On the SDMB, I believe that the scum have won only twice. M2 and You-Solve-It Mafia. I’m not sure how many games have been played here – seven?
There have also been a bunch of off-board games, but I don’t know anything about them.
In the beginning, scum never won. Lately scum have been consistently winning. I feel this is largely due to the fact that Town have adopted a ‘keep your head down’ attitude and aren’t as active as they used to be in earlier games.
Day One of the earlier games often stretched over several pages. Much of it was dreck, but people were talking… which is better for Town than Not Talking.
Hal mentioned an interest in setting up a newbie-only Mafia game sometime soon(-ish). Given your quick lynch, I think you’d still qualify. My guess is, it won’t happen until he’s out of the current game. I can’t imagine trying to participate in that and then running your own at the same time.
NAF just suggested as much and BM jumped right on it:
Whether he was or was not recruited, this is a good play and puts NAF on the spot.
Hypothetically speaking, of course.
I’ve been contemplating the potential longness of this game, but I came up with a weird argument that shows that scum have a really bad situation:
Assume Vig never nightkills (bad assumption, but I’m assuming this for now).
Assume Scum always recruit every night and are always successful (favors scum).
Assume Town lynches Town every day (favors scum).
With these assumptions, the population forecast is:
Day Three (Today): 19 Town, 3 Scum
Day Four: 17 Town, 4 Scum
Day Five: 15 Town, 5 Scum
Day Six: 13 Town, 6 Scum
Day Seven: 11 Town, 7 Scum
Day Eight: 9 Town, 8 Scum
That’s seven mis-lynches needed by Scum to win.
Now let’s assume the Vig does kill every night from now on and always kills TOWN (favors scum).
Day Three (Today): 19 Town, 3 Scum
Day Four: 16 Town, 4 Scum
Day Five: 13 Town, 5 Scum
Day Six: 10 Town, 6 Scum
Day Seven: 7 Town, 7 Scum – Scum Win
That’s five mislynches needed by Scum to win and five Vig kills of Town only. Yikes! This doesn’t look good for scum.
Calculating the burden on the Town to win is much harder, as the ‘best’ case is very simple:
Day Three: lynch Boss
Day Four: lynch scum
Day Five: lynch scum
The best way I can think of so far to look at the Town’s chances is to see what the game set-up looks like when the Town finally lynches the Boss. A Day Three Boss lynch leaves the Town in excellent shape 19 Town 2 scum heading into Night.
Lynch Boss on Day Four: 17 Town, 3 Scum (Town needs 3 lynches {in addition to the 1 that already happened}, scum need 7 {+2 that already happened}: strongly favors Town)
Lynch Boss on Day Five: 15 Town, 4 Scum (Town needs 4 lynches{+1}, scum need 5{+3}: favors Town)
Lynch Boss on Day Six: 13 Town, 5 Scum (Town needs 5 lynches{+1}, scum need 4{+4}: favors Town)
Lynch Boss on Day Seven: 11 Town, 6 Scum (Town needs 6 lynches{+1}, scum need 2{+5}: “even”)
Lynch Boss on Day Eight: 9 Town, 7 Scum (Town needs 7 lynchs{+1}, scum need 1{+6}: favors Scum)
I think the game setup strongly favors the Town, really strongly.
To establish similar lynch needs with Town, The Boss needs to recruit successfully at 6 times. That’s quite a bit that has to fall scum’s way before the game merely becomes even odds. The Vig could end up helping scum, but generally Vig’s are considered balance neutral.
sachertorte, I don’t disagree with your analysis, but I’ll point out that this game was intentionally structured to be very difficult for scum to win on paper. Why? Because, generally, what the town has access to is fairly scant information from detection (given that recruitment is a strong disincentive for role claiming). After all, what generally gets scum voted for - their voting record, their posting record - and in this game, you can’t really ever have trusted town. As soon as a powerful role claims - say, the Detective, you risk Capo’ing which is extremely bad for Town, so you have to kill the person at minimum the next Day.
You have a lot of investigatory roles, sure. However, other than the Detective, you’re only getting a town/scum result. Add together the statistical unlikelihood:
- 20% cumulative Beat Cop failure chance to get any result
- Boss/Capo 50% chance to show town
- The number of players that need to be investigated to find one Boss
- The Beat Cops can’t work together to avoid duplicating investigations
- Beat Cop is an easy fake role claim
It’s rough. It really comes down to trying to peg the Boss based on his voting record and hope that by the time you do that there aren’t too many scum in play. An average game of Mafia this size has, what, 4ish scum? In statistical terms it’s not hard for the Boss to get to that point before he’s lynched, and then it’s still hard for town because of the aforementioned past record being a limited result.
In any case, I’ll be curious to see how this pans out. I don’t want to post spoilers but I will say that I am incredibly surprised by the results so far. In any case, I’d love to run this ruleset again with some tweaks for balance.
Just to add to the above…
Let’s say there are 3 Beat Cops in play and 21 players. (Not a spoiler, just a hypothetical.)
