[OLD] Open Setup Ideas and Discussion

[mith]

As of March 2, 2009, the process for choosing Open Setups to run under the Open Game Queue system is undergoing some changes. The former process is quoted below reference purposes, until we have settled on a definite system.

Please continue to use this thread for posting setup ideas and discussing them.

---

Original thread.

We will soon have a new administrative game category, Open Games.

Rather than being Moderator designed, Open Games will be chosen by the players. The signup thread will have a small number of games forming at any given time, and when a game is full the first Mod on the waiting list will take that game, and another setup will take its place.

This thread is for discussing potential setups and nominating them for the Queue thread.

Setup Guidelines

In order to be eligible for the Open Game list, a setup must fit the Normal Game definition.

In addition, Open Games will have standardized rules and role PMs (more on this later).

When a setup is designed, it can be posted here, and a list of setups will be maintained.

Nominations

Users may nominate posted setups for inclusion in the signup list. Whenever a new setup is needed, the setup with the most nominations will be taken, and nominations for it will be dropped.

If you are posting a new setup, please nominate in a separate post.

Initially, the Vanilla setup will have a "permanent" place in the signups; when a Vanilla game is ready to run, a new Vanilla signup will take its place on the forming games list. As such, the Vanilla setup does not need to be nominated. It is possible that other setups will be given permanent places as well, in addition to or instead of the Vanilla setup.

[mith]

As discussed here...

White Flag Mafia

2 Mafia
8 Townies
Night Start

Mafia win condition: The Mafia wins if

it comprises one third of the town

.

Town win condition: The Town wins if

the Mafia has fewer than two members

.

(Town EV is 44.44...%, compared to 35.21% for the usual 2-10 vanilla.)

[mith]

There's no one standard for AitP; multiple variations have been tried.

[mith]

I have a couple of points... I've never really understood why 2:10 is supposed to be balanced. I've always wondered if optimal strategy there would be for one mafia to claim start of day 1. The remaining mafia member would have no one to tie himself to -- there are no links to look for. More links to look for between players is easier for town.

This game is like 2:10 except more balanced in the town's favor. There are more links to look for, and there will always be an odd number of players. Moreover, the one shot cop adds interests to the game. How long can he save it? Should he claim on an innocent (imo not necessarily, at least not immediately). Should he claim on a guilty (likely immediately, but saving it a day or two has merit). 3 scum also opens the door to scum counter claiming, which would add interest to the game.

The cop is the "one shot" at impacting the game positively, and there being one one-shot cop adds quite a deal of dimension to the game. Games in general are too complex. One power-role is enough to make for an interesting game.

Er...

1. 2:10 isn't "balanced", it favors the scum EV-wise, but it's a compromise between game size, having a scum group rather than a lone scum, and balance. 35% is fair, since we expect the town to do better than the EV would suggest (so far they have done much worse, though the sample size is not yet significant).

2. I welcome you to try your strategy if we are ever in a 2:10 game, you are scum, and I am not... your suggestion would make it difficult on the town in that there would be much less to look for, but the swing in EV having one less scum is

huge

(a D1 scum lynch moves it from 35% to 59%).

3. If you think 2:10 is in favor of the Mafia, why on earth would you think that adding another Mafia and a one-shot Cop would swing the balance toward the town?

2 Mafia, a 1-shot Cop, and 6/8 Townies would be playable. Heck, I don't have a problem with games that are unbalanced every now and then; give the townies a real challenge sometimes. But 3 Mafia in a small game requires significant power to balance.

[mith]

A specific Smalltown setup

could

qualify as a semi-open normal.

I don't think Guppy understands how the Open queue works, though.

[mith]

Texas Justice shouldn't be run again as-is. It shouldn't have been run here in the first place. I though everyone understood after the original games that it was broken, but I guess it's been long enough that people had forgotten.

[mith]

Doesn't matter (much). Scum were allowed to counter in the original newbie setup, but that didn't keep it from being broken (primarily because countering the cop claim just makes things worse for them).

Here, they've got double the chance of limiting the Cop to one investigation, but even in that best case scenario they've got two named roles to deal with.

I actually wouldn't be surprised if the best play for the town is to do a full massclaim D1; they're guaranteed 2 confirmed innocents at a minimum.

[mith]

Massclaim D1, scum counter Cop and Townie. Lynch Townie. 1/3 chance of hitting scum (Town win), 2/3 chance of missing. In the latter, scum kill Doc, Cop investigates Townie, scum fakeclaims the reverse result, and it's a coinflip. Town wins 2/3 of the time (slightly better than the original newbie).

[mith]

I suspect it's still no better than original-newbie. The only change is that the Mafia are more likely to stop the Cop by N2, but even if they hit the enabler, they aren't in as good a position as if they hit the Doc, and so I don't think that would have a drastic impact on the EV.

It's worth remembering that the problem with original-newbie wasn't just that the town's chances of winning were too high; it's that the town's

best

chance of winning was to follow the "breaking strategy" (and it was a dramatic difference; I believe there was talk initially that the setup might be too much in favor of the scum). This suggestion doesn't change that.

[mith]

I don't think the Death Miller Cop thing unbreaks that setup. Cop should still come out D1; Mafia still have the option of countering, but IIRC the correct strategy at that point is to keep both alive and let them "investigate". The Mafia still confirms the real Cop if they kill him. (Someone coming up Mafia on a NK = Cop in that setup.)

[mith]

(I find it slightly peculiar that people are trying to "fix" original-newbie without, apparently, giving much though to whether their fix actually helps the problem.)

[mith]

Per discussion in Site Ideas, I am splitting Open Setup discussion into an "ideas" thread (this one) and a "certification" thread (here). Please read that thread for more details.

[mith]

I would have to go through it again, but I believe the breaking strategy for the newbie setup has the town lynching the other Mafia first (in the case that the Mafia counters; if there's only one Cop claim, that's the Cop, end of story). The death miller addition has no effect if the other Mafia is already dead - the town knows whether or not they have lynched Mafia or Cop based on whether or not the game is over.

[mith]

Hm, I may be remembering wrong. It's been a long time since I worked out those strategies, and I don't think I wrote them up anywhere. I'll have to do some more thinking about it, but it may be that the correct strategy was to lynch a claimed Cop.

The plan I had in mind was something like this:

1. Cop and Mafia both claim Cop.
2. Doc claims Doc; Mafia can't counter, because then you have three confirmed Townies, and it's just a matter of having three chances to win two coinflips (75%).
3. Now, during N1, assume that the Doc always protects one of the claimed Cops (I'm pretty sure this is optimal, for reasons to be discussed). If the Mafia adopts a strategy of always killing the real Cop, then if the Doc chooses wrong, the Mafia will win 2/3 of the time (the fake Cop is lynched, of course, but then we are left with a 3 person endgame after the Doc is kill N2). However, if the Doc chooses correctly, the Mafia loses

if the town knows that the Mafia will always kill the Cop

(real Cop is confirmed by protection, and will have two investigations with which to find the Mafia hiding amongst the Townies). So, always killing the Cop would give a 1/3 expectation for this situation, and another 75% for the Town overall. Thus, the correct strategy is either to always kill the Doc or to have a mixed strategy of sometimes killing the Cop, sometimes the Doc (and perhaps sometimes not killing).
4. If we assume the real Cop has survived going into D2, we now have two claimed investigations - one real and one fake. While these investigations obviously cannot guarantee the town will lynch scum, they may allow us to eliminate someone (if one Cop claims Mafia on player A, and the other claims Innocent on player B, player B is definitely innocent), or they may allow us to link Cops to claims (if one Cop claims Mafia on player A, and the other claims Mafia on player B, then the pairing is either Cop1/B or Cop2/A), or both. It would be an interesting problem to work out the optimal claim strategy (almost certainly mixed) for the fake Cop.

In any case, while I am less confident that the town has the same breaking strategy as in original-newbie, I am still pretty convinced that the town can play *a* breaking strategy that yields better guaranteed results than they would get otherwise.

[mith]

the breaking strategy will now slightly favor scum and is thus not a breaking strategy.

Be careful with this statement... this isn't entirely true. A breaking strategy is one which is:

a. Optimal (maximizing the town's chances)
b. "Boring" (in the sense that it takes away scumhunting and becomes formulaic).

An optimal strategy may not increase the town's chances above 50%; it's quite possible that any other strategy or lack of strategy that they take is even worse. If the best thing the town can do is something that ruins the game, it's not a good setup.

(I'm not saying that's the case ehre, but you might want to consider what the odds are for the town if they don't follow the potential breaking strategy.)

