[EV] Blood Bank Multiball

[Kaiveran]

BLOOD BANK

m

Mafia A

m

Mafia B

n

Townies

(where

m

is at least 2)

• The game starts with
  m
  -1 "kill credits" in the bank. 1 credit is automatically deducted each Night, and 1 credit is added upon each Mafia death.
  
• The following mechanics apply to nightkills:
  • If there are credits in the bank and both scumteams have equal numbers, both teams can kill.
    
  • If there are credits in the bank and the scumteams have
    unequal
    numbers,
    only the smaller team
    can kill.
    
  • If there are credits in the bank and one team has been eliminated, the other team can kill until credits run out.
    
  • If there are
    NO
    credits in the bank (regardless of numbers),
    no
    team can kill.

So a little bit Alternating Multiball, a little bit Vengescum, a little bit of an inverted Semi-Nightless, with proportions depending on how things go. It could be considered a "Vanilla Variant" specifically for multiball.

The problem is, how to actually balance it? I'm totally new to EV calculations and am not confident in my ability to accurately do a normal singleball game. So if somebody else could at least give me a guide, that'd be fantastic!

[Kaiveran]

>attempting to balance multiball with multiple nightkills

Not exactly.

I would say read the game, but I fully acknowledge that I suck at explaining things, so I'll attempt to outline the concept of this credit system more clearly:

There's only multiple nightkills to

start

with. If one scumteam ends up behind (they get lynched/killed and the other one doesn't), they

deny the other team a kill

the upcoming night. Plus, if the game goes a couple of phases and only townies have been killed (including in the case where only one scumteam remains), the game will effectively become Nightless from the scum running out of credits, allowing the town a chance to make a comeback.

Since the credit system gives an advantage to whichever faction got pwned in the phases immediately previous, it's an

anti-swing

mechanic, which is very significant, as swinginess is a major complaint against multiball.

[Kaiveran]

Thank you for your contributions, peeps.

Nah, Awoo is right. Balance should in fact be similar to multiball, calculations wise. If anything, it's going to be more complicated, given that you're adding cases that need to be considered (a teams kill is stopped). Actually writing a formula to calculate EV on this is going to be a nightmare and a half.

More to the point, what kind of game are you looking for here? Mini or Large? I'd say Micro is an option, but it's probably really not. If m >= 2 (which it should be or the game is intrinsically altered from your intended purpose), then a micro would mean at most 5 town players.

Considering that case 5v2v2 it's just too likely to have town completely out of the running by N1 for my tastes.

If you're going for a mini, I'd strongly recommend 11p with m=2, because I think your setup is distinctly more townsided than the accepted 13p multiball setups given that no scum deaths brings the setup to Nightless.
If you're going for a large, my guess for m=3 would be 17p and m=4 would be 25. I wouldn't try for a setup larger than that, as even at 25p you're courting a particularly long stretch of nightless in a scum win endgame.

Lol at Micro starting in PLM¹.

Yeah, definitely gonna try this out on a Mini first, and it feels like the natural size for this, although I may try a Large later just for funsies . The numbers you're giving make sense, as they're in between the most even Standard and Nightless games according to mith's analyisis. I feel like they'd be a tad bit more biased toward Standard though.

------

I've been hammering out a Mini game tree in the spare moments where I'd rather be doing something,

anything

other that what I'm supposed to be doing. As to be expected, it's a pretty substantial PITA, but I will return with results once it's fully baked.

1.

P

otential

L

oss of

M

ajority, my special term for the weird form of LyLo in multiball where town is not

guaranteed

to lose on mislynch, but it'll take a miracle and/or working with scum to come back from the brink.

[Kaiveran]

Yikes. Yeah, those endgames are a fucking clown fiesta. I think most of us can agree that none of that is in the province of a "better" multiball, and that two-faction draws are quite enough, never mind a mechanically-forced HAE.

I don't like hacking around things with number of players in the game, but otherwise, that last suggestion is Gucci. I think I've found a way to elegantly incorporate it, and reached a great middle ground WRT "should last team standing get a kill or not", like so:

The game starts with

m

-1 kill credits in the bank.

1 credit is lost each night.
1 credit is gained for each Mafia death.

The following mechanics apply to nightkills:

If there are credits in the bank and both scumteams have equal numbers, both teams can kill.
If there are credits in the bank and the scumteams have

un

equal numbers,

only the smaller team

can kill.
If there are credits in the bank and one team has been eliminated, the other team can kill until credits run out.
If there are

NO

credits in the bank (regardless of numbers),

no

team can kill.

Kill credits are universal now, not per team. It's a lot simpler and a lot less of a headache, and ensures that there won't ever be much more than (total_amount_of_scum)+1 nightkills in the game. I might actually have the will to finish graphing this version out! Thanks a lot!