start of game, one of which is not to be looked at until end of game. You deal them out at the beginning, so you can build the two-card stacks following some protocol to couple the probabilities of the two cards. (If you wanted to let the two halves be independent, then you could just deal out the second card at midgame.) The pairs of cards could be place in envelopes, for easier random assignment to the players.
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Brandon Powell
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Seems like the easiest way would be to have 2 decks; one for the first round and one for the second. So your first deck would have some set ratio of 'good' and 'evil' cards, say 3 good for every 2 evil, and you deal these out to 4 or5ayers.

You're seconddeck should be easy; instead of your second deck assigning 'good' or 'evil' teams, have it indicate 'stay' or 'switch' instead.

So if you have 6 players, starting off with 4 good and 3 evil cards in Deck 1 (to introduce some element of guesswork, suppose), your deck 2 will have 6 cards: 4 'stay' and 2 'switch'.
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Daniel Blumentritt
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Quote:
You're seconddeck should be easy; instead of your second deck assigning 'good' or 'evil' teams, have it indicate 'stay' or 'switch' instead.


This works as long as there is no particular "final ratio" of teams you need to achieve. If you need to end up with either a 2/3 or 3/2 split, though, it won't work, and you'd need to probably put the cards in stacks of 2 like Andres suggested.
 
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Stefan Lopuszanski
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Santiago wrote:
Presumably, you also do not want players to know during the first half of the game what role they will have in the second half (or otherwise they would likely play according to their final role instead of their current role).


Yes, that is the case.

Santiago wrote:

To keep the second half role hidden, you could go with dealing out two cards at start of game, one of which is not to be looked at until end of game. You deal them out at the beginning, so you can build the two-card stacks following some protocol to couple the probabilities of the two cards. (If you wanted to let the two halves be independent, then you could just deal out the second card at midgame.) The pairs of cards could be place in envelopes, for easier random assignment to the players.


Yep, that's the solution someone else offered. They basically said deal out sleeved cards with 2 cards in it. The front card is your current role and the back card is your second role. I had a similar system but it involved bags (much less elegant).



Someone else had an idea with stones in a bag. White for good and black for evil. The bag is seeded with 3 black and 4 white. Everyone takes a stone out at the start for their starting role. Then, in the second phase another bag seeded with 2 black and 3 white. Everyone passes around the bag twice. In the first pass around only the "evil" people take a stone out (the good players pretend to take one out) and the second pass the reverse happens. I'm unsure on the probability since someone who starts drawing from the bag has different odds than someone later on technically (kind of like the Monty Hall problem).

So far those are the only two solutions people have come up with. Definitely curious about hearing others though.
 
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Andrés Santiago Pérez-Bergquist
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Stexe wrote:
Someone else had an idea with stones in a bag. White for good and black for evil. The bag is seeded with 3 black and 4 white. Everyone takes a stone out at the start for their starting role. Then, in the second phase another bag seeded with 2 black and 3 white. Everyone passes around the bag twice. In the first pass around only the "evil" people take a stone out (the good players pretend to take one out) and the second pass the reverse happens. I'm unsure on the probability since someone who starts drawing from the bag has different odds than someone later on technically (kind of like the Monty Hall problem).


If you're not adding more stones to the bag between passes, the order of drawing is completely irrelevant and just amounts to randomly assigning the five stones to the five players independently of what they were in the first round.
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Darrell Pavitt
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Possibly you could use a sort of chit draw system, with each chit having a unique value dependant on the number of players (such as 1-5 for a 5 player game).

In the first round, anyone with a chit rated 3 or more is on the evil team.

In the second round, each player draws a second chit (again 1-5) and anyone with a combined total of (say) 5 is evil.

Using something like wooden blocks rather than cardboard counters would add to the aesthetic.
 
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B C Z
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When solving this, a few questions on which states and state transitions you want to allow:

For "0 evil, 5 good", it is clear that exactly 2 good must flip to evil.