[mith]

It's not a stupid question; it's probably a quite difficult one, too.

[mith]

I think you've got a couple extra townies in there somewhere. D2 is lynch-or-lose (if the town doesn't hit scum D1).

I think you're missing my point. There are three options when the scum counters the cop claim:

1. Town lynches a claimed Cop immediately.
2. Town lets them both live, and scum tries to kill the real Cop N1.
3. Town lets them both live, and scum kills (or tries to kill) the Doctor.
(or some mixed strategy involving 2 and 3)

Only in the first case does the Death Miller Cop make a difference. It may be that this is the correct play in original newbie (and not in the DM setup, in which case the DM has made a difference, though there still may be a breaking strategy), but if not, the DM can't make a difference, whether the Mafia should try to kill the Cop or otherwise. Once the town has decided to let both Cop claims live until they get the partner, the DM has no effect on the setup.

---

To correct myself, the correct play is not for the Doctor to come out immediately in the case of both Cops coming out; the correct play is to choose a lynch victim D1, and then if that victim is the Doctor, they claim and you choose someone else. The Mafia still can't claim Doctor (or they are immediately countered and Town wins 75%), and this way the Doctor remains hidden N1 80% of the time; thus, if the Mafia's strategy is not to kill the Cop N1, trying to hit the Doctor isn't nearly as effective (as it reduces the pool of potential suspects).

[mith]

Oh, I guess I only saw the nomination and not the proposal. 2v7 is definitely broken in the manner I described; just leave the Cop claims alive, and try to lynch the partner. There's just too much time for investigations, too many chances for the town to lynch.

[mith]

Yeah, I suppose you may as well keep nominating things here and farside can grab setups as she has been until we settle on some system over in the certification thread.

[mith]

If town has higher than 50% then they can random play and more likely than not win.

This is similar to shaft.ed's statement on the previous page (in the other direction). Just because the town *can* do better than 50% by playing random

doesn't mean they should play random

. We assume that the town can scumhunt better-than-random (and we have to, in order for Mafia to be worthwhile), and that assumption doesn't magically go away for games where the town is favored in the EV.

If I gave you a weighted coin that came up heads 60% of the time when flipped, and then told you that I'll give you a dollar if the coin is showing heads the next time it is on the floor, would you flip it? No, you'd set it down on the floor heads-up and take your dollar 100% of the time.

There are very few Mafia games that are perfectly balanced (whatever you consider that perfect balanced to be, whether the Town gets 50%, 40%, 35%, whatever), but games that are unbalanced to either side can still be playable (you could play a game where the scum is only expected to win 10% if you wanted, it would just be that much more impressive when scum actually pulled it off).

[mith]

You don't seem to understand what "broken" means. Broken means that there is an optimal strategy for either side that "breaks" the game - turns it into a different game ("Outguess the Mod after Massclaim", or "Cop Claim + Protect + No Lynch", for example). Broken does not say anything about the chances either side has of winning.

[mith]

Empking, obviously "game-breaking strategy" is going to have a different meaning depending on what game you're talking about. But let me rephrase my previous post:

You don't seem to understand how "broken" has traditionally been used in the context of Mafia.

I'm not sure how I can make it any clearer, though, if you don't understand it after all the attempts that have been made to explain it.

[mith]

I'd quite like to see that one run tomorrow/later in the month during a Marathon Day/Weekend.

[mith]

EV-wise, that is identical to Treestump (the only differences between the two being that a sub-optimal town could lynch an innocent before they stump/an innocent could refuse to stump, resulting in an extra kill for the scum, and that the stumps can keep talking in Treestump... neither of those affect the EV, though). 3:8 is 33.4% Town, 3:9 is 38.7%.

[mith]

Guardian, we've previously run 3 Mafia, 1 (every night, sane) Cop, 8 Townies. The scum won

easily

. One game isn't conclusive for balance, but it did demonstrate what I would expect - most games, the cop will get traded for one of the scum (sometimes the scum will hit the cop at night first, sometimes the cop will have another investigation or two first). It's not a good balance. Not unplayable, by any means, but not balanced.

"In 2:10, the scum are less likely to have a bad scum player who throws the game." - If we start to base balance on how likely a scum player is to throw the game, I fear for the future of the site.

"In addition, there are less interactions to go off of once you get one scum dead. With three scum, if that first dead scum has a pattern of behavior towards two other players, you can really take that and run with it. With two scum, that one scum probably will not give much information. His partner is also less likely to, since I think in 2:10 there is almost no incentive to protect your partner or treat them specially in any way." - Quite the opposite! There is far more incentive to protect your partner in 2:10, because you only have one of them.

It's always a tradeoff - scum can distance and hope they are able to mislead the town in later days in exchange for an increased chance of getting one of them lynched early, or they can protect and hope power in numbers outweighs the risk of giving away the whole group. Balance can't (shouldn't) take that into account; whether the town does better (or worse) than the balance of the game depends on how good the scum (and town) are at what they are trying to do.

In 3:1-shot:8, the random EV balance is hugely in favor of the scum (3:9 Vanilla is 16.5%, I'd guess this is around 25%). Sure, the town might have more information to work with, but they are further behind (and 2:10 is on the slightly questionable side of "balanced" as it is).

"Moreover, in most 2:10 games I have read, towns have lynched and scum NK'd every day until lylo." - 2:10 games typically start with a NK (so they're really 2:9). Even if they didn't, you're basically saying that because towns have played a game out wrong in the past, we should use that wrong strategy in determining the balance?

(FWIW, the difference is about 3%; 35% NLing D1, 32% only NLing in Lylo.)

All that said, it would possibly be less difficult to figure out the EV of a larger setup with a one-shot cop than a smaller setup with a full cop (California). So I may try to do so sometime soon.

[mith]

And by that I mean, if there is more buddies, more likely the bad scum player gives away connections to at least one of them. More buddies is more chances for bad players and moreover more chances for those players to mess up.

Ok, that's a difference sense of "throw the game" than I read it as, but even so. This is a poor argument; getting a bad player in the group hurts the scum, sure, and it's more likely with a larger group (although arguably more deadly with a smaller group, since if you are in a 2 man group with said bad player and he gives you away, you lose). You're also more likely to get a really good player in the group. You seem intent on assuming the worst for the three man group and the best (or at least neutral) for the two man group and then drawing a comparison. It's silly.

In 2:10 vanilla, the inventive is to play as much like a townie as possible. Make the town have to randomly lynch you to find you correctly. In a 3:8 game with a cop (let's say a full cop for the sake of argument) you want to protect your partners as long as the cop lives, because if a few of you die early the cop will break the game later.

The incentive in

every

game is to play as much like a townie as possible. I'm not talking about defending your buddies in obvious ways, just nudging things slightly as necessary.

The fact is, most players aren't good at acting "like a townie" when they are scum. That's what makes Mafia a viable game, why it's not in the town's interest to lynch randomly. At the same time, Mafia have the advantage of numbers; if they were a good enough player to act completely townish, they would still have the incentive to push lynches away from their buddy some of the time (and if we're assuming they are good enough to act town, they are good enough to do this as well). Only bad scum players

want

the town to lynch random; good scum players want to control the lynch as much as possible.

Anyway, for this specific setup, going out of your way to protect your partners has just as much risk as reward; if you are successful, but then the cop pegs one of you, you may have just lost two scum instead of one.

(FWIW, there is a 7/180 - ~4% - chance that the town will randomly lynch scum the first two days and the scum will miss the cop the first two nights. And even then, the cop is by no means certain to catch the final scum with his investigation. You are badly overstating the cop's chances of "breaking" this setup.)

I really disagree with this.

~shrug~ Then you are wrong. Sorry.

This is a strawman/misunderstanding. People are comparing 3:8 to past 2:10 games, based on how those 2:10 games actually went.

Er, yes. People are comparing to how those games actually went, which was generally

starting with a NK

; at least, the three of them I ran did (all scum wins).

For the record, Strawberry has been run three times; two were scum wins, and in the game the town won, the Cop died the first night. Additionally, one of the first Mini games was a 3 Mafia, 1 Cop, 8 Townie setup (mentioned in my previous post) which the scum won handily (essentially trading Antrax for the Cop). So no, so far the results don't agree with you, and while that's not a large enough sample size to say anything definite, it's with a full cop, where as you are arguing for a one-shot.

I would suggest that your time would be better spent thinking of how the town could have improved their play in those games than arguing that your setup is balanced; it clearly is not.

