[SETUP] 15 Love

[xyzzy]

mith proposed this version of the setup in post 5 and it's much better than my original idea:

5 mafia lovers
10 townies

on night 1, the mafia splits up into two sets of lovers, one with 2 people, and the other with 3.

Spoiler: original post

I haven't done the math on this literally at all (largely because it's been a decade since I last spent serious time doing open setup math and I honestly don't remember how to be sure that I'm doing it correctly) but here's a setup:

5 mafia lovers
10 townies

on night 1, the mafia gets to select one of their members to become a regular non-lover goon.

[mith]

Are the lovers paired or poly?

I think I have numbers for the paired version somewhere.

[mith]

Paired 5:10 is only 23%. (However, I just realized that paired doesn't make any sense if Mafia aren't removing one until N1.)

Poly version shouldn't be difficult to calculate, I'll see if I can throw something together.

[xyzzy]

poly; which faction's win % is that?

[mith]

I always do town EV.

So, if I'm understanding the setup correctly now:

D1: If any Mafia is lynched, town win (they're all lovers together).
N1: Mafia remove one from the lover group.
D2: If one of the 4 remaining lovers are lynched, they all die (but the lone goon is left); if the goon dies, the 4 lovers are left.

If that's the case, EV is 50.16%, so thumbs up there. That said, most of the town win percentage is concentrated in day 1 (1/3 chance of winning immediately); the town EV is cut in half if it gets to day 2. (This isn't a problem - in fact, it's a feature since Mafia are forced to avoid the day 1 lynch and give town more information if it goes to day 2.)

[mith]

You could also have scum split 2-3 (a pair of lovers and a triplet of lovers), and EV doesn't change all that much. (5:10 is 53.03%; 5:9 is 46.43% vs. 45.71% for 1-4 split)

Anyway, I quite like the idea.

[xyzzy]

You could also have scum split 2-3 (a pair of lovers and a triplet of lovers), and EV doesn't change all that much. (5:10 is 53.03%; 5:9 is 46.43% vs. 45.71% for 1-4 split)

Anyway, I quite like the idea.

oh yeah, 2:3 actually seems like a much more interesting split; that compounds the complexity of the choice which will probably make it a lot more interesting to play.

[callforjudgement]

This sounds like it might be a more balanced version of Red Flag (in terms of later-day gameplay being meaningful). As such, it may well be worth testing.

I think the 2:3 split is probably better, because of what happens if four scum get lynched day 2. (The game is likely to become very tedious / drag out at that point; town are favoured but it'll probably take them a while to actually win.)

[xyzzy]

btw, this was recently run to conclusion as how good is vonflare at laser tag, ending in a perfect mafia win -- coordinating a quickhammer between 5 people turned out to be a lot of effort, but after several days they managed to pull that off. I'm very curious to see how a version of this with a day 2/3 mafia lynch plays out, so I'm a bit sad that that didn't happen here, but I think the setup worked in this case.

[Irrelephant11]

I actually loved it! I complained itt, but that was part of my scumplay that game. I really liked the thrill as scum of watching a teammate get run up toward a lynch and trying to decide whether or not to get on wagon. I will say I would have really struggled with lylo as town, it doesn't sound fun to be in that position, but D1 and D2 I think were objectively v v interesting to play through

[mith]

Revisiting this: 6:11 with Mafia splitting into three pairs has an EV of 49.09% (and just a hair under 50% at 6:12). One interesting thing about this version starting with an odd count vs. the previous is that after hitting the first pair, you are left with even numbers but

don't

want to no lynch (because lynching another pair will restore parity for you). With 5:10 splitting 2:3, you want to no lynch after hitting the pair. With an even count, you don't want to no lynch at 6 or 4, but do want to no lynch at 2.

[mith]

(17 Love doesn't make any sense for a setup name, though. )

[Gamma Emerald]

Call it Love Triangles?

[singletonking]

I just realised that the name was a reference to Tennis, not sure if intentional

[xyzzy]

I just realised that the name was a reference to Tennis, not sure if intentional

yup, that was intentional.

mith, out of curiosity, can you calculate the EV for 17p where the mafia split into 3:2:1? I'm not sure if that would be better gameplay-wise than 2:2:2 but it's worth knowing what that number is.

