[SETUP/EV] Connect

This forum is for discussion of individual Open Setups, including theoretical balance.
BulletNLynchproof
Mafia Scum
 
User avatar
Joined: September 16, 2015
Location: EDT+12
Pronoun: He

Post Post #0  (ISO)  » Mon Dec 24, 2018 7:20 am

2 Mafia Goon
2 Vanilla Townies

There is a Day 1 discussion period, then the game moves into Night 1 where the townies try to connect by privately guessing who the other townie is.

If the townies connect, they win
If none of the townies find each other, they lose.

Otherwise there’s a second discussion period on Day 2, and the townies are given a second chance to connect on Night 2. If they manage to do so, they win, otherwise scum win.

I think this might be runnable as a tiny Marathon, but I want to make sure there isn’t a broken strategy. Can anyone figure out the optimal strategies and the EV?

As a bonus question, what’s the EV if there is no discussion on Day 1?
GTKAS - BNL (Updated, check it out!)
The Room Odds is in singups! 3/9 slots filled.
Pre-in for The Wise, Old Judge! 0/5 slots taken.

Michael Scott
Goon
 
User avatar
Joined: November 29, 2018

Post Post #1  (ISO)  » Mon Dec 24, 2018 8:14 am

Hi; I'm still pretty much new to Mafia so I'm doing this as an exercise.
1/9+8/9*1/8 should be the EV with zero discussion overall. Which equates to 2/9, really low chances.
Is a townie who successfully connected, informed at the start of D2? That would change things.

Michael Scott
Goon
 
User avatar
Joined: November 29, 2018

Post Post #2  (ISO)  » Mon Dec 24, 2018 8:15 am

In that case, the EV would be:
1/9 + (4/9)*(1/2) = 33%. Still pretty low.

Michael Scott
Goon
 
User avatar
Joined: November 29, 2018

Post Post #3  (ISO)  » Mon Dec 24, 2018 10:07 am

Don't think there are any breaking strategies.
D1 discussion, apart from reads, is only meaningful functionally to govern pairings. In the case of each VT being paired with a goon, both goons simply say they didn't connect, making their other scum. From a VT's perspective who didn't connect, it's impossible to distinguish between both of the other pair when they both claim they didn't connect, thus D2 discussion doesn't even matter.

If it's unknown pairing, scum simply each fake declare a town as "not paired".

callforjudgement
Mafia Scum
 
User avatar
Joined: September 01, 2011

Post Post #4  (ISO)  » Mon Dec 24, 2018 1:50 pm

If town are told whether they connected or not, there's a 67% EV strategy: each player targets the next player on the playerlist D1, leading to a 33% chance of a scum autowin (which happens if the scum are not adjacent in the playerlist), but if scum don't win, come day 2 both townies know for certain who the other townie is (either because they connected or by elimination if they didn't), making winning trivial.

If town aren't told about the success rate of their connections, I can't see a strategy above 33% EV, although there are several different strategies which all hit 33%. (The simplest is likely pair-targetting N1, i.e. the top two players on the playerlist target each other, so do the bottom two players. After doing this, D2 is irrelevant; you either win instantly or lose instantly.)
scum · scam · seam · team · term · tern · torn · town

BBmolla
Open Book
 
User avatar
Joined: May 29, 2011
Pronoun: He

Post Post #5  (ISO)  » Mon Dec 24, 2018 3:12 pm

Similar to Magic Train.

What happens if in Day 2 mafia have to select one of their own to die?

Edit: Literally nothing lmfao. Lemme think.

mith
Godfather
 
User avatar
Joined: March 27, 2002
Location: Plano, TX
Pronoun: He

Post Post #6  (ISO)  » Tue Dec 25, 2018 3:52 pm

I agree with the 1/3 or 2/3 depending on whether town is told they were successful. I don’t think the 1/3 would be hard to prove just by exhaustive search of the day 1 strats. (Here’s a less obvious one: pick one player; everyone else targets him, he targets someone at random. There is a 1/2 chance of losing - you picked scum - but if you don’t the player is confirmed town, so do the same thing again. 1/2 chance of picking town and 2/3 chance of that player targetting the other town in two tries, so 1/3. In practice this one would be hard to actually do withiut provable randomness, since scum could block ever picking town; at some point, either someone has to switch or the players voting together just target each other. Pretty much every other strat is more practical. :))

Gamma Emerald
Survivor
 
User avatar
Joined: August 09, 2016
Location: The Sea Kingdom
Pronoun: She

Post Post #7  (ISO)  » Thu Dec 27, 2018 3:17 pm

maybe edit setup size? might have to tweak mechanics for that
Get to know an Emerald! Stop by sometime, would you kindly? ♪
I love the sea! (Himiko told me to say hi and that she’s having a great time at the witch world!)
i would unironically put mafia loyal vigs in games for the record - Acidphoenix

mith
Godfather
 
User avatar
Joined: March 27, 2002
Location: Plano, TX
Pronoun: He

Post Post #8  (ISO)  » Thu Dec 27, 2018 4:06 pm

3 Mafia, 2 Town might be interesting, actually. With a playerlist type strategy, it's 50-50 whether town are consecutive, and if town are told they were successful you could have some interesting games with scum claims. Running through all the possible strategies is a little more complicated though, and no time for that now...

[edit]I was thinking this, but managed to not type it: obviously in this version you would need to remove the scum day 1 win condition.[/edit]

BulletNLynchproof
Mafia Scum
 
User avatar
Joined: September 16, 2015
Location: EDT+12
Pronoun: He

Post Post #9  (ISO)  » Fri Jan 11, 2019 9:53 pm

What do you think of this if townies survive to Day 2 no matter what, but the number of connected townies is revealed?
GTKAS - BNL (Updated, check it out!)
The Room Odds is in singups! 3/9 slots filled.
Pre-in for The Wise, Old Judge! 0/5 slots taken.

callforjudgement
Mafia Scum
 
User avatar
Joined: September 01, 2011

Post Post #10  (ISO)  » Fri Jan 11, 2019 11:16 pm

At 2:2, there's a strategy that gives a 5 in 6 chance of a town win (A and B target each other, C targets A, D targets B; day 2, A and D target each other and B and C target each other if the night result was 0 (50% chance) for a 2 in 3 victory chance, otherwise (50% chance) both townies can deduce the other's identity for a guaranteed win). I can't see a way to bring it up to 100%, though.

At 3 scum 2 town, things are more complex, and a good EV analysis would likely involve brute-forcing through all the possible day 1 strategies.
scum · scam · seam · team · term · tern · torn · town

BuJaber
Mafia Scum
 
User avatar
Joined: November 09, 2017
Pronoun: He

Post Post #11  (ISO)  » Tue Jan 15, 2019 6:32 am

In post 9, BulletNLynchproof wrote:What do you think of this if townies survive to Day 2 no matter what, but the number of connected townies is revealed?


Reveal the number of connected players publicly without telling anyone if they connected?
That would make things very interesting.
Friday and Saturday are typically family days. Expect a drop in activity.


[ + ]

Return to Open Setup Discussion