[mith]

I went through the vanilla-variants spreadsheet the other day and pulled out a bunch of near 50-50 setups over a range of game sizes, mostly to see what it looked like. But I thought I might as well post it here.

Terms should be obvious except for White Flag (which I think can be found in this thread somewhere, but I include the definition below so you don't have to go looking for it). Treestump is functionally equivalent to only giving the scum a nightkill if a scum member is lynched.

White Flag - Win conditions are changed to "Town wins if there is only one Mafia remaining" and "Mafia win if they make up one third of the Town".

5 Players - Vengeful; 2:3 Lovers
6 Players - 2:4 Lovers Nightless
7 Players - 2:5 Lovers; 2:5 Nightless
8 Players - 2:6 Nightless
9 Players - 2:7 Treestump; 2:7 White Flag
10 Players - 4:6 PairedLovers Nightless
11 Players - 3:8 Nightless; 2:9 White Flag
12 Players - 3:9 Nightless; 2:10 Double Day
13 Players - 6:7 PolyLovers; 2:11 Vanilla
14 Players - 6:8 PairedLovers Nightless; 4:10 PairedLovers; 3:11 Treestump
15 Players - 4:11 PairedLovers; 3:12 Treestump; 2:13 Vanilla
16 Players - 4:12 Nightless

(Worst balance EV-wise is 2:11 Vanilla, at ~39%. Everything else is in the 40-60 range, and most are very close to 50-50.)

[mith]

Maybe downgrade it to unknow alignment neighbours, who are determined randomly

In EV terms, this would effect the balance at all. No idea how it would affect it practically.

I should figure out the numbers for the 2-masons-but-otherwise-vanilla setup, it ought to be doable.

[mith]

Doing some quick pencil-and-paper calculations, here's one strategy. The numbers for the Cop not coming out D1 are obviously a bit more complex (I suspect it's not a good idea for him to wait, though).

Massclaim randomly (or based on early suspicions). Scum shouldn't claim Cop, and should probably split 1 and 1 on BPM/VT claims - because of that, it really doesn't matter what order the claims happen in. The preference would be to have the Cop claim later, so the scum wouldn't have any read on who the Cop might be more likely to investigate.

After the claims, Cop reveals investigation. There's a 1/8 chance the investigation is useful (and I don't think this can be improved - however claims come out, it is clear one scum should claim BPM and the other VT), in the case where the Cop has investigated the scum claiming VT. In this case, you have two chances to hit the other scum, with a 2/3 EV.

If the Cop gets a guilty on a BPM (3/8), you have one confirmed innocent (the Cop), 1 scum hiding with 2 BPMs, 1 scum hiding with 4 VTs (EV = 14/45). If the Cop gets an innocent, you have two confirmed innocents, 1:2 BPM, 1:3 VT (EV = 13/36).

In both cases, you are slightly better off lynching amongst the BPM claims first assuming that scum are forced to kill if the town no lynches in a 1:3 endgame (otherwise, I don't think it matters what order you do it in).

Overall, that gives an EV of 137/360 = 38.1%. Which isn't terrible. This basically falls in the class of "Census" games, though (a known number of scum hiding in different groups of a known number of innocents) - with the particular setup essentially being "selected" through the cop investigation.

(EV if both scum claim BPM is 50%. EV if both scum claim VT is 45%.)

[mith]

Scratch that. Thought of an alternate strategy which is not so boring, and should be an improvement on the above. I've decided against typing it out, in case the game is run and the players want to determine their own strategy.

[mith]

Max, I like the basic idea, though not the implementation... for one thing, if 2:2:9 is considered "fair" (I still need to run numbers on that, huh), adding the potential for several power roles while only dropping the number of pro-town players by one may nudge things too far in the town's favor (maybe not, though; perhaps all it does it make it more likely one group will get wiped out quickly, allowing the other side to win more often... in which case it's more a swinginess problem than one of balance).

Perhaps something to differentiate the scumgroups would be appropriate - if you have the potentail for the anti-Mafia town powers to be stronger than the anti-Werewolf powers (or vice versa), perhaps also include the possibility of Mafia powers (or Werewolf powers). Or, you could take it a step further and have a different set of possible town powers assigned to each scumgroup... make the Tracker a Werewolf-only possibility, for example.

[mith]

I feel like I'm being misquoted on *both* sides. (Ok, not quite misquoted, but my name is being dropped.)

Here's what I've said/done:

1. Established as one of the current

Normal

requirements than the game must contain a Mafia

Group

.
2. Stated that Open Games should meet the requirements of Normal Games in general, though accepting that on occasion we have bent a rule in order to admit a setup which is especially suited to run in the Open Queue - for example, the Vengeful Townie is arguably not a "normal" role, nor is the mechanic of the scum losing if the Godfather is lynched, but obviously the Open Queue is the best place for repeat Vengeful Games.
3. Played in a

Closed

setup which happened to have only one scum in it. And that scum's role was "Serial Killer", not "Mafia", IIRC.
4. Said that games with only one "Mafia" aren't really games of "Mafia", they are games of "Serial Killer", which has many of the qualities of "Mafia" but does not have the group dynamic. It is nevertheless a perfectly valid variant/game.

FWIW, I'll add:

5. I've played one game of AitP - FtF, as the Assassin, and won (by lynching all the Guards). I like the game.
6. It really isn't Mafia, and probably shouldn't be in the Open Queue.

[mith]

Following this discussion...

My Name Is Earl (F11 Variant)

Setup randomly selected from:

1 Mafia Goon, 1 Mafia Roleblocker, 1 Cop, 1 Doctor, 5 Townies
2 Mafia Goons, 1 Cop, 1 Earl, 5 Townies
2 Mafia Goons, 1 Doc, 1 Earl, 5 Townies
1 Mafia Goon, 1 Mafia Roleblocker, 2 Earls, 5 Townies

Earl is a Named Townie - no special abilities, but can claim the role name "Earl". (Scum can, of course, fake claim "Earl".)

[mith]

Reverse Vengeful is basically Treestump without the Treestumps; in Treestump, correct play is for town to stump before they are lynched, and so the only way scum get a kill is if one of them is lynched.

So, no, giving the last remaining goon a kill the rest of the game wasn't my intention, but it may make more sense balance-wise; I'll have to run the numbers sometime.

[mith]

I get an EV of 35.40% for 2:5 Reverse Vengeful, and an EV of 27.62% for Zorblag's variant. Might be a tad hard on the town, but then again they won Mini 993, so based on that small sample...

I kinda like that it reverts to a vanilla setup if scum is lynched day 1 (whereas RV reverts to a Nightless setup after the kill), but I don't like that the remaining scum effectively gets two NKs if the game goes the way Mini 993 did (town lynch, scum lynch, nk, no lynch, nk).

[mith]

After town-lynch, scum-lynch, nk it's 1:3, and if the remaining scum is able to nk the correct play is to no lynch down to 1:2 (EV 1/3 vs. 1/4). If the scum doesn't have a nk, then the town has two lynches (EV 1/2).

[mith]

Some numbers related to the Rival Vig setup:

In a 2:(2/6) Census game (2 Mafia, 6 townies, 2 identically named townies), and assuming immediate massclaim, the scum are better off both claiming vanilla (31% for the town vs. 45% if one scum claims named townie).

The town can massclaim in the Rival Vig setup and do a bit better - if scum both claim townie, both vigs flip a coin and shoot on heads. Mafia don't know which to block, so there's a 25% chance of a kill happening - and better if the town manages to lynch the blocker D1.

The plan of having one of the vigs claim D1 so that the other can (probably) shoot gives better odds on a kill happening, but risks a fake claim by the scum. Perhaps some sort of mixed strategy is optimal: decide on a method for one vig claiming (perhaps let D1 go for a bit and then run down the list of most suspicious players until one claims vig), but then flip a coin (probably weighted, but since I'm too lazy to figure out the EVs for the various strategies I'm certainly not going to figure out what weighting to use) and have some chance of jumping into massclaim straight away.

Anyway, I expect the EV is around 35%... and probably to get that much out of the rival vig ability, the town needs to adopt a strategy which makes the ability boring.

(Pretty meh on the Fruit Vendor one...)

[mith]

That's kinda like saying in 4:8 Nightless scum just have to make sure only townies get lynched. I suspect it's probably fine as is.

[mith]

A couple of vanilla variants I came up with playing around with my probability spreadsheet...

Blind Rage

If an unrevealed Mafia is lynched, the Mafia group chooses another of their members to be revealed by the Mod the following Day.

