[EV] Blood Bank Multiball

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[EV] Blood Bank Multiball

Post Post #0 (ISO) » Sun Mar 17, 2019 7:19 am

Post by 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!
Last edited by Kaiveran on Tue Apr 02, 2019 7:40 pm, edited 1 time in total.
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Post Post #1 (ISO) » Sun Mar 17, 2019 8:28 am

Post by Awoo »

>attempting to balance multiball with multiple nightkills

Welcome to hell, mith will be your guide

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Post Post #2 (ISO) » Thu Mar 21, 2019 4:44 pm

Post by Kaiveran »

In post 1, Awoo wrote:>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.
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Post Post #3 (ISO) » Fri Mar 22, 2019 11:15 am

Post by Jingle »

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.

FWIW, I would support this as a valid Open setup for multiball as an 11p if it's run a few times without being an obvious roflstomp.
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Post Post #4 (ISO) » Fri Mar 22, 2019 11:40 am

Post by Awoo »

Yeah. I read your post.

It's even worse then normal multiball in terms of complexity. Lmao.
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Post Post #5 (ISO) » Fri Mar 22, 2019 2:24 pm

Post by Kaiveran »

Thank you for your contributions, peeps.
In post 3, Jingle wrote: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 :P. 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.
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Post Post #6 (ISO) » Mon Apr 01, 2019 4:51 pm

Post by callforjudgement »

This setup has some really screwy endgames (even more so than normal multiball). I'm assuming that 1:2:1 with the 2 as a scumteam is a win for that scumteam. In that case, look at what happens from 1:2:2 town;scum:scum and no kill credits; if you lynch scum from one faction, they have to immediately shoot scum from the other faction in order to avoid an instant loss, so the setup is now 1:1:1 where one of the scum has a kill credit but not both, leaving town in a situation where they mathematically can't win, but can determine which of the other scum wins. So town are completely lost in the 1:2:2 setup, too; but if scum don't cooperate to lynch the townie, the townie will get to play Kingmaker over
two
rounds, which removes any disincentive to blackmail strategies (town always has the last word). This means that town can honestly threaten to throw the game to the opponents of any scumteam that takes steps towards ending the day in something other than a no-lynch; town have absolutely no chance to even draw other than a no-lynch, thus the only way to play to their win condition is to try to create a no-lynch loop. This in turn prevents scum from lynching the townie (as attempting to do so would give their opponents a forced win). This is even weirder than the normal broken 1:1:1 endgame situation (where, AFAICT, the mathematically correct outcome is that town specifies that they will vote for the first scum player to post, and scum don't post at all as a result, leading to a town win after the scum slots get replaced several times and the deadline times out), because town can't actually win; all they can do is stop scum progressing the gamestate by threatening to throw the game to their opponents if they do.

I think 2:2:2 is also broken, but it's complex enough that I'm having trouble working it out in my head.

The situation in 2:1:1 is also weird: when both scum have kill credits, it's a forced town win (town force no-lynch and scum are playing against their win condition by not cross-killing), when neither does, you get 2:1:1 nightless, which is not a forced town win (if the scum's alignments aren't known, it almost plays out like normal Mafia, if they are, it's a happily-ever-after because scum don't have the votes to lynch town and will lose if they lynch each other, but town don't have the votes to lynch scum either). So scum actually do worse as a consequence of having more kills available.

I believe much of the screwiness can be avoided with the simplification of "if the factions have unequal numbers of surviving players, the smaller faction kills, otherwise both scum kill if at least
n
players are alive, neither scum kill if the game is smaller"; I'm unsure of the correct value for
n
but it's likely to be at least 8. I'm not sure offhand whether you'd want to give the remaining scum faction a kill once one is eliminated.
scum
· scam · seam · team · term · tern · torn ·
town
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Post Post #7 (ISO) » Tue Apr 02, 2019 7:32 pm

Post by 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!
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