[SETUP] [EV] Secrets of the Anuket Topaz

[northsidegal]

Secrets of the Anuket Topaz

Roles

:

• 10 Vanilla Townies
  
  
• 3 Mafia Goons

Mechanics

:

• The first two nights are skipped.
  
• Day 1 and Day 2, if a member of the Mafia is lynched, they must confirm 5 living players to be aligned with the town.
  • This will result in their loss if Mafia is lynched both Day 1 and Day 2.
• Starting from Day 3, the Mafia will begin escaping.
  • Each night, in addition to a mandatory kill, one of the Mafia must choose to escape, and will exit the game being revealed to be Mafia.
    
  • At this point, if just one of the Mafia is lynched, the Mafia loses.
    
  • The Mafia win when all living members escape.
• If no Mafia were lynched Day 1 or Day 2, one member of the mafia will escape immediately following the end of Day 2.

This was my attempt to eliminate some of the problems with extradition mafia and make escaping a viable core concept. It was originally conceived as an open, ran as sort of a quasi-closed theme, and now returns here to you to the open setup forum for dissection.

This is the way that schadd_ went through the EV way back when:
0 scum lynches days 1/2 -> Town EV is 1-(7/9 * 6/7) = 0.3
1 scum lynch days 1/2 -> Town EV is 1-(4/6 * 4/5) = .466
2 scum lynches days 1/2 -> Town EV is 1.0000

So aggregate EV is:
(10/13*9/12) * 0.3 + (3/13 * 9/12 + 10/13 * 3/12) * .466 + (3/13 * 3/12) * 1.0000 = .40

Although I think that last parenthetical maybe should be (3/13 * 2/12)? In which case EV is .38


Thoughts?

[popsofctown]

It'd be a little more readable if you'd specify the unique win condition instead of leaving me to reverse engineer it to get something that's not a 100% town winrate.

The setup seems to naturally disincentivize bussing, if a d1-2 lynch triggers force IC'ing, you can mostly choose on-wagon players and kind of consolidate the losses there. That's probably a good dynamic.

[northsidegal]

oh, sorry, that's my mistake. Mafia wins when they've all escaped.

[popsofctown]

It's better but the wording still makes it confusing whether lynching mafia day 3 cause town to immediately win the game. The intent is almost certainly that it does, because otherwise in some gamestates it would immediately lose town the game. But that's genuinely hard to describe clearly and concisely since you have the onset of nights, escapes, and a white-flag-condition-that-doesn't-look-backwards all happening all at once.

On paper this game looks balanced, in practice when thinking about "white flag with a twist" Fusion Mafia is a whiteflag with a twist game we had recently where the setup seemed much harsher on scum compared to how everyone thought of it in the review phase. I kind of still prefer the papery assessment that this is balanced, Father Time doesn't join the town the first time scum gets lynched here the way he does in Fusion, kind of?? I worry about fool me once, shame on you, though.

[schadd_]

This is the way that schadd_ went through the EV way back when:

EEK!

[Fredrick A Campbell]

The probabilities failed to take into account that if scum were lynched on day 1, the execution (lynching) would occur between 7 players since 5 players would be confirmed town.

Reworked probabilities.

(10/13*9/12)=0 scum lynched in first two days.
(3/13*5/7+10/13*3/12)=1 scum lynched in first two days.
(3/13*2/7)=2 scum lynched in first two days.

Recalculated Town EV (whatever it is):
(10/13*9/12)*0.3+(3/13*5/7+10/13*3/12)*.466+(3/13*2/7)*1=.4056538462

Conclusion: Despite initial inaccuracy, the initial calculation wasn't that inaccurate.