Setups with good EV:

11p: 3:8 (33%), 4:7 (32%)
13p: 3:10 (39%), 4:9 (43%)
15p: 3:12 (44%), 4:11 (51%)
17p: 3:14 (48%), 6:11 (27%)
19p: 5:14 (30%), 6:13 (34%)
21p: 5:16 (34%), 6:15 (41%)
23p: 5:18 (38%), 6:17 (46%)
25p: 5:20 (41%), 6:19 (51%), 8:17 (28%)

Odd scum counts are worse for town, of course. Somewhat similar to the Paired Lovers setup in terms of EV, but in practice gives the scum more flexibility in when to bus and who to sacrifice, and the days with a revealed scum to lynch speed things up (though not as much as with Lovers), while also giving the town the option to slow down and discuss a bit before the lynch happens.

The Bus Stop

If the day 1 lynch is Mafia, the Town wins immediately.

Setups with good EV:

7p: 2:5 (38%)
9p: 2:7 (40%), 3:6 (37%)
11p: 2:9 (43%), 3:8 (36%)
13p: 2:11 (45%), 3:10 (36%)
15p: 2:13 (48%), 3:12 (37%), 4:11 (33%)
17p: 2:15 (50%), 3:14 (38%), 4:13 (33%)
19p: 3:16 (39%), 4:15 (33%)
21p: 3:18 (41%), 4:17 (33%), 5:16 (31%)
23p: 3:20 (42%), 4:19 (34%), 5:18 (31%)
25p: 3:22 (43%), 4:21 (35%), 5:20 (31%)

The goal here is to force the generation of more information day 1, as the Mafia can't bus. The theoretical percentages stay relatively flat for long ranges here, as two factors balance: when the Town only outnumbers the Mafia by a small count, the likelihood of winning day 1 increases (approaching 50% for large X:X+1), but the after day 1 the town is better off with more mislynches.

The Bus Stop 2

If the day 1 or day 2 lynch is Mafia, the Town wins immediately.

Setups with good EV:

13p: 2:11 (55%)
15p: 2:13 (55%)
17p: 2:15 (56%)
19p: 2:17 (56%), 3:16 (50%), 4:15 (51%)
21p: 3:18 (50%), 4:17 (49%), 5:16 (52%)
23p: 3:20 (50%), 4:19 (47%), 5:18 (49%)
25p: 3:22 (50%), 4:21 (47%), 5:20 (47%), 6:19 (50%)

[mith]

(And actually the Bus Stop 2 would be just fine at even player counts; EV would be a bit less than with one fewer townie, as the probability of winning days 1 and 2 are lower but afterward the town has to no lynch to restore parity.)

[mith]

If that were the case, optimal play for town would be to lynch one of the people clogging the thread. (If they end up with a no lynch day 1, shame on them - the whole point of the setup is that much of their win chances come there.)

That said, the larger setups are more for FTF. I don't really expect many would want to play them on the forum (either it's over really quickly, or it takes forever!)

[mith]

Extrapolating Empking's Simple Mafia setup to larger setups (the Mafia Don dies night 2 unless another Mafia has been lynched):

9p: 2:7 (41%)
11p: 2:9 (50%)
13p: 2:11 (56%), 3:10 (27%)
15p: 3:12 (33%)
17p: 3:14 (37%)
19p: 3:16 (41%)
21p: 3:18 (44%)
23p: 3:20 (47%), 4:19 (29%)
25p: 3:22 (49%), 4:21 (32%)

(The even counts are in the middle percentage-wise of the odd counts surrounding them, but they don't make as much sense thematically - on day 2 it doesn't matter whether town or scum is lynched, because if they manage to lynch scum they have to no lynch after to restore parity, whereas the Mafia Don dying does that for them as well.)

[mith]

I think TeChNoWC was talking about the "Simple" setup.

Short Answer: No
Longer Answer: It doesn't

encourage

that behaviour. It does make it less punishing on town to mislynch the first two days, sure. However, there is still an advantage to lynching scum day 1, vs. lynching scum day 2, vs. missing on both and the Don dying at night - each case lowers the scum count by one, but with different numbers of mislynches remaining.

I don't know that I personally would like playing this setup, I'm just looking into vanilla variants which allow for a greater ratio of scum to town.

[mith]

The Coalition

5 Mafia Goons
12 Vanilla Townies

Nightless. Each day, rather than lynching a single player, a coalition of half (rounded up) of the remaining players is formed. The remaining players are lynched, and their alignments are revealed simultaneously. So day 1, a coalition of 9 forms, and 8 are lynched. Day 2, the coalition is 5, and 4 are lynched. Day 3, the coalition is 3, and 2 are lynched. Day 4, the coalition is 2, and 1 is lynched. (There are lots of ways this could work, mechanically. I kinda like the idea of them having to actually all agree on a coalition and vote for it as a block, though voting in or out players one by one would work too. The key point is that no one is eliminated or revealed until the whole coalition is chosen.)

Balance-wise, it seems like it would be the same as a regular Nightless setup, but the town actually does slightly better as they effectively get more shots at getting out of "LyLo". For example:

2:3 Nightless
Probability of getting to 0:3 = 2/5*1/4 = 1/10 (EV 1)
Probability of getting to 1:2 = 2/5*3/4 = 3/10 (EV 1/3)
Probability of getting to 2:2 = 3/5 (EV 0)
1/10*1 + 3/10*1/3 = 1/5

2:3 Coalition
Probability of getting to 0:3 = 2/5*1/4 = 1/10 (EV 1)
Probability of getting to 1:2 = 2/5*3/4

+ 3/5*2/4

= 3/5 (EV 1/3)
Probability of getting to 2:1 = 3/5*2/4 = 3/10 (EV 0)
1/10*1 + 3/5*1/3 = 3/10

5:12 has an EV of 47% (vs. 41% for Nightless); 6:11 has an EV of 38% (vs. 29% for Nightless) and would be interesting too. For a smaller version, 3:6 has an EV of 40% (vs. 33% for Nightless).

[mith]

Revenge of the Vengeful

Nightless

4 Vengeful Goons
7 Vengeful Townies

(A role with the Vengeful modifier may, when lynched, kill another player.)

Other possible setups with EV:

5p: 2:3 (47%)
7p: 2:5 (51%), 3:4 (33%)
9p: 3:6 (51%)
11p: 4:7 (41%)
13p: 4:9 (52%), 5:8 (33%)
15p: 5:10 (44%)
17p: 5:12 (52%), 6:11 (36%)
19p: 6:13 (45%)
21p: 6:15 (52%), 7:14 (39%)
23p: 7:16 (46%)
25p: 7:18 (51%), 8:17 (40%)

[mith]

The Coalition, v2

3 Mafia Goons
12 Vanilla Town

Each day, rather than lynching a single player, a coalition of some of the remaining players is formed (see below). The non-coalition players are lynched, and their alignments revealed, simultaneously. The Mafia then may kill one living player as normal.

Day 1: 15->11 (4 lynched)
Day 2: 10->7 (3 lynched)
Day 3: 6->4 (2 lynched)
Day 4: 3->2 (1 lynched)

3:12 is 40%. 2:8 (starting from Day 2) is 44%.

[mith]

Seems like the Mafia groups will figure each other out too quickly for that size of setup. Which I guess could be interesting in its own right? But I would expect town to win most games. I'd get rid of the Mafia Cops.

[mith]

Revenge of the Vengeful, LyLo Variant

Nightless

3 Vengeful Goons
10 Vengeful Townies

The Mafia wins as soon as they comprise 50% of the town; if a Townie has just been lynched, they do not get a Vengekill.

Other possible setups with EV:

7p: 2:5 (38%)
9p: 2:7 (52%)
11p: 3:8 (38%)
13p: 3:10 (48%)
15p: 4:11 (37%)
17p: 4:13 (45%)
19p: 5:14 (36%)
21p: 5:16 (43%)
23p: 5:18 (48%)
25p: 6:19 (41%)

[mith]

I am also working on a spreadsheet to get online at some point. The list of variants included so far, in order from scum-friendly to town-friendly:

Vanilla
Blind Rage Odd Mafia Count
Paired Lovers Odd - All but one Mafia is part of a Lover pair. 3:10 (42%) and 5:17 (42%) are good setups here (the latter having the added bonus of being an even player count).
"Vengescum" - Vengeful Goons vs. Vanilla Town; equivalent to Treestump. 2:8 (43%) and 3:10 (43%) are both reasonable setups for Micro/Mini.
RotV Lylo Variant
Nightless
Blind Rage Even
Paired Lovers Even - The Mafia consists entirely of Lover pairs. 2:3 (40%) and 2:5 (57%) are both reasonable Micro counts (the latter just being the non-nightless version of Lovers Mafia); 4:9 (43%) is the Mini setup, and 6:14 (40%) is solid as well.
Revenge of the Vengeful - Town gets a huge benefit from being able to Vengekill at 50-50.

