[SETUP] Shoutout to Antihero

[pieguyn]

3 - Mafia Goon

11 - Vanilla Townie

• In addition to the factional kill, scum has a compulsive factional ability which they must use to gift a town player a night-desperado shot, for use the following night. They must gift this to someone on every night, and in pregame (for use on N1). They may not gift and kill the same player in the same night.
  
• They may not gift this to the same player on consecutive nights.
  
• They may not gift this to themselves.
  
• The player who is gifted this finds out at the start of the next day.
  
• The night-desperado shot is not compulsive.
  
• Scum wins when they compose 50% of the town at any time during the game, to prevent weird 1-1 endgame shenanigans.
  
• The name of the setup is somewhat of an in-joke, and mostly exists for lack of a better name. It comes from a game where I was a night-desperado, and bluffed that there was someone in the game who was inventing night-desperado shots to people; Antihero proceeded to speculate it was a scum role and that it'd be a cool role if it was.

it's 14p so that if town hits scum only once, the game reaches 2-3 LYLO at 5p. the rationale for this is that I wanted town to have a final shot at hitting scum overnight if they don't lynch/vig scum all game.

mechanically, whoever gets the desperado shot is clear, so in practice it will be important for scum to wrap the game up before it reaches 3p. 3-5 with a clear isn't hard as long as they can dodge the final desperado shot, 2-3 with a clear is significantly harder, and 1-2 with a clear is lololol.

I tried to calculate the EV for this, on the assumption that scum will kill every night, desperado will shoot every night unless the game has reached LYLO , there's always exactly one clear in play, and the clear won't get lynched. it seemed balanced as I was working up to 3-11 and then Excel crashed. -.- I don't know if the way I was doing it was correct, though, since I was somewhat lazy, so I'd be interested in seeing if I'm just horribly off.

[Realeo]

45% town win rate and 55% scum win rate.

The following strategy equilibrium is made:

1] Mafia always kill the gifted player next day
2] Desperado always shoots

Edit:
I am sorry. I am wrong. I forgot that 3] Desperado always claim

I am glad to announce that after 200,000 Monte Carlo simulation--the setup is 50/50 balanced, just a little bit scum sided.

Well done. Creating a 50/50 is always a impressive feat.

Pedit:
I haven't consider what happen if gifted is shot.

[pieguyn]

when I first thought of this, how I expected it would be played is that whoever gets the desperado shot claims it sometime during that game day and claims their target. from there, if they're shooting town, scum {gift, kill} {that town, another player}, and if they're shooting scum scum kills them and gifts someone else. in this way, there is always exactly one clear alive at any given time. I had the EV for 3-11 calculated to be ~41% under these conditions, but realistically it's probably higher since scum has so little choice in who they can kill.

I think I made an incorrect assumption, though. if whoever receives the desperado doesn't claim their target, it ends up like this:

1. if they shoot town, their clear is lost, but there's still another clear in the game (whoever gets the shot next) and scum are free to kill/gift whoever
2. if they shoot scum, then there's suddenly another clear running around (due to non-consec rule), and thus scum is screwed if they don't kill them on that night.

so I honestly don't even know. it seems like a lot more of a crapshoot than I first thought it'd be.

the ratio at which this is balanced if we assume scum will always NK the person they gifted the previous night is 3-9, I think, but I could be wrong again.

[Realeo]

According to your analysis, it will be strictly better for desperado claim target. Wouldn't it be better if desperado claim simply "desperado" and not outing his target?

In this game, "desperado" is basically a seal of innocence so increasing the chance that the next gifted player alive is pro-town?