For "1 evil, 4 good". Which are desirable:
a/ 1 evil becomes good, 2 good become evil
b/ 0 evil become good, 1 good becomes evil

For "2 evil, 3 good", Which are desirable:
a/ 2 evil become good, 2 good become evil
b/ 1 evil becomes good, 1 good becomes evil
c/ no change has to happen, but it is still possible
d/ no change *can* happen.

I believe that /a/ above isn't desired. I'm not sure if your desired solution allows for /b+c/ or you want only /d/.

For "3 evil, 2 good"...
a/ 3 evil become good, 2 good become evil {complete reversal!!}
b/ 2 evil become good, 1 good become evil
c/ 1 evil becomes good, 0 good become evil

Again I don't think you want /a/. Not sure on your stance for /b/ vs /c/


Lastly, an entirely separate question:
Is it permissible that a player knows what team they will end up on after knowing their role from round 1? In other words, is it legal that a player is "definitely good" or "definitely evil" and thus will not be eligible to flip sides and will know this fact?
OR...
Are all players on a given side equally likely to flip sides?
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Robyn Dawson-Ruiz
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Stexe wrote:
Santiago wrote:
Presumably, you also do not want players to know during the first half of the game what role they will have in the second half (or otherwise they would likely play according to their final role instead of their current role).


Yes, that is the case.

Santiago wrote:

To keep the second half role hidden, you could go with dealing out two cards at start of game, one of which is not to be looked at until end of game. You deal them out at the beginning, so you can build the two-card stacks following some protocol to couple the probabilities of the two cards. (If you wanted to let the two halves be independent, then you could just deal out the second card at midgame.) The pairs of cards could be place in envelopes, for easier random assignment to the players.


Yep, that's the solution someone else offered. They basically said deal out sleeved cards with 2 cards in it. The front card is your current role and the back card is your second role. I had a similar system but it involved bags (much less elegant).



+1 to this idea. Here's how I would approach it.

First define a term for a pair of alignment cards placed in a single sleeve with only the top card showing. I'll call them alignment packs (you could put more than 2 cards in an alignment pack, but that's besides the point). The game comes with more than enough alignment packs, sorted based on the final alignment. All the packs that end in good alignment are in one pile and evil in another. At the start of the game you shuffle each pile separately than take a fixed number from each pile. So for a 5 player game you would take 3 good and 2 evil.

If you include unique alignment cards like "good + forced behavior", make sure to only put them on the final alignment card. Otherwise players will see that unique card and remember what's below it.



 
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Stefan Lopuszanski
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byronczimmer wrote:
When solving this, a few questions on which states and state transitions you want to allow:

For "0 evil, 5 good", it is clear that exactly 2 good must flip to evil.

For "1 evil, 4 good". Which are desirable:
a/ 1 evil becomes good, 2 good become evil
b/ 0 evil become good, 1 good becomes evil

For "2 evil, 3 good", Which are desirable:
a/ 2 evil become good, 2 good become evil
b/ 1 evil becomes good, 1 good becomes evil
c/ no change has to happen, but it is still possible
d/ no change *can* happen.

I believe that /a/ above isn't desired. I'm not sure if your desired solution allows for /b+c/ or you want only /d/.

For "3 evil, 2 good"...
a/ 3 evil become good, 2 good become evil {complete reversal!!}
b/ 2 evil become good, 1 good become evil
c/ 1 evil becomes good, 0 good become evil

Again I don't think you want /a/. Not sure on your stance for /b/ vs /c/


Lastly, an entirely separate question:
Is it permissible that a player knows what team they will end up on after knowing their role from round 1? In other words, is it legal that a player is "definitely good" or "definitely evil" and thus will not be eligible to flip sides and will know this fact?
OR...
Are all players on a given side equally likely to flip sides?


I want to definitely avoid "complete reversals." (Thus no "1 evil becomes good, and 2 good become evil"). The "b+c" sounds like it would work.

I'd also try to avoid someone knowing what team they are on 100%, although I'm not dead set on that one.