The Bus Stop variants don't really fit on this scale, due to their wacky probability curves; for close to even counts, town is much better off (even than Revenge of the Vengeful), but then the probability drops as townies are added.

Note that only odd player counts are considered for Vanilla, Blind Rage, and the RotV variants; the town is better off no-lynching to restore parity if they start with an even count. In the others, the town improve their chances by lynching (in Paired Lovers, you are less likely to lynch successfully at an even count, but when you do it gets you to an odd count, and for 3+ Mafia this is a net benefit).

[mith]

I could calculate that, sure. Maybe later tonight, I'm out of time right now.

[edit]I expect it will be much closer to Vanilla (21%) than Vengescum (43%).[/edit]

[mith]

Actually, a Vengecop setup might be interesting too (lynched player gets to investigate someone with the result revealed to everyone) - it'd be somewhat comparable to an all-Vengeful setup, with a trade off between having to spend a lynch on a revealed scum and clearing townies instead of killing them.

[mith]

Dying Docs

3 Mafia Goons
10 Vengedocs (Protect a player the night after their lynch)

Is there a way to find out the EV for this mith ^

Actually, the EV for this is

exactly

the same as Vanilla. The issue is that with an even count, you have worse lynch odds than with one less townie, and this outweighs the potential benefit of getting a second protection.

Consider:

1:2 - 1/3
1:3 - 1/4 (lynch mafia) + 3/4 * 1/3 * 1/3 (lynch town, protect town, 1:2) = 1/4 + 1/12 = 1/3

2:3 - 2/5*1/3 = 2/15 = 30/225
2:4 - 2/6*1/3 (lynch mafia, 1:3) + 4/6 * 1/5 * 2/15 (lynch town, protect town, 2:3) = 1/9 + 4/225 = 29/225

[mith]

If I've got my formulas right, a 3:10 Vengecop game has EV of 45%. It's actually slightly better (for the town) than Vengescum, slightly worse than RotV LyLo for lower player count (but overtakes it eventually).

[mith]

Actually, there are three different variants I can come up with, based on how the Venge-investigation happens:

1. Result is revealed before Night happens. (Mafia can then kill the target, so there is never a confirmed innocent during day unless the Mafia decide to leave one alive for some reason. 3:10 is 38%, and overall is somewhat worse than Vengescum.)
2. Result is revealed after Night happens. (Mafia

might

kill the target by chance. 3:10 is 44%, overall better than Vengescum.)
3. Result is revealed before Night happens

and that player is protected from the Mafia's kill for that night

, to ensure a confirmed townie always exists after a townie lynch. This is sort of a combo Vengecopdoc mechanic, and has the EV above. (I only calculated it by mistake, forgot the Mafia's chance of killing the target in 2.)

Dead Boy Detectives

3 Mafia Goons
10 Vengeful Cops (on being lynched, get one investigation, the result of which is revealed publicly at the start of the following day)

7p: 2:5 (35%)
9p: 2:7 (53%)
11p: 3:8 (31%)
13p: 3:10 (43%)
15p: 3:12 (54%), 4:11 (28%)
17p: 4:13 (37%)
19p: 4:15 (45%)
21p: 5:16 (32%)
23p: 5:18 (39%)
25p: 5:20 (45%)

Variant 3 is only 1-2% different for these... and I kinda like that it guarantees a confirmed innocent, especially since that confirmed innocent will likely be one of the more suspect players.

[mith]

I think in practice, vengecop would be a bit more townsided than percentages show, just due to town always picking scummiest players and forcing scum to kill them, leaving towniest players alive at the end.

Agreed... It does add an interesting layer though, in that the scummy players are the ones getting to investigate, and possibly confirming as innocent players who

they

thought were scummy. Often the players who get lynched are under fire because their suspicions don't align with groupthink.

Vengewatch might be an interesting one too, and closer to what you were trying for with Vengedoc.

[mith]

3:10 Vengewatch is 30%... Still closer to Vanilla, but not a bad option. 2:7 is 41%, 2:9 is 51%.

[mith]

3:10 Vengevig (that is, X Mafia Goons vs. Y Vengeful Townies) has some nice options:

9p: 3:6 (40%)
10p: 3:7 (46%)
11p: 3:8 (47%)
12p: 3:9 (51%), 4:8 (35%)
13p: 4:9 (36%)

Higher than Nightless for all but the last one; Nightless does eventually overtake it, but it gets that LyLo benefit that made RotV so strong.

[mith]

TierShift, I think EV of 50% (or higher) is perfectly fine... I aim for slightly lower because I find it makes it a more interesting game if the town is at a slight disadvantage, so that they have to overcome it with good scumhunting.

Note that for Vanilla itself, town has tended to do worse than expected, but for others (Nightless) town has done just fine with <50% EV (presumably because of the inability of scum to eliminate strong town players). We ought to mine some stats on this, really.

[mith]

Screwing around with my Vanilla Variants spreadsheet again... Here's one that seems interesting:

Unnamed Combo Variant

3 Mafia
9 Townies
(

Daystart

)

If Town lynches Mafia on Day 1, Town wins immediately (from The Bus Stop).
If Town lynches Mafia on Day 2, Mafia may not kill Night 2 and must instead choose one of their remaining members to be revealed at the start of Day 3 (from Blind Rage).
After Day 2, the Mafia may only kill at Night if one of their members was lynched the previous Day (from Vengescum).

EV is 44% for Town, dropping to 25% if they mislynch Day 1 and to 13% if they also mislynch Day 2 (but back up to 54% if they lynch correctly Day 2). The intent here is that busing is suicide Day 1 and punished heavily Day 2 (though not as severely as in The Bus Stop 2, of course), while the Vengescum condition at 3:5 keeps the EV for the comeback too low.

And another:

Red Flag

Town wins when any two Mafia are lynched.

1-2 Mafia Setups are equivalent to Vanilla Mafia; 3 Mafia Setups are equivalent to White Flag. Other good counts:

11p: 4:7 (35%)
13p: 5:8 (37%), 4:9 (46%)
15p: 6:9 (39%), 5:10 (50%)
17p: 7:10 (41%), 6:11 (53%)

EV converges to 50% for the N:(N+3) setups, for large N. Such games are guaranteed to last at most 3 days (either side loses on two bad lynches).

[mith]

Unnamed Combo Variant reminds me of the White Flag Gambit. (That is, the worse bussing becomes in a setup, the more value scum get if they pull it off successfully; in this case, you'd be hoping that the bus lynch doesn't go through despite how hard you're pushing it.)

I basically invented the White Flag Gambit, how is this not in the wiki entry? Bah.

(I also didn't know there *was* an entry for it until just now, so I guess I can't complain too much. On the other hand, Equinox was in that game so double Bah.)

Anywhere, there needs to be a better term for "trying to look like you're busing when you're not because your buddy actually dying would be terrible/losing". Busing to me implies an actual lynch, not the threat of one.

[mith]

You mean distancing?

I mean, sure, technically correct. But this seems like it warrants a stronger/more specific term than "distancing". Distancing is very broad, covering the spectrum from "vague suspicions thrown in the direction of a scumbuddy" to "throwing them under the bus, jumping in the driver's seat, running them over, and backing over their mangled corpse".

My current pet name for it is "whiplashing", as in playing the role of Snidely Whiplash, tying up your poor innocent scumbuddy on the train tracks only to have them saved at the last moment by the Dudley Do-Right of pairing analysis. #mithramblesaboutmafiavocab #mithisoldandusesoldreferences

[mith]

It just occurred to me that in a Red Flag setup as worded, there might actually be cases where Mafia would want to nightkill one of their own (that is, one of the Mafia might be so obvscum that they consider his/her immediate lynch more likely than town lynching a different scum in two chances).

Probably the wording should just be "Town wins when two Mafia are dead.", but maybe leaving it as "Town wins when two Mafia are lynched (or all Mafia are dead)." is slightly more interesting.

[mith]

Yeah, it's pretty easy to counter the 50% EV claim. (The 50% EV would hold if all blocs were formed randomly without regard to information gained from previous blocs and nightkills, because if a random bloc is decisive one way its complement is decisive the other way.)

