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[Leafsnail]

Instantly voting nolynch would give you a less than 50% chance of victory (since voting as mafia essentially makes you lose).  Probably not a good idea

[Toaster]

Interestingly, a nolynch vote is a 100% win for the other player.  Someone with a better knowledge of game theory than I could have fun with that.

[Leafsnail]

A lynch vote is also 100% loss for the other player, so with your vote you already know if the other player has won or not.

[Toaster]

Might as well just do Systematically Make Others Lose again.

[Nerjin]

I'd say go for it. I read a bit of the first one so far and the set-up seems rather interesting.

[Dariush]

There is no point in a game where mafia doesn't have any difference from town apart from wincon. If scum doesn't know (or have) any teammates, any skill element is removed from the game. There was no point in Prince's Guard. There is no point in this game.

[Nerjin]

For which game? If it's the random gamble one I have to agree. I find the political aspect of System... sort of intriguing.

[Leafsnail]

There is no point in a game where mafia doesn't have any difference from town apart from wincon. If scum doesn't know (or have) any teammates, any skill element is removed from the game. There was no point in Prince's Guard. There is no point in this game.

That's not true.  In this game a mafia member is significantly different from a townie in that
a) they don't have a vote, and thus have to be careful to avoid committing
b) they know that the other person is town, and thus know exactly what needs to happen in order for them to win

These are both pretty big differences from a townie who has a vote and needs to work out what has to happen for them to win.

[webadict]

A lynch vote is also 100% loss for the other player, so with your vote you already know if the other player has won or not.

Actually, not quite. There's a 25% chance of you being scum, and with being scum, you cannot lynch the other person, making it a 100% loss for you. So, a lynch vote on the other person is a 75% chance loss for the other person, and a 75% chance for you (50% chance for both of you to lose, 25% for you to lose and opponent to win, 25% chance for you to win and opponent to lose), whereas a no lynch is slightly different.

Spoiler: Whoops, this assumes 50% chance both town (click to show/hide)

Bleh. Gotta organize:

You vote lynch:
25% Opponent Scum, You Win
25% You're Scum, Opponent Win
50% Neither Scum, Both Lose

Overall - (25%:75% for both players)

You vote no lynch and opponent then votes lynch:
25% Opponent Scum, Opponent Win
25% You're Scum, Opponent Win
50% Neither Scum, Both Lose

Overall - (0%:100% for you, 50%:50% for opponent)

You vote no lynch and opponent then votes no lynch:
25% Opponent Scum, Opponent Win
25% You're Scum, You Win
50% Neither Scum, Both Win

Overall - (75%:25% for both players)

So, voting no lynch:
25% Opponent Scum, Opponent Win
25% You're Scum, 50%:50% Both (Exclusive)
50% Neither Scum, 50%:50% Both

Overall - (37.5%:62.5% for you, 62.5%:37.5% for opponent)

This is without knowing you're alignment. That makes a bit of a difference.

(25%) Scum:
No Lynch (50:50)
Lynch (0:100)

(75%) Town:
No Lynch (33.3:66.7)
Lynch (33.3:66.7)

Let's find the best course of action for each alignment:
Scum's best course of action is to let the other person vote first, but assume that's not possible.
Scum cannot vote lynch, as they lose. (0:100)
Scum votes no lynch. (50:50)
Town's best course of action is to also let the other person vote first, but again, no possible. (75:25)
Town can vote either lynch (33.3:66.7) or no lynch (33.3:66.7). Both have the same chance, if you assume the next guy votes randomly.

Though, this depends on how you rate each outcome. Assuming no dispositions, each is rated as follows:

Each Win is worth 1 point.
Each Loss is worth -1 point.

Then, it's better to vote no lynch if you want the opponent to help you, because the outcome becomes:
(You, Opnt)
Both Town, Both NL (33.3%): (+1, +1)
Both Town, Opnt L (33.3%): (-1, -1)
Opnt Scum, Opnt L (33.3%): (-1, +1)
NL Total: (-1, +1)

Both Town, You L (66.7%): (-1, -1)
Opnt Scum, You L (33.3%): (+1, -1)
L Total: (-1, -3)

Where a no lynch gets a zero sum, and a lynch quickly goes negative.

Therefore, vote no lynch, regardless of alignment, as you really need to count on your opponent. There's a 66.7% chance the opponent is Town if you're Town, and it's the only action as Scum. If you're out to hurt the opponent, you might as well lynch if you're Town. It really depends on how you rate a win and a loss, though.

[TolyK]

That's pretty damn rigorous.
It hurts that it's not zero-sum though...

[Leafsnail]

Yeah, webadict's analysis shows why there's a 33% chance of there being two townies rather than a 50% chance.  Thus in the actual setup there's a 50/50 chance of your opponent being town/scum if you are a townie.

If you're scum then you shouldn't vote anything at all since that would tell your opponent you are scum.

[webadict]

Yeah, webadict's analysis shows why there's a 33% chance of there being two townies rather than a 50% chance.  Thus in the actual setup there's a 50/50 chance of your opponent being town/scum if you are a townie.

If you're scum then you shouldn't vote anything at all since that would tell your opponent you are scum.

Well, that's another assumption I made incorrectly. If that's true, then there's a lot more and less calculations. It means that only one person has to vote to hammer.

Let's start again:
33% Both Town
33% You're Town
33% You're Scum

Assuming you're scum, you cannot vote or else you lose. Therefore, the trick is to convince your opponent to vote no lynch.
This ALSO works if you're Town. If your opponent is unable to vote, you win, and if he's Town, you also win.

The ultimate way to win is to get your opponent to no lynch.

Now, as for the zero sum, it still favors no lynching yourself if you're looking for an overall benefit.

You are scum and vote:
100% (-1, +1)

You vote NL:
50% (+1, +1)
50% (-1, +1)
Total (+0, +2)

You vote L:
50% (+1, -1)
50% (-1, -1)
Total (+0, -2)

If you always instantly lynch your opponent, regardless of alignment, you both equally lose points as time goes by. If you instantly no lynch, you slowly lose points, but he gains them back more rapidly. So, the optimum strategy is to take turns no lynching. (Technically, the optimum strategy is to do nothing and wait for the opponent, but that's not going to solve anything. Someone has to make the first move.)

Spoiler: Opponent Votes First (click to show/hide)

Opponent L:
0:100

Opponent NL:
100:0

You have a 50% chance to win if opponent votes first.

In actuality, it's 50% to win no matter what happens, excepting stupid things like voting first as scum.

[Leafsnail]

Yeah, that's all true.  Although under the same logic we could all concede every game as scum and thus win the majority of our games (since there are fewer mafia members than townies).

[Nerjin]

I suppose. Anyway, it was a fun experience near the end. Very tense. Very Tense. Hopefully the next one plays out better.

[Urist Imiknorris]

Does anyone have any fun and exciting games to start?