There are still a lot of systems to design. The basic idea is similar to Battlestar Galactica and Dark Moon but with more focus on card play / figuring out identities and a lot shorter than BSG (trying to shoot for the same length of Dark Moon or maybe slightly longer).

Some other systems I'm trying to work in are "push your luck" aspect (which I think is missing from a lot of hidden identity games, since some people are more prone to risk without being "evil") and "must do evil things as a good guy" and "must do good things as an evil guy." But again, I haven't done any play testing yet. Just lots of notes on systems that I'm trying to formulate and hook together to make a meaningful game.
 
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JT Schiavo
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I think the sleeved cards would be the best implementation. This is how I'd do setup:

Start by putting the back cards in, 2 evil and 3 good. Take one of the sleeves with evil and put another evil card in front, then set that sleeve aside. Shuffle 4 good and 2 evil, then randomly put one card in front of each of the other sleeves.

This guarantees that one evil will stay evil so there is no complete reversal. Part of the evil first-round game will probably be trying to determine if you are solo-evil so that you know you will not change, or try to figure out if it's tri-evil because there's a good chance you might change and not want to mess your own game up.

This requires twelve alignment cards and a little set up time for a five player game, and could scale as well.
 
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Stefan Lopuszanski
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crinaya wrote:
I think the sleeved cards would be the best implementation. This is how I'd do setup:

Start by putting the back cards in, 2 evil and 3 good. Take one of the sleeves with evil and put another evil card in front, then set that sleeve aside. Shuffle 4 good and 2 evil, then randomly put one card in front of each of the other sleeves.

This guarantees that one evil will stay evil so there is no complete reversal. Part of the evil first-round game will probably be trying to determine if you are solo-evil so that you know you will not change, or try to figure out if it's tri-evil because there's a good chance you might change and not want to mess your own game up.

This requires twelve alignment cards and a little set up time for a five player game, and could scale as well.


Yeah, we've come to a similar conclusion when I asked for ideas on Facebook with my designer friends. There is a few refinements that might be done with opaque sleeves and double sided cards to reduce the number of needed cards.

There could even be a further refinement where cards are double sided and the front has two halves. You'd just need square cards and to "twist shuffle" (so both their order and rotation are randomized) before sleeving them.

A few other people had a couple of other ideas that I'll post later on if I think they might contribute to the discussion. The other suggestions involve a bag with tokens passed / manipulated under the table (which actually fits with another mechanism in the game that you do under a table), a dial for each player that determines identity, and an idea with a triangular piece that displays colors on the corners of the triangle and is used for role purposes.

Going to work on other systems in the game before I go back on this one now that there are enough solutions for me to find one that works when other elements are better solved. Although I'm always up for more suggestions in case people come up with something neat or clever or more elegant.
 
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John Breckenridge
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You could do it with just one card per player, and have some other randomizer. For example, suppose after Phase 1, a die is rolled and all players use the same result.

Then one card might say something like:

Quote:
For the First Phase, you are Team Good.

For the Second Phase, if the die roll is
1 Team Good
2 Team Good
3 Team Good
4 Team Good
5 Team Evil
6 Team Evil


And you can work it out so whichever case you have there are the right number of players on team Evil.

The main downside to this technique is you might need to have special cards for certain player counts, in order to maintain the distribution you want.

If you don't want to use a die, you could have a set of randomizer cards with numbers or colors or letters on them and draw one.
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Jeremy Lennert
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I like John's die roll suggestion above. But if you don't, here's another option that I don't think was suggested yet:



Put 2 black stones and a bunch of white stones in a bag, and start passing the bag around.

If you are currently Good, draw 1 stone from the bag. If you are currently Evil, draw 3 stones from the bag.

If you draw a black stone, you are Evil. If you draw both black stones, put one back.

Keep passing the bag around in a circle until all the stones are gone.