Counterexample:
4:2, indecisive bloc is hammered.
Information gained: there is one Mafia in each bloc.
Mafia is forced to nightkill one Mafia and one Townie. If the Townie is not in the same bloc as the Mafia, the town now has two confirmed townies and wins. Otherwise, the town has one confirmed townie, and can include that townie in the bloc with each other possibility, and a win is guaranteed.

So the EV for 4:2 is the chance of not hammering a scum win on the first attempt (if the first is indecisive, town can just hammer the same bloc two more times and go to night) - there's a 20% chance of the scum win, so EV is 80%.

[mith]

(It's an interesting idea though, and similar to The Coalition. One could mash up various pieces of this into The Coalition framework for some more variants.)

[mith]

I was reasoning on the basis that if a bloc's indecisive, there's not enough information to tell why. I'd missed that that wasn't the case when only 2 scum were left. (The scum controlling both kills was intended to allow scum to eliminate players who had been confirmed as town or scum.)

It might need a small mechanical tweak to allow for the balance issue, or might not. An earlier version of the setup just had scum win if town failed to hammer a townbloc at :2, and that would probably fix things here. Not sure though.

Any indecisive bloc gives the information that there is at least one Mafia and one Town in the bloc

and

in the bloc's complement. At X:2, that's game winning, but at larger counts it is still information that adds up. I suspect I can break 5:3 as well, messing around with that now.

A simple fix is to have Mafia nightkill one Townie, and then that Townie get a vengekill, and change the ratio (maybe 8:4). But figuring out the balance of something like that would be pretty difficult. Reducing the number of attempts per day would also help (4:2 after an indecisive bloc is no longer a guaranteed win if town only gets one or two chances at 3:1 and if scum win after they fail).

Let us try this

7:2 Nightless is already an EV of 56% for the town; town can obviously increase this a bit just by attempting a mass touching at the beginning of the game - there's a 1/6 chance that a random bloc of 5 will be all town, so just pick such a group and have them touch each other. If that doesn't insta-win, you can probably also increase the EV slightly with the additional information that at least one of the bloc must be scum.

[mith]

What most people call "mountainous" (which I have always thought was a terrible name[/rant]) includes a nightkill already. The EV cannot be lower. The same reasoning applies as before - town can do a mass touching day 1 to try to win that way, with a 1/6 chance of success. If they fail, they still have an EV of

at least

29.8% (slightly greater, actually, because they have the small amount of information that at least 1 of the 5 touchers is scum). If we assume they didn't have that information for some reason, their total EV is 41.5%... which isn't an unreasonable EV, but you're not really making full use of the mechanic. (The nightkill curing a sick town doesn't matter at all; the most points town can safely get after 2 days is 6, I think, and there's not really any safe touching to be done after that.)

That's a long way of saying that this is a reasonable setup, removing the theme entirely:

The Bus Coalition

7 Townies
2 Mafia

On day 1, the town may attempt to form a townbloc of 5 players. If all members of this block are town, the town wins immediately. Otherwise, proceed as a normal Vanilla game. (This variant is somewhat interesting in that the scum must make an effort to get one of their members in the bloc, but getting both in is not optimal because town will have slightly better odds lynching from that group until they hit the first scum, and if both are in the group this will happen more quickly on average. In that sense, it sort of has a Resistance feel to it - one baddie on the mission = good; two baddies on the mission = dangerous)

As stated, EV is slightly greater than 41.5% (no time to calculate exactly right now - "at least 1 in this group" is not a simple bit of information to add to the spreadsheet).

[mith]

I mean, presumably in such a game the deadline for day 1 would be longer to compensate, or day 1 would be split entirely into two deadlines, one for the bloc and one for the lynch. The thing about townblocs with a strict majority (vs. the Townbloc setup proposed where the blocs are 50%) is that you only need the people in the townbloc for the vote to succeed.

The logistics are ultimately up to the town - there is an obvious incentive to *try* to form a townbloc (1/6 chance of winning outright), and the negotiations would provide a lot of information to work on if the townbloc failed.

You're right that the touch system has added flexibility - my point in previous posts is that this flexibility doesn't actually add much to the optimal strategy. If you make a bloc of 4, all town, you've got 6 points. If each bloc-er touches an outsider, you win if they all touch town - I'm pretty sure the way to maximize those chances is to pick a single person to touch, not to touch multiple different people. (Consider an example case where the 4 person bloc is all town, and 3 of the 4 think player X is town, but the 4th disagrees. If the 3 are wrong, it doesn't matter who the 4th touches; if the 3 are right, then the 4th should touch X as well to win.) But even if there is a better plan, whatever that plan is should be attempted at the start of the game in a way that you can't autolose, and then you're mostly done with touching.

(It occurs to me that there is a possible improvement with the healing mechanism:

Pick a 5 player bloc. Have 4 of them touch each other first, then all touch the 5th. You win if all 5 are town (1/6). Otherwise, pick 3 of the remaining 4 to touch each other. There is a 1/36 chance that you now have 9 points, if the scum were players 5 and 9. Now players 1-4 are sick town and players 6-8 are healthy town. If scum kills healthy town, they can have their lists set up so that one of players 1-4 becomes healthy, and one of 6-8 can try touching that player. You win in that 1/36 case; otherwise there was scum in players 1-4 or 6-8 and you're probably done trying

The thing is, this only improves the EV if scum actually kill one of those healthy townies - otherwise town can never get to 10 points. There

might

be a slight improvement by taking into account whether or not any of the nightkills are among players 6-8, but I doubt it. Player 9 also becomes unlynchable, at least temporarily, with this plan, because everyone else might be sick, if one scum is in 1-5 and the other is in 6-8. And if player 9 is nightkilled, now there are

two

players who are potentially unlynchable as the potential last healthy town - say 9's list was 1>2, so either 1 is town and becomes healthy or 1 is scum and 2 becomes healthy, but you don't know which is the case and can't lynch either to find out. So, basically, this is all probably a net negative on the EV.)

[mith]

Yeah, the EV is the same because you're still attempting a townbloc of 5, just in two stages. Another variant:

Progressive Townbloc

7 Town
2 Mafia

During the first X hours of day 1, the town may choose one player to start a townbloc. If a majority agrees on a player, that player then has 24 hours to choose a second player. Those two players have 24 hours to agree on a third player, and so on until a bloc of five has been selected. If all five players are town, the town wins immediately. If at any point the town or bloc cannot agree on the next player, or if a bloc of five is formed which contains at least one scum, start the actual deadline and proceed as a Vanilla game.

(You could mess with the dynamics further by adding a scum instant win condition, though I haven't found one I like. In the original version with a townbloc of 5, both scum being in the bloc could be an instant win like the split-in-half townbloc, but then an indecisive bloc would mean a "neighborhood" game of 1 scum in the bloc and 1 scum out, which isn't as interesting as the Resistance-like element of scum wanting 1 in but not 2. And in the progressive version, it's obviously too strong a condition, since an early scum pick can likely push through his buddy. Something like "1st pick is scum *and* 5th pick is scum" could be interesting I guess, though not particularly elegant - probability is a little better than 1/36, though it's not clear what optimal strategy is as 1st pick scum; assuming 2nd and 3rd are always town, the probability would be 1/27 (2/9*1/6 - there are 6 slots left for the other scum to fall in), but it may not be best for 1st pick scum to always go for the instant win, in order to muddle the information available in the Vanilla part.

Anyway, if you added a scum instant win condition you'd probably want to adjust the numbers and/or limit the factional kills in some way.)

[mith]

24 is probably too fast, considering weekend V/LAs and the like. Apart from that, I like the setup, and agree that it probably shouldn't have a scum instant win condition.

One interesting property I note here is that a scum townbloc member has no incentive to pick anyone in particular other than trying to look town, in much the same way that scum in a (two-faction) normal game have no incentive to scumhunt other than keeping up appearances. I consider this to be a feature, rather than a bug.

Yeah, maybe just 5 days total for the whole process; town could use most of it arguing about who to pick first if they want. And of course you could allow provisional picks (the first player chosen in particular can provisionally choose a second to take effect immediately, since they are the only vote that counts there). The neat thing is that there's no incentive for scum to stall the process once their chosen - the bloc has already failed.

It's true that scum, once chosen, should just try to look town, but trying to look town has some subtle differences in this situation that make it interesting. If the bloc fails, the town knows at least one of the bloc is scum, and possibly both scum are in the bloc, so there is a small incentive to pick a lynch from among those players rather than from the outsiders. Given that, you would want players chosen who would be more likely lynch targets than yourself. It's a small thing, since it's a big enough group to hide in, but it would be interesting to see how it played out if scum were chosen early.