The Detective has a 1/20 chance to investigate the Boss. However, the Boss has a 50% chance to return a random role. Of course these roles include other scum rules, the Detective role (obviously false) and the improbable Doctor role (who’s probably protecting himself). So let’s be generous and give the Detective a 3.5% chance each night to find the Boss. Now, the Detective also knows that 1) recruitment is in play and 2) the Boss can read as a false role, so he’s likely to reinvestigate scummy-looking power roles. That’s assuming he never tries the general investigation of finding out how many scum are in play, too. So he’s not even getting a cumulative 3.5% chance each Night.
The Beat Cops fare much worse - they have even more reason to investigate numerous times, they can investigate the same people on the same night, they have 60% chance to fail if they all attempt it, then a 50% chance to misdetect on the Boss.
The best strategy - if everyone could work together - would be for the Beat Cops to be watching for recruitments, not looking for the Boss. They are much more likely to get a positive result. They could get lucky, but it’s not very likely. As such it’s pretty much up to two factors to find the Boss - the Detective, and his past play style. We’ll see but I think that scum has a good chance to win based on the ruleset.
fluiddruid, you have interesting points, but my intent was a quick analysis that ignored most town and scum powers and just look at the numbers. While there are many pitfalls that the Town will want to avoid, the analysis I tried to envision looked at the situation in the most favorable way things could happen for scum, and still the results are rather grim for scum. I didn’t even consider the Beat Cops or Detective in the analysis and implicitly assumed that all scum avoid detection.
Ignoring recruitment, 25% scum tends to be the norm which translates to 5 scum for a 20 player game. With a 24 player start I think 6 is a decent number. One could argue 7 due to the town power roles.
I think an additional balance issue is the recruitment process is an additional burden. What I mean is starting with 1 and requiring the creation of a scum army. Even if getting 4 scum would be sufficiently ‘even’ (I would argue that it is not), getting four successful recruits is an additional burden that normally isn’t present in a game that starts with 4 scum. (Did that make sense?)
Furthermore, on the nights that scum recruit, they can’t kill, so even if scum manage to recruit a sufficient number to achieve the theoretical 25% balance, x Days will have passed where Town gets to lynch and scum have nightkilled none. Therefore scum need to recruit an additional number of players beyond the theoretical 25% balance to regain the ground lost during the time required to reach 25%. (I’m babbling now, I know). Anyway. It’s an interesting problem.
I think unbounded recruitment is an inherently difficult power to balance. My guess is a balanced game would have very high variance, and I question whether that is a good thing.
I’m also very curious to see how the game develops. Unfortunately, one instance won’t tell the whole story. I was just surprised because my initial reaction to the game setup was “unbounded recruitment? what the hell?” But closer analysis seems to show that starting with 1 scum is a big burden for scum. I didn’t even consider recruitment failures, investigation, etc. that will make the game even harder for scum.
I hope you don’t take my criticism personally. I tend to look at these games and pick apart the rulesets. It’s kind of my thing. Balancing a game is a non-trivial task, and there is no guarantee that my analysis is even correct. For the current off-board game, I simulated the ruleset to check the balance. Even relatively simple rulesets provide unexpected results.
ETA: On the other hand, I should also consider the ramifications that recruitment insulates scum from lynches (scum don’t recruit dead townies). On the other other hand, I think recruitment failures probably offsets this issue. Hmmm.
Aaaaand… OneCentStamp just edited a post. :smack: Seems like we get one every game. I don’t remember what the penalties are in this game, but I’m sure fluiddruid will address it shortly.
Modkill! Modkill!
dotchan has jumped onto my radar now too. I don’t understand how moderating the other game would take her attention so much at this time. Right now all she has to do is sit back and wait for someone to get lynched.
That and the excuse that she doesn’t want to post for posting sake is very bad for the Town. Kind of scummy, but not scummy in the sense that scum wouldn’t be so openly scummy.
It may not be scummy, but it certainly is lazy, and I hate lazy players. Play the frikkin’ game or don’t sign up! Lazy Townies lost it for us in You-Solve-It.
Plus your own wily play, you scum you.
Me? I’m just an innocent chocolate cake.
Fair enough. Your posts have been very interesting for me as my take was the exact opposite - I presumed scum had an automatic advantage if only due to the fact that the standard strategy is inherently difficult in a recruitment game. Sure, you only start with a single scum, but there are some advantages to that - the more scum you have, the more easily you can pick off one early by chance alone, and it’s very hard (in my opinion) to have scum posts analyzed in hindsight without implicating one or more others. Not only this, but recruitment isn’t just a numbers game - you have the opportunity to draw the strongest players, with the strongest strategies, and pull them to your side. Almost always, a small handful of players will rise to the top. They may not be listed as trusted townies but they sway town influence inevitably. People want leaders.
