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[Leafsnail]

I have thought of a way to fix Trust Mafia - at some point the day ends (perhaps when both players agree for it to).  The townies then privately PM the moderator their action - to shoot at the other player or to shoot at the sky.

It's a town win if there is no mafia member alive and there are no townies dead.

It's a mafia win if the mafia member survives.

Nobody wins if neither of these conditions are fulfilled.

The statistics - a mafia member exists 50% of the time.  That means that:

- If you're town, the chance of your opponent being mafia is 33%.  So if you shoot your opponent there's a 33% chance that you'll win.
- The chance of your opponent being town is 67%.  Assuming their decision on whether or not to shoot is 50/50, that means your chance of winning on a "no shoot" is also 33%.  Therefore the decision on whether to shoot or not shoot is completely unbiased, statisically.
- One interesting thing that arises in this game - regardless of your alignment you'll probably want to make it seem like you don't intend to shoot the other person.  If the other player is a townie and is convinced that you will shoot them then they have no reason not to shoot you, which will make you lose.
- The main issue here is that mafia would be just a straight-up easier role than townie, and you could basically play it in the same way.  I'm not sure if there's a good way of resolving this problem.

[Leafsnail]

Wait, no.  I think I've finally made this setup work.

As above, there's a 50/50 chance that a mafia member exists among the two players.

At any time,  a townie may either fire their gun at the other player or in the air.  A mafia member can only fire their gun in the air - they cannot shoot the other player.

The game ends when either:
- Any townie has shot another player
- Both players have shot the air (the game can of course be called if a townie shoots the air in front of a mafia member)

Win conditions are as before - town wins if there is no living mafia member and no dead townie, mafia wins if they survive.

[webadict]

- If you're town, the chance of your opponent being mafia is 33%.  So if you shoot your opponent there's a 33% chance that you'll win.
- The chance of your opponent being town is 67%.  Assuming their decision on whether or not to shoot is 50/50, that means your chance of winning on a "no shoot" is also 33%.  Therefore the decision on whether to shoot or not shoot is completely unbiased, statisically.
- One interesting thing that arises in this game - regardless of your alignment you'll probably want to make it seem like you don't intend to shoot the other person.  If the other player is a townie and is convinced that you will shoot them then they have no reason not to shoot you, which will make you lose.
- The main issue here is that mafia would be just a straight-up easier role than townie, and you could basically play it in the same way.  I'm not sure if there's a good way of resolving this problem.

This isn't how statistics work. If you're Town, there is a 50% chance the opponent is Town. That's because there are two situations:

1 Town, 1 Scum
2 Town

Each situation has a 50% chance to occur. So, I dunno where you got your statistic.

[Leafsnail]

There are two possible setups, yeah.
2 townies (50%)
1 town, 1 scum (50%)

However, you can further subdivide the second case into
I am scum, they are town (25%)
I am town, they are scum (25%)

So our scenarios are:
1. We are both town (50%)
2. I am scum, they are town (25%)
3. I am town, they are scum (25%)

However, scenario 2 is impossible if you've received a town role PM, so we can eliminate it.  Scenario 1 is twice as likely as scenario 3, therefore your opponent is twice as likely to be town as they are to be mafia.

[notquitethere]

Isn't this kind of trust mafia game just a rather dull gamble? With only one round of voting there's nothing to base your decision on. Game show-like prisoner dilemmas are an interesting gamble because you're asked to trust whether the other person will act decently, whereas here the gamble is over a random role generation.

[Leafsnail]

That's what makes it mafia.

[Nerjin]

"I am town. I have a 50/50 chance of having mafia as the other guy. Might as well shoot every single time as they'll say whatever it takes to make me not shoot so there's no way to really gauge whether he's town or not because for town to win I have to Not Shoot and for Mafia to win I have to Not Shoot."

[notquitethere]

What Nerjin said. How is this a game?

[Leafsnail]

The difference is pretty large: the townie is trying to genuinely gauge your alignment while the mafia member already knows.  The mafia member is also kindof railroaded - trying to accuse the other person of being mafia is dangerous because you can't actually make good on your threat to shoot them.

