Flash Survey: How would you balance a Vanilla Multiball?

[mith]

Since I'm talking to myself in the Open Discussion thread, I'll try this.

You have some number of players, N. You want to play a Vanilla Multiball game (X Mafia, X Werewolves, Y Townies). What is X for different values of N (say N in [8,25])?

The EV is very complicated to calculate exactly, so don't worry about that. Just give me your best guess.

[Infinity 324]

Just going to give some numbers intuitively, I have no idea if this is accurate

1:1:6 seems slightly townsided
2:2:9 or 2:2:10 may be balanced
3:3:15 may be balanced

[Infinity 324]

Balanced in the sense of 50% town winrate, not equal winrate for all factions.

[Infinity 324]

Bleh the fact that town has no power makes those way more scumsided.

Something like

1:1:8
2:2:13
3:3:19

[mith]

1:1:8 is probably reasonable. My best guess in the EV thread has it at 50.48%, though I've convinced myself it's higher now. It's also the first count at which town should lynch normally day 1 (at least with my current numbers, this may change once I adjust strategies at lower counts) - lynching scum at 1:1:6 for example gets you down to 1:5, no lynch to 1:4, which is EV 46.7%, worse than what you get by no lynching and letting the scum try to cross-kill.

I suspect most everyone's intuition on the 2:2:X and above setups will be way off. I wouldn't be at all surprised if 2:2:8 is reasonable.

[mith]

I get (based on my not yet updated numbers for the 1:1:X setups):

2:2:8 - 30-35-35
2:2:11 - 34-33-33
2:2:17 - 40-30-30
2:2:33 - 50-25-25

That's a big range of reasonable EVs, really.

[TierShift]

I have no idea of multiball EVs. However, wouldn't it be easy to make a script that runs a certain setup 1000 times assuming compulsory random lynches and compulsory random nightkills? It should do pretty well for a basic model but you can complicate it however you like (for instance let the program check if it is 3:1 mylo every loop and then no lynch if you hit that).

Not a beautiful solution from a mathematics point of view, but very workable.

It would also be interesting to see how small corrections in the model would affect EV. I don't think it would matter more than maybe 1-3% over the course of an entire game.

[PokerFace]

M:W:T
2:2:11
33:33:34
Looks balanced to me

Mountainous is 2:11 with n=13

If we apply stoofer's 4th law of "When experimenting with new mechanics, keep everything else as simple as possible." then:
take mountainous add extra scum group and you get 2:2:11

So 2:2:11 supports stoofer's law too

In my book it does not need to be town have 50%. Town just needs more than any other faction and since 34 > 33 >= 33 I believe it works

[Ircher]

Since I'm talking to myself in the Open Discussion thread, I'll try this.

You have some number of players, N. You want to play a Vanilla Multiball game (X Mafia, X Werewolves, Y Townies). What is X for different values of N (say N in [8,25])?

The EV is very complicated to calculate exactly, so don't worry about that. Just give me your best guess.

For N = 8, I think shos Dem Tryouts run shows that X=2 us terribly scumsided in a Vanilla Multiball.

My guess would be that 9-2-2 would be fairly closed to balanced.
Perhaps 5-1-1 would be too except that isn't really mafia.

[mith]

I have 2:2:4 at 27% right now. (That goes down to 17% without all my crazy forcing strategies at 1:1:2, 1:1:3, and 2:2:2 though.) Adding roleblockers and 1-shot BP doesn't help town a whole lot, I suspect.

[mith]

(I've already decided to just leave White Flag Nightless as our sixth vanilla variant on the sample setup cards; for these counts, 2:2:X is really the only reasonable option, I think, and not worth including. Vengescum Multiball is much more promising as a viable setup, I think.)

[mith]

PokerFace's intuition isn't bad here, it turns out:

2:2:9 (33.6%) vs. 2:9 (35.2%)
2:2:15 (40.2%) vs. 2:15 (46.0%)
2:2:18 (42.9%) vs. 2:18 (48.5%)
2:2:28 (49.5%) vs. 2:28 (57.3%)

3:3:20 (33.8%) vs. 3:20 (35.5%)
3:3:30 (40.0%) vs. 3:30 (44.1%)
3:3:36 (42.9%) vs. 3:36 (47.9%)
3:3:56 (50.0%) vs. 3:56 (56.3%)

4:4:32 (33.7%) vs. 4:32 (32.9%)
4:4:48 (39.9%) vs. 4:48 (41.8%)
4:4:57 (42.7%) vs. 4:57 (45.9%)
4:4:88 (49.9%) vs. 4:88 (54.2%)

5:5:46 (33.5%) vs. 5:46 (32.1%)
5:5:69 (40.1%) vs. 5:69 (40.5%)
5:5:82 (42.9%) vs. 5:82 (44.4%)
5:5:125 (49.9%) vs. 5:125 (52.7%)

I'm curious now whether the percentage at which the two EV curves X:X:Y and X:Y intersect converges for large X.

[vonflare]

I think that in actual games the larger the game gets the more the town winrate would be lower than expected for town because with more people it becomes harder to play for town. This makes it so there can be no perfect ratio for town to scum because the winrate will be slightly different if you multiply it by X.

[mith]

Remember that the EV assumes random lynches. I would propose that for actual games, the larger the game gets the closer to random the early lynches get (for the same ratio).

That said, there is no "perfect ratio" for most vanilla variants simply because the balance is not linear - the relationship between number of Mafia and number of Townies needed to achieve the same EV is quadratic for games with a nightkill. (Nightless is different, and is, in fact, linear. EV is exactly 50% at 1:3, 2:6, 3:9, ... X:3X.) The task is not to find a constant ratio, but to find the correct balance for a given player count (or scum count).

[GreyICE]

Remember that the EV assumes random lynches. I would propose that for actual games, the larger the game gets the closer to random the early lynches get (for the same ratio).

In a large, heavily vanilla game I think towns do significantly worse than random, especially multiball. Random lynches always assumes that votes are more-or-less random, but scum have significant incentive not to vote their buddies, and no real way to call them out on it early game if the game is large enough. Because of these semi-masonries I think the chances of an early game scum lynch in a large heavy-VT game is worse than random.

But really the town needs power roles.

Oh and for multiball you have to define the goal. 33/33/33 is "balanced" for each team to win, 50/25/25 is probably closer to what most people would think of as "balanced" in multiball games. So you could run a 9:2:2 as a game since each team would have virtually the same chance to win, but it'd be hyper depressing for the townies, since the opposing scumteam would basically be the town power role.

[Gamma Emerald]

Is there a setup that would give the mafia joint-win ability and 33/33/33 win rate?