In any case I’ll be interested to see how this game pans out, but already things are very surprising. Not just in terms of play, but how the statistics are working out randomly. I think my first plan for the next game is to decrease the randomness overall. I included a lot of percent failures because I didn’t want a) recruitment to go unchecked too quickly and b) the Boss to be easily found, but I think there are stronger ways of doing so.
If you kill a mafia thread, is that a scum tell?
At first, I had the same impression.
I’m now looking at the game as a two phase game:
Phase One: Boss Lives
Phase Two: Boss is Dead
Phase Two of the game is essentially the same as the more standard no-recruitment games we’ve seen (Dead Boss = No recruitment, and everyone knows it). So all the balance ideals found in previous games should apply to Phase Two. While I am intrigued by the notion that recruiting the ‘best’ players offers a strategic advantage, I’m not so sure this advantage outweighs pure numbers. In either case, scum will need to establish a base group to compete in Phase Two. Therefore Phase One needs to be dramatically ‘won’ by scum to establish a feasible position in Phase Two. Failure to survive and recruit sufficiently in Phase One pretty much dooms scum in Phase Two. The question is then, to what extent do we expect the Boss to survive and recruit in Phase One, and is this expectation sufficient to establish a fair position for scum in Phase Two.
E(Death of Boss) = ?
E(Recruitment) = ?
Assume random lynches
Assume 100% vig kills
Then P(Death of Boss = Day One) = 1/24 + 23/241/23 = 2/24
P(DOB = Day Two) = 22/241/22 + 21/24*1/21 = 2/24
etc…
Therefore, E(DOB) = 2/24 *(1+2+3+4+5+6+7+8+9+10+11+12) = 6.67 Days
Which is actually better for scum than I had thought, but still leaves them in a hole (I think).
E(Recruitment) is more difficult to calculate, but if we assume a 7 Day expected lifespan for the Boss, E(Recruitment) is bounded by 6 recruits. With the addition of recruitment blocking and immunities, E(Recruitment) is probably closer to 5.
At first glance, achieving 5 recruitment means 6 total scum in a 24 person game, which under normal circumstances would be a good indication of balance. However, in achieving 5 recruits, scum needed to forgo killing for 5 Nights. Five Nights of skipping nightkills translates to 2.5 mislynches needed by scum to counter-balance. So I think the expectation shows scum in the hole. If the Boss dies before Day 6, I’d expect scum to lose handily. If the Boss makes it to Day 7 or 8, I expect scum to lose a close one. If the Boss survives to Day 9, I think it is even odds.
I am the furthest thing from a statistician, so maybe this is a stupid question, but doesn’t the lack of scum increase the chances of a mislynch, making 2.5 mislynches not that hard at all, but in fact extremely likely?
Also, IIRC, the Boss has the ability to recruit multiple power roles, including cops, making the Town much easier to manipulate down the stretch. I agree that if the Boss dies early, it’s bad news, but I think it could easily swing in the scum’s favor if he can recruit the right people. Big if, of course, but that’s why you play the game 
Allow me to elaborate.
I posit that one definition of an even game could be:
Town require X lynches of scum to win and Scum require Y lynches of Town to win. If X and Y are sufficiently close (ideally equal), then the game is balanced.
In a standard game with 24 players, this condition is met with 6 Scum. Town lynches 6 scum, they win; scum gets the Town to lynch 6 Townies, scum wins.
What I was trying to say is that with the ‘start with one and recruit from there’ set-up, 6 is no-longer sufficient. Attaining the 6 scum through 5 recruits means there were at least 5 Nights without kills. These lack of nightkillings puts scum behind. The amount behind is 2.5 mislynches, so while Town would need 6 mislynches to win, Scum need 8.5 mislynches to win. The discrepancy is ameliorated by the relative small number of scum, but despite early lynches being more likely Town than not the bar is still higher for scum than for Town. It is certainly not impossible for scum to win, my point is just that the likelihood of a scum win is smaller than a Town win.
For instance, if the Town continues to pressure the Vig not to kill at night and the Vig complies, I’d say that a big portion of the Town’s advantage goes out the window, which is the result of gameplay, not the game setup. (I’m still hoping that the Vig has been trying to kill every night, but was blocked last night.)
I’ve been thinking about this idea of ‘nearly-free’ lynches since there are so few scum:
Town opted not to lynch in the game on Day One. I’ll assume they lynch all the time for this look.
I’ll also ignore Vig kills since that makes mislynches more probable.
P(Lynch Boss Day One) = 1/24;
P(Lynch scum by Day Two) = (23/24)(2/23) + 1/24 = 3/24;
P(Lynch scum by Day Three) = (21/24)(3/21) + 3/24 = 6/24 = 1/4;
So I’d estimate the 2.5 added mislynches needed about equivalent to a single “standard game” mislynch. So the added burden on scum is still present, but not as bad as I was thinking.
ETA: Actually the potential to net more than one scum is non-zero, so the 2.5 added mislynch need for scum is probably slightly more onerous than a single standard mislynch, but not as bad as a full 2.5.