[mith]

I'd be tempted to try a massclaim in that setup, assuming the townies know which parity they are. Also assuming Vig is full BP, I suspect he should always claim Odd... that way if the scum want to try to kill him night 1, they have to use the Strong Man shot (if Vig claims Even, they can take a normal shot first and then use the Strong Man if it fails). Not totally sure how scum should claim, but I'll bet we can find a EV >50% in all cases. Unlimited BP is really strong, but I'm not sure making the Vig 1-shot BP is much better?

[mith]

I'm not sure I totally follow your notation, but obviously massclaim is a bad idea if the townies don't know their parity. The Vig claiming only helps the Mafia; this should only happen D1 if he's in danger of being lynched.

I still haven't worked through what the correct massclaim strategies are in the known-parity case; regardless, I think the known-parity version is far more interesting (and more of a puzzle), and unknown parity is questionable in Normality (I don't think this case has ever been clarified on the wiki or elsewhere, but I personally don't like the idea of a player having a modifier that he is unaware of). I think it's probably worth running that way just to see what, if any, massclaim strategy the town tries to use, and what the scum do in response.

[mith]

I'd say having an unaware modifier isn't Normal, but it's entirely acceptable to have a "your role is either X or Y but you don't know which" style of role in an Open. (Dethy is a good example of that; it's imbalanced and emphasizes puzzle solving over scumhunting, but I don't have any rules-based issues with it being in the Open queue.)

Does the rule that Open setups have to be Normal technically still exist? Because that isn't really being enforced atm (e.g. I'm pretty sure White Flag would fail a Normal review under the current Normal guidelines).

This is really several discussions rolled up into one, most of which should probably take place outside of this thread, but:

1. dethy would not be considered Normal currently; non-sane Cop variants are explictly non-Normal.
2. I don't know that an "Open Queue games must be Normal" rule currently exists, and you're probably right that it isn't being enforced if it does. I'm certainly not trying to (re)create that rule now.
3. There's a distinction between "Open Queue games don't have to be Normal" and "This particular non-Normal game is a good fit for the Open Queue", but that's not really relevant to this particular discussion.
4. "Normal" is something that I bring up and that has been important to me because it provides a standard of "fairness". Which isn't to say "Even or Odd but don't know which" is unfair, exactly, but I do think this setup loses something in the event that the townies have no way of determining which parity they are. There's still a "puzzle" (sort of) on the scum side, but it's basically random at the start (you can try to kill this player, it may or may not work, if it doesn't you can kill them the next night). There's a good chance that the scum's first non-strong kill will succeed or fail on a purely arbitrary basis, whereas if the townies know their parity I would argue there's an added element of scum trying to work out those parities (if there's no massclaim) and town slightly modifying their behavior to induce a kill attempt on the correct night. It's subtle, but it's there.
5. White Flag should absolutely pass as Normal, and if it doesn't currently the guidelines should be changed. [/slightlybiased, but still] There is nothing I can see in the guidelines that rules out (reasonable) modifications to the win conditions.

[mith]

Perfect 11 seems quite reasonable at first glance. I dig it.

(If it's breakable my massclaim, my instinct says the way to do it is a partial claim of power role or not. Particularly with the headstart result, the scum are put in a bit of a bind. Wolves will obviously avoid both claiming PR, but they don't have any way of coordinating with the Sorcerer to avoid a Wolf/Sorcerer double PR claim. It's obviously not enough to win outright, but it

might

be enough to give the town better odds than they would otherwise have.

Btw, Wolf-Sorc-VT-VT seems interesting on the surface, but it should be easily winnable by scum. Scum don't need a lynch on town, they just need any lynch, and the real Sorcerer is the only one who can cooperate in making that happen. Wolf votes, the real Sorcerer follows and the fake ones can't.)

[mith]

Gambler Nightmare

Rolelist

Mafia Goon
Mafia Goon

Town Vigilante
Vanilla Town
Vanilla Town

Special mechanisms

Town wins if:
- Both mafia are dead
- Mafia shoots a vanilla town
Mafia wins if:
- The vigilante is killed
- The vigilante shoots town
- There's only the vigilante left
(One of the win conditions is enough)

If the vigilante decides to kill someone, mafia won't use their factional kill.
Mafia may choose to not kill.

Here's the best I can do in terms of maximizing the EV for town:

You're missing that the Mafia win if the Vig is killed (at least in one case, I didn't review the whole thing).

[mith]

Oh, I was analysing it as though the Mafia won if the Vig was

lynched

.

If kills count too, it's almost certainly scumsided, given that I couldn't get it to come out townsided even with the more lenient win conditions.

Yeah, I'd be surprised if town can do better than the 1/3 they can get with the "obvious" strategy.

(Vig claims immediately; if Mafia counters, lynch someone else and Vig kills fake claim. If you mislynch, you've got another shot day 2, so 2/3 EV. So Mafia doesn't counter. If you no lynch, Vig has a 50-50 night 1, and if successful town again has two shots to get the last scum with the lynch or night 2 kill, 1/3 EV. If you lynch, if you miss (1/2) then it's 1/3 again, 2/3 for the Vig and 1/2 for the lynch (or night 2 Vig if you no lynch, doesn't matter), but if you hit (1/2) it's still 1/3 because Vig is forced to shoot.

But hey, at least we've found a scenario where it absolutely doesn't matter if you no lynch, mislynch, or lynch scum.)

[mith]

Sacrifice Mafia is likely scumsided unless there's a breaking strategy. It's complicated enough that I won't be trying to find an exact EV. My attempt at a breaking strategy (since that seems to be what I do lately in this thread) would be:

Cop claims.
If there's no counter, Doc protects as long as possible while Cop racks up results. I suspect town should keep lynching and vig should keep shooting, but Cop should also reveal all results as they are received and town should maybe hold off on lynching/vigging confirmed guilties (to maximize PR survival time).
If there is a counter, Vig now claims. If no counter to that, Doc protects Vig, Cop can keep getting results until the Mafia kill him (or lynch/Vig hits the enabler), at which point the counter is confirmed scum.
If both are countered, maybe Doc should claim, not sure. Probably no lynch anyway, Vig should shoot his counter at night; Mafia are forced to get rid of the Cop pretty quickly so he can't rack up results (best way is by countering the Vig with the Cop Enabler), and that outs the other, but town again should probably wait on lynching/vigging - if scum have nightkilled the Vig, this might be the Doc Enabler and town avoids giving scum an extra kill; if they left the Vig alive, this might be the Vig Enabler and we're more likely to get an extra kill out of the Vig. Regardless, town is in pretty good shape here.

[mith]

If a townie is lynched D1, scum get a "free shot" at the vig overnight (automatically winning if it hits, and going to a 50% EV endgame otherwise).

Maybe I'm missing something in the setup, but if townie is lynched D1, the Vig has a 1/3 shot of hitting both scum if he shoots, while letting scum shoot has an EV of 1/4.

Also, Vig shooting in the scum lynch case has the same EV - 1/3 hit, plus 2/3*1/2 lynch. Doesn't matter if Vig is outed or not, or if the lynch is scum or town, Vig can shoot. EV is exactly 50%. I doubt they can improve on this.

[mith]

If a townie is lynched D1, scum get a "free shot" at the vig overnight (automatically winning if it hits, and going to a 50% EV endgame otherwise).

Maybe I'm missing something in the setup, but if townie is lynched D1, the Vig has a 1/3 shot of hitting both scum if he shoots, while letting scum shoot has an EV of 1/4.

Also, Vig shooting in the scum lynch case has the same EV - 1/3 hit, plus 2/3*1/2 lynch. Doesn't matter if Vig is outed or not, or if the lynch is scum or town, Vig can shoot. EV is exactly 50%. I doubt they can improve on this.

Ah right, I missed that the vig would shoot after a townie lynch (which is weird, because I considered that case correctly in my previous analysis).
After a scum lynch, though, the vig dies if they shoot and miss, leading to a 1/3 rather than 1/2 chance of lynching correctly, so the EV in the "lynch scum then vig someone" case is 1/3 + (2/3*1/3) or 4/9. (Unless I've missed something again, which is quite possible.)

Yeah, you're right (well, except that it's 5/9, not 4/9). I had this right in a previous version and then forgot the Vig would die I guess. So it matters whether Vig is outed for that case, and total EV is:

1/10*5/9 (Vig outed, scum lynch) + 2/5*2/3 (Vig not outed, scum lynch) + 1/2*1/3 (town lynch) = 44/90, just barely under 50%.

[mith]

I am enjoying the discussion.