If players don't all take an equal number of turns, then the players who take more turns have higher odds of being Evil, but the more white stones you use the less that matters. It might also be possible to calculate a number of stones to use so that everyone will take an equal number of turns regardless of how many people were Evil in phase 1 (but it might be a lot of stones). Alternately, if you're OK with using some mechanism to count the number of people who were Evil in phase 1 (without revealing exactly who), you can calculate the number of stones based on that so that everyone will draw exactly once.



Obviously, that requires that the other players can't see how many stones you are drawing or when you put one back. If you can't work with those constraints, you could try something a little more complicated, like:

Put 2 black stones and a bunch of white stones in a bag.

Everyone takes turns drawing 3 stones.

If you draw all white stones, but one back.

If you draw one black stone, and you were Evil in phase 1, put back a white stone.

If you draw one black stone, but you were Good in phase 1, put back the black stone.

If you draw both black stones simultaneously, or if you are already holding a black stone from a previous draw and you draw a new one, put back one black stone (keep the other).

If there are less than 3 stones left in the bag, draw them and keep them all.

If you kept a black stone at any point, you are Evil in phase 2, otherwise you are Good. Evil people have a higher chance of staying Evil because they keep a black stone if they ever draw one, whereas Good people only keep one if they drew both at once or got one at the very end.

If there are exactly 2 stones left in the bag on the final draw and they are both black, you have to do the whole thing over again in order to get 2 Evil people. But the number of stones left in the bag decreases by 2 each time, so if you start with an odd number, that can't happen.

However, if the second-to-last person puts a black stone back in the bag, then they know that the person who draws last is going to be Evil. That might be undesirable.

In fact, whoever draws last probably has a higher probability overall of being Evil.
 
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Stefan Lopuszanski
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Antistone wrote:

In fact, whoever draws last probably has a higher probability overall of being Evil.


I'm trying to keep player position to not have an impact on who is evil and who isn't at the moment. But thanks for the suggestion.
 
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Bjorn B
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I have a different version of the stone and bag principle. I'm assuming identies have to be secret in both rounds.

Get a bag with 3 black and 5 white stones. Everyone picks one out for round 1 so there is between 0 to 3 evil people.

To assign identities for the second round. The remaining stones are revealed and some are put back (see below). The goal is to take 1 black and 2 white stones out, so the second round can start with exactly 2 evil persons.

Now every person takes turns putting their existing stone in the bag and taking out stone (could be the same one). After everyone is finished switching their stone. Take another look at the stones in the bag and see if another round is needed.

These are all possible conditions:
starting conditions
3w: put 1w back
2w 1b: put 1w and 1b back (you could finish immediately, but I would do it this way for some randomness)
1w 2b: put 1b back
3b: put 2b back

1b taken before
2w: finish
1b 1w: put 1b back
2b: repeat

1w taken before
2w: put 1w back
1b 1w: finish
2b: put 1b back

2w taken before
1w: repeat
1b: finish

1w 1b taken before
1w: finish
1b: repeat

This method guarantees 2 evil persons in the second round, while giving an increased chance of staying what you are (because you put your own stone back first before taking out another).
The downside is that it might take a lot of time in some situations. In most cases it would be solved in 1 or 2 rounds, 4 or more rounds would be rare. More rounds obviously means more players would have switched roles. Complete reversals are possible.
 
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Nathan Woll
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The simplest solution is to have a moderator.

After phase 1, the moderator looks at all identities then either randomly changes good to evil or randomly changes evil to good, or does nothing (based on the distribution he sees)

I would guess you don't want this game to require a mod?
 
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Stefan Lopuszanski
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jbrecken wrote:
You could do it with just one card per player, and have some other randomizer. For example, suppose after Phase 1, a die is rolled and all players use the same result.

Then one card might say something like:

Quote:
For the First Phase, you are Team Good.

For the Second Phase, if the die roll is
1 Team Good
2 Team Good
3 Team Good
4 Team Good
5 Team Evil
6 Team Evil


And you can work it out so whichever case you have there are the right number of players on team Evil.

