[SETUP] Bipartite Mafia

[callforjudgement]

Town can guarantee a 50% win rate by using the free pair immediately, then choosing the scummier of the two players in it and voting them three times. Whichever player gets voted three times will lose for their faction; they have a 50% chance of being scum, so that's 50% EV.

This seems like it might miss the point of the setup, though, and I'm not convinced that it isn't possible to do better.

[callforjudgement]

It's probably townsided in theory, but not in practice (you need a disciplined town to pull the optimal strategies off).

I thought there should be some way to win if you accidentally pick a townie to make the first non-free pairing. I found the strategy you listed a bit hard to follow, so with letters:

Free pair: {A, B}
Town vote for a scummy player C
C pairs with their choice of A and B; let's say A (the choice of B is symmetrical)
B and C collectively choose a player D; B and C both pair with D

And the EV calculation seems correct (I thought it was wrong but miscounted, so here's the full calculation):

• 40%: C is scum; no scum strategy avoids a town win from here
  
• 60%: C is town:
  • 50% (30% of total): A is also town, scum win (town C paired with town A)
    
  • 50% (30% of total): A is scum:
    • 50% (15% of total): D is town (scum win; town C paired with town D)
      
    • 50% (15% of total): D is scum (town win; three successful pairings B-D, C-D, C-A)

Total = 55% to town, 45% to scum.