So in other words the mafia is weaker but has superior knowledge.

[Nerjin]

But again why would you try to accuse the other player of being mafia? What does either alignment gain from that?

Mafia: Gains nothing, all it does is annoy the other person.
Town: Gains nothing, all it does is annoy the other person.

Again, the basic idea for either player is to simply get you to NOT shoot. Mafia has superior knowledge I guess but what can they do with it? Try to convince me not to shoot. The town player already knows 50% of the puzzle. What do they do with this? Try to get you not to shoot.

I dunno, maybe it's different in practice but I can't really see a way to play this other than saying "Regardless of what their alignment is I should always shoot."

[Leafsnail]

Well the other player is twice as likely to be town than they are to be mafia, so always shooting isn't a good strategy.  It has a 33% chance of making you win, just like the not shooting strategy  Your proposed strategy is basically the same as just lynching on a dice roll in any other game.

The thing is that town isn't just trying to not get shot - they're so trying to work out the alignment of the other player.  If you work it out then you boost your winrate, and in addition a genuine investigation makes you look more town.  That's your incentive to talk to them and investigate.

The mafia knows the other player is town, so they can focus on manipulating the othe person into not shooting them.  However, to do this they need to fake an investigation, and do it in such a way that the other person doesn't call their bluff. e: by which I mean their investigation must reach the artificial conclusion that the other person is town, or it needs to never end.  Concluding the other person is mafia isn't an option.

[Nerjin]

Well the other player is twice as likely to be town than they are to be mafia, so always shooting isn't a good strategy.  It has a 33% chance of making you win, just like the not shooting strategy  Your proposed strategy is basically the same as just lynching on a dice roll in any other game.

Oh well in that case I rescind my statement. You should NEVER shoot. As town your win rate becomes 2/3 of the time.

The thing is that town isn't just trying to not get shot - they're so trying to work out the alignment of the other player.  If you work it out then you boost your winrate, and in addition a genuine investigation makes you look more town.  That's your incentive to talk to them and investigate.

But how do you work out the alignment? Mafia and Town both want you to not shoot. But even then it's a one-day game so all you have is their word to go on and you'd have nothing to base their reactions off of.

[webadict]

There are two possible setups, yeah.
2 townies (50%)
1 town, 1 scum (50%)

However, you can further subdivide the second case into
I am scum, they are town (25%)
I am town, they are scum (25%)

So our scenarios are:
1. We are both town (50%)
2. I am scum, they are town (25%)
3. I am town, they are scum (25%)

However, scenario 2 is impossible if you've received a town role PM, so we can eliminate it.  Scenario 1 is twice as likely as scenario 3, therefore your opponent is twice as likely to be town as they are to be mafia.

Ah, I see the flaw in my logic.

Then, why not have it be 1/3 chance for each of the following:

TT
MT
TM

That way, the probability that your opponent is either alignment is 50% given you're Town.

[Leafsnail]

That's what I did in the original Trust Mafia, but it's not what I want here.  If there's a 50% chance of the other person being scum then the correct option is to shoot them - shooting a mafia member is a guaranteed win while not shooting a townie isn't (they may still go on to shoot you).  This is made up for by the fact that they are twice as likely to be a townie.

Oh well in that case I rescind my statement. You should NEVER shoot. As town your win rate becomes 2/3 of the time.

That's why this statement is wrong - the other person might still shoot you.  Your win rate is 1/3 if you shoot and 1/3 if you don't shoot.

But how do you work out the alignment? Mafia and Town both want you to not shoot. But even then it's a one-day game so all you have is their word to go on and you'd have nothing to base their reactions off of.

You can make the same argument for any other mafia game - town and mafia both want to not get lynched, so how you meant to work out anybody's alignment?  Answer: find out if they care about lynching scum or not.  It's the same in this game.

[notquitethere]

But it's impossible to scum hunt in Trust Mafia: scum are revealed by their actions: who they vote and for what reasons, and what they claim to have done at night. None of this applies in this set up. By all means, run a random finger-pointing game, but don't be surprised if its baseless and unsatisfying.