The main downside to this technique is you might need to have special cards for certain player counts, in order to maintain the distribution you want.

If you don't want to use a die, you could have a set of randomizer cards with numbers or colors or letters on them and draw one.


I've been trying to think how that distribution would actually work for each card and be scalable. Do you have a better example of that? It doesn't seem like it would work very well in actuality. At least I'm not grasping it.

nswoll wrote:
The simplest solution is to have a moderator.

After phase 1, the moderator looks at all identities then either randomly changes good to evil or randomly changes evil to good, or does nothing (based on the distribution he sees)

I would guess you don't want this game to require a mod?


Yes, it would be too easy.

Quote:
Note: Requiring a digital device is not allowed as that makes it too easy to solve and has a huge burden on players.


Digital device is basically a moderator.
 
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Jeremy Lennert
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Stexe wrote:
I've been trying to think how that distribution would actually work for each card and be scalable. Do you have a better example of that? It doesn't seem like it would work very well in actuality. At least I'm not grasping it.

Card | #1 | #2 | #3 | #4 | #5 |
-------------+------+------+------+------+------+
Phase One | Good | Good | Evil | Good | Evil |
-------------+------+------+------+------+------+
Phase Two | | | | | |
Die Roll = 1 | Good | Good | Evil | Evil | Good |
Die Roll = 2 | Good | Good | Evil | Evil | Good |
Die Roll = 3 | Good | Good | Evil | Good | Evil |
Die Roll = 4 | Good | Good | Evil | Good | Evil |
Die Roll = 5 | Good | Evil | Good | Good | Evil |
Die Roll = 6 | Evil | Good | Good | Good | Evil |
-------------+------+------+------+------+------+


If playing with 3 players, shuffle and deal out cards #1-3. If playing with 5 players, shuffle and deal out cards #1-5. When phase 2 starts, roll a die to determine everyone's new alignment. Characters who start evil have a 2/3 chance of staying evil, and characters who start good have at least a 2/3 chance of staying good. With 5 players, all possible die rolls result in exactly 2 evil people in phase 2. With 3 players, all rolls result in exactly 1 evil person.

It gets more complicated if you also care about the number of evil people in phase 1 being variable, of course.
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Jake Staines
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Antistone wrote:

If playing with 3 players, shuffle and deal out cards #1-3. If playing with 5 players, shuffle and deal out cards #1-5. When phase 2 starts, roll a die to determine everyone's new alignment.


In general I like this approach, but the first thing that comes to mind is that - for example - if the die roll is a 3 or a 4 then everyone around the table knows that the players who were evil in round one are still evil in round two, which probably isn't desirable.

To avoid that problem you'd need the players to not know what the distribution on the cards was at the beginning of the game. The most obvious answer there is to package the game with randomisable envelopes with sets of alignment cards in, but that would mean that you can't really choose to just use three of them for a three-player game, 'cause that would mean examining the cards to determine which three to use. You can't realistically mark the cards uniquely because that would give away to some or all players which set is being used, if they play the game a lot. So you're introducing a lot of components!
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Jeremy Lennert
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Yes, I am assuming that you successfully kept your phase 1 identity secret. This approach won't work if it's necessary to prevent players from knowing how many players have switched sides (unless you do a lot of extra work, or are willing to have the number of evil players in phase 2 be variable).
 
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Stefan Lopuszanski
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Bichatse wrote:
Antistone wrote:

If playing with 3 players, shuffle and deal out cards #1-3. If playing with 5 players, shuffle and deal out cards #1-5. When phase 2 starts, roll a die to determine everyone's new alignment.


In general I like this approach, but the first thing that comes to mind is that - for example - if the die roll is a 3 or a 4 then everyone around the table knows that the players who were evil in round one are still evil in round two, which probably isn't desirable.