I am just assuming in a setup like this that playing things by the numbers is the right play without considering overall Optimal play? What I mean by Optimal is taking into consideration the psychology of the game as well as the numbers. Obviously depending on the setup the Optimal play is going to change. Take for example a Vanilla game where most of the game is itt. Is there a point where weighing in on the psychological components outweighs the EV?

The EV is basically the "baseline" play that town use if they don't have anything better. You can normally assume that town do better than the EV in practice. (For example, if you're in 2:1 lylo with one confirmed town, EV says that town have a 50% chance of winning, but in practice the confirmed townie gets to choose who to lynch and thus (you'd hope) town actually have a better than 50% chance.)

When you have a breaking strategy present, the simplest thing you can do is to follow the strategy, but use scumhunting to decide which choice of player you make to lynch/vig/investigate/etc. when you the strategy gives you a free choice of player. This is a pretty common play (and leads to town scoring well above EV in Nightless games; oddly, this doesn't seem to happen to so much of an extent in games with a normal day/night cycle). Much riskier is deviating from the strategy because your reads are strong enough that a normally low-percentage play becomes a good one. It's rare for players to be this confident in their scumhunting ability, and even players who are that confident are often incorrect to be, so it doesn't happen very much and doesn't succeed all that much when it does.

In your example of a vanilla/mountainous game, EV theory just says "lynch any player", which in practice becomes "lynch the scummiest player", and thus theoretically allows town to win above EV. (In practice, town do well below EV in vanilla-heavy setups with a normal day/night cycle such as 11:2 Mountainous and (as of the most recent statistics, although I suspect they're out of date) White Flag, but that may be the result of a small sample size.)

A quote on this from way back in 2009:

Anyway, the EV is calculated for some theoretical "optimal play" by both sides. If there *were* a clear advantage to be gained by the scum in playing a certain way, the town can always counter it by lynching in a truly random manner (by "random" here I mean "lynch independent of argumentation", not "lynch any living player with equal odds", since clearly there will be some situations where we want power roles to out themselves before being lynched, or we want to lynch from a subset of the living players, or whatever).

And the assumption that the scum are playing optimally ensures that the town can never do better than random, either.

In practice, it doesn't actually work out this way; but that's because players don't play optimally. In other words, balance = EV, deviation from EV = skill.

So, yes, random lynches and NKs (depending on optimal strategies which depend only on the information that we the outside observers have, and not on in-game tells and so forth), justified by the above hand-wavy pseudo-math.

Emphasis added. I think there's a temptation to argue that with optimal play, town can do better than random, but this neglects the fact that EV assumes

both

sides are playing optimally.

[mith]

The counterpoint assumes town can evaluate whether or not they will play below random-EV, which is not a valid assumption.

I'm working under the assumption that optimal means optimal. "Plausible small deviations" from optimal are non-optimal and could absolutely change the town's win rate, depending on what they are. (But yes, it's equivalent to assume either that the scum are perfect at blending in or that town are perfectly incapable of scumhunting.)

I agree that in practice players are sometimes terrible at strategy, and this can cause towns to play below EV. (Conversely, scum are often terrible at not being scummy, and this commonly leads to towns playing above EV. If that weren't the case, Mafia wouldn't be a very interesting game.)

The rule against provable randomness has more to do with not allowing players to make provably random votes, which would be impenetrable to reads. (And probably some other weird specific situations that came up a long time ago, but I'm not latching onto any in my memory at the moment.) But yes, it does have the added benefit of preventing agreed-on truly random lynches.

[mith]

Why would town lynch at all in that game? A massclaim and everyone-shoot strategy is winning in all cases. (The trickiest is the 1-1 split claim case, with 5 vig claims and 4 VT claims. Assign a Vig to each VT and have them shoot; the remaining doesn't shoot. Scum among the Vig claims is outed by the shooting, and the other is hit unless his buddy is assigned to him - in this worst case, it's still 2:3 so town wins)

Probably solvable even if town must lynch day 1.

[mith]

I think you can do better:

No lynch. Split the town into groups of 2 and 6. Have the group of 6 shoot in a circle.

Case 1: 2 scum in group of 2 - Scum win, probability 1/28.
Case 2: 1 scum in each group - The target of the group of 6 scum survives, so 3 players left. No lynch again, and the remaining vig who hasn't shot can kill the scum.
Case 3: 2 scum in group of 6 - If they aren't next to each other, they both die. If they are, one survives along with his target and the group of 2, and the surviving scum is caught.

EV 27/28.

Games with too many Vigs are usually breakable, it's just a matter of finding the optimal way to do it (and I'm not certain we can't get to 100% in this one, just don't see it right now).

[mith]

"If there is not a switching mechanic, it is just too town sided" is not equivalent to "it is a good idea to have a switching mechanic".

If you get to day 3 with both Cops alive, and you haven't already lynched scum, that means there is only one Townie left. It's certainly possible that the Cops will be able to piece together whether they have been switched or not (investigating the same player on different nights would do it),

if

there is no counterclaim, but if you are in this situation obviously one of the scum will claim Cop and muddy the results further.

If you don't get to day 3 with both Cops alive, as Jason points out there is not enough information for the remaining Cop to go on.

When you say "investigate your strongest reads", what you seem to be implying is that you should rely on those reads to determine what your sanity is, rather than relying on your results to determine what your target's alignment is. Which you should be doing anyway, so what is the Cop role adding?

[edit]Also, if what you're after is "Cops should try to stay alive so they can solve the game day 3", just make that their role:

2 Masons
5 Townies
1 Mafia Rolecop
1 Mafia Goon

If both Masons are alive when there are 5 players remaining, town wins.
[/edit]

[mith]

I know what the difference between a Mason and a Cop is; I wasn't suggesting that they are equivalent. All I am saying is that in the setup as presented (with 9 players), there is a very small chance of the Cops getting useful information out of their abilities, that that very small chance primarily lies within the case where both of them survive to day 3 and can compare results, and that you can get the same feel of "try to survive to day 3" without the investigative nonsense. (Making the two survivor roles Masons is just a twist to make the setup more interesting - it gives the scum something to look for, vs. having two named townies who don't know each other.)

The fact that you're suggesting it might be a good idea for a Cop to investigate the same player repeatedly until the result changes is just emphasizing the point that these "Cops" are basically useless. Further problems with this idea include:

There's a chance the Switch will be the day 1 lynch, in which case they will never get a different result.
There's a chance their target *is* the Switch, in which case they will never get a different result until their target dies and they have to change targets, and won't know that the switch has happened when they start getting results on that target.

Now, I grant that I am stating all of this a little strongly. There are chances for a single Cop to get

something

useful (if only in terms of probabilities rather than certainties). But these considerations don't outweigh the badness of a hidden santiy-switching role.

(A setup with a single Cop who doesn't know his sanity might be reasonably balanced at 2:7; by day 3, if he survives, he will at least know whether two players have the same alignment or not, and if either of them has died he will know what the other one is. That plus the named townie effect might be enough of a boost to get the town to a reasonable EV. Of course, we can get around the "sanity" thing entirely by just defining a new type of investigative role who gets results of same/different alignment from a reference chosen night 1 (or night 0).)

[mith]

I guess what I'm saying is that roles like a "hidden sanity switcher" are a really bad idea unless there is a really compelling reason to have them, and that you haven't established that this game is such a compelling reason. The closest comparison is dethy, which was as much a puzzle as a Mafia game (IIRC, town can either win outright or get it down to a 50/50 with best play, and the scum is at the mercy of the claim order in affecting which happens). This setup is not as interesting a puzzle, the puzzle is unsolvable most of the time, and neither side has much control over whether the puzzle ends up solvable or not.

[mith]

I would assume the answer to 2 is yes, or they wouldn't have the 1-shot Avoid.

It's a pretty interesting idea. The list gives a lot of information to work with from day 2 on.

[mith]

I suspect that is very scum-sided if scum have their normal factional kill (not clear from the setup). Not sure if they don't - scum still have the advantage of never wasting their abilities, because they know which ones will be enabled.

I feel like there is an interesting seed of an idea in there somewhere, but it's too much of a crapshoot (in terms of what abilities town has and whether or not they are enabled) for me to be at all interested in actually playing it.

[mith]

(I am really starting to think we just need a separate subforum for open setup ideas. On the other hand, I'm not sure what the ideal way to organize it would be; a separate thread for every setup could get overwhelming, and sometimes setups build off each other in ways that should be preserved somehow.)

[mith]

New subforum!

I will leave this thread open for general discussion.