[mith]

I can; it’s a little trickier, but I’ll put together something more general for this eventually.

[mith]

6:X for 2:2:2 split, X=9..13
0.4632967033
0.4609616574
0.4908539826
0.4974676118
0.5249451104

For 1:2:3 split:
0.4675990676
0.4538542311
0.4884004884
0.4834281311
0.5128695178

Interesting that it's slightly higher at 6:9 and 6:10 but slightly lower at 6:11+ (and also doesn't have the same parity behavior, obviously).

For 1:1:4 split:
0.4622177822
0.4483064059
0.4748535996
0.4708326891
0.4911861948

2:2:3 is pretty good at 7:10 or 7:11:
0.4891888068
0.4936253561

1:2:4:
0.4837294006
0.4799735611

For larger numbers of Mafia and 3 groups, the only setups below 50% are the trivial Day 1 LyLo ones.

[mith]

For 5:X and a 1:2:2 split, X=8..17

0.4326858327
0.4266780045
0.43997928
0.4476065287
0.4580623385
0.4715407106
0.479645703
0.4954129621
0.5016927563
0.5180462932

And 1:1:3:
0.4464202464
0.4217068646
0.454959855
0.4379273504
0.4693985753
0.4571161349
0.4856055995
0.4764199852
0.5018892356
0.4948137986

[mith]

(5:10 with 2:3 split is more interesting to me, but 5:15 with 1:2:2 is quite close to 50% and still has a 15 you could use for the name. )

I wouldn't be surprised if town does somewhat worse in this type of setup than you would expect from EV, just because the EV is so concentrated in day 1 and scum have such a strong voting bloc.

[xyzzy]

so when I ran this awhile ago, I just gave the mafia daytalk, but I think there might be some merit in only granting the mafia private communication of any kind with their lovers (in other words, once day 2 begins, sort them into separate PTs -- have them decide on any system they prefer for deciding who decides nightkills so long as it ensures that someone always makes that decision). it might be interesting to try out 5:15/1:2:2 with this rule.

I quite like that 5:15/1:2:2 works out to be nearly exactly .5 for the game as a whole and .25 for winning on day 1. that way, the town is only giving up about half of their shot at winning if they mislynch day 1.

something that might be interesting is a white flag variant on this, where starting with day 2, once only one set of lovers (or unpaired goon in the case of things like 1:2:2) remains, the mafia lose -- one attribute of this setup that I really like is that you can have a balanced game where the mafia start out with a ludicrous number of players. 7:10/1:2:4 is pretty close to balanced with nearly half of the players being mafia. white flag could potentially push that aspect to its limit.

[callforjudgement]

I don't think it'd be much fun being scum in a group of 1 with no communication.

Based on this idea, though, what about scum starting as a large group on D1, but as soon as the lynch happens, they split into groups of 2 which

each

have a kill (and are lovers, thus die as a group)? They'd still be winning together, but wouldn't have communication outside their groups (however, I assume they'd agree on a plan during the split in order to avoid accidentally targeting the same person with two scumgroups in the future).

12:4 (splitting into 11:2:2 after D1, with the two scumgroups independent but winning together) looks like good numbers; it's 25% (exactly) for town to win on D1, 34.286% for town to win after a D1 mislynch, leading to a total EV of 50.325%. 11:4 (preserving the setup name) has an EV of 51.810% to town. (All numbers assume I've done the EV calculations correctly.) The "every scumgroup gets a kill" mechanic was designed to allow large numbers of players without the game dragging out; however, it seems to suffer from the "you need a huge number of townies to catch a large number of scum" issue, with the 50% EV point for a 6-player scumgroup being at 27:6 (but with a reasonably good EV even for smaller numbers of townies, e.g. 18:6 still has a town EV of 42.987%.) As xyzzy suggests, making that White Flag probably helps (i.e. town has to lynch scum on D1, or else kill 2 out of 3 scumgroups after the split); 16:6 looks like good numbers for that, with a town EV of 51.239% (15:6 would have a town EV of 49.722%, so might be even better).