To avoid that problem you'd need the players to not know what the distribution on the cards was at the beginning of the game. The most obvious answer there is to package the game with randomisable envelopes with sets of alignment cards in, but that would mean that you can't really choose to just use three of them for a three-player game, 'cause that would mean examining the cards to determine which three to use. You can't realistically mark the cards uniquely because that would give away to some or all players which set is being used, if they play the game a lot. So you're introducing a lot of components!

Yeah, that's a good point I didn't think about. Might not be the best solution then since I'm trying to go for the "if discovered evil at the start can bluff / tell the truth they are not evil in the second half." At least that's the plan right now, but if that changes I could look into doing this die rolling method as it does simplify a few things.
 
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Anthony Haines
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Here's a method I don't think has been mentioned. For 5 players with 1-3 evil initially, it needs 14 cards.

The cards are divided into two separate decks of cards - A and B, each with cards (for the sake of illustration) numbered 1 to 7.

Deck A is shuffled and dealt one per player. This is their secret identity. The remaining two cards are placed aside for later (unrevealed).
Deck B is shuffled and three cards placed in a row visible to all. These are the potential evil players. The remaining four cards are placed aside for later.

Since each player knows their own identity, they can tell whether they are evil. It's not apparent to anyone how many evil players there are, because zero, one or two of the evil identities shown may be inactive.

Phase 1 then occurs (with 1-3 evil players).

Before phase 2, the unused cards in deck A are examined, and the appropriate action taken, dependent on how many of these are in the evil section:

0 : The three evil cards from deck B are shuffled, and one is removed. (This player has transitioned to good.)
1 : No changes necessary
2 : The unused four cards of deck B are shuffled, and one is placed next to the evil cards. (This player has transitioned to evil)

Phase 2 can the occur (with exactly 2 evil players).

I think this entirely fits the specs given in the original post, and uses relatively few, cheap components for the job. The players do know whether someone has transitioned at the start of phase 2, and if so in which direction.

Also, if my calculations are correct the distribution of evils in phase 1 is this:
3 evils : 60/210 = 0.286
2 evils : 120/210 = 0.571
1 evil : 30/210 = 0.143


So most of the time there are 2 evils throughout, and conversions evil->good are about twice as common as the reverse.
If a different distribution is desired, it would be helpful to know what the tolerances are.

It is possible to tweak this system to for example create more conversions and hide the initial state by e.g. taking one of the unused identity cards and passing it round, with a dice roll to determine whether to switch to it.

On the plus side, this method is extensible to arbitrary numbers of good and evil characters.
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Graham Muller
South Africa
Cape Town
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Bit late to the party but it is an interesting problem.
I think the double sided cards with sleeves is the best solution for differing playing group sizes (assuming that the game is not just 5 players)
But possible tweak it so that you can get the 0-3 evil in the first round:

If you had a set of cards the following combinations for the 5 player example
Front / Back : Number of cards
Good / Evil : 3
Evil / Evil : 2
Evil / Good : 1
Good / Good : 3

Place the cards with Evil Backs into their own pile
All cards should be placed into sleeves

Shuffle the cards with evil backs and draw 2
Shuffle the cards with good backs and draw 3
Shuffle the drawn cards together and this is your game pile.

On the second round players can draw remove their cards form the sleeves for their new alignment.

The number of cards in each pile could then be tweaked for larger or smaller groups
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Olivier D.
France
Brulain
Unspecified
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I like the bag idea, although I feel the solution presented before was too complex.

How about this:

(this assumes 5 players)

Round 1 :
1) seed the bag with 5 Good and 3 Evil stones
2) each player secretly draws 1 stone, which determines their identity for round 1

Round 2 :
1) add 1 Good and 2 Evil stones to the bag
2) each player in turn puts their stone back into the bag, then draws 3 stones. They keep 2 identical stones and put the 3rd one back into the bag.

After this, you should be left with 1 Evil stone into the bag, and each player has a pair of stones which determines their allegiance for round 2. Players generally have a slightly higher chance to keep their alignment than switch, but there are always exactly 2 Evil players in round 2.
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