Come to think of it, that would be a spoiler, so I really oughtn’t to say here. I really should have cleared that up before I died.
<PUBLIC SERVICE ANNOUNCEMENT>
Any dead or never-alive folks who want to talk spoilers:
I have, at sachertorte’s request, created a spoiler discussion forum. PM me here for the URL and password.
Thanks!
<PUBLIC SERVICE ANNOUNCEMENT>
Shhh. That was my attempt at keeping it from being a spoiler. 
Man, I finally get to check out all the hot gossip and it’s all about balancing theory and other games, and not about whether I’m scum or a genius.
I guess my “we totally shouldn’t make everyone post their role PM” didn’t go unnoticed, since I doubt I was killed for how successfully I was finding scum… waves to Wanderers.
So, I see that Meeko is back to “we don’t dare make any information at all public, because the Scum might find out”. Ugh.
And I’m frankly baffled by the day thus far. How many votes have we had for Oredigger with no stated reason beyond “we should have voted for him yesterday”? I don’t know, maybe he is Scum, but what’s the case? And what happened to the case on Tom Scud?
Speaking of Oredigger, Tom’s typo-based case does have at least something to it. I know that when I ran Cecil Pond, I copied-and-pasted the corresponding line in every PM, and it’s reasonable to think sach might have, too. Then again, he also might not have, and even if it’s a valid case, it might still be a bussing (I notice that Tom didn’t point it out until after it was clear momentum was shifting to Oredigger).
I have no idea what’s going on. Haven’t been able to keep up, going to ask for spoilers.
For what it’s worth Jimmy you never pinged me in the slightest. Who voted for you the couple of times you collected votes? Possible it might be scum despairing of ever making anything stick against you, more so than any slip. Or just that scum noticed nothing was sticking, even after OAOW.
It is striking that this train is picking up such significant steam so early when it didn’t have the same traction yesterday. The case is just that he made a silly vote on you, but nobody seems very concerned whether it was a silly scum-type vote.
And what happened to the case on Tom indeed.
TexCat voted for me, Wanderers did, and Oredigger at some point. I think there were more but those are the ones I remember. I don’t think there was ever any push by scum to lynch me in particular. I’m just a little shocked that they’d wipe me out based on my play, since I was getting townies killed left and right.
Yeah but you’re good enough that wouldn’t continue indefinitely.
Well I’m off to be spoiled. Ta!
You know, seeing Meeko struggle with the game has made me wonder: could there be some sort of Mafia Mentoring program? Yes, he’s getting better, but he’s still missing basic concepts*. I think direct instruction by someone he can trust might help. His most significant improvements in play were when he was able to talk to others.
*IN this case, I’m referring to the fact that the whole point of Mafia is that people cannot trust you. Part of their purpose is to figure out what you really mean. That means that they are going to pick apart what you say. It’s not a scum tell just because they misinterpret you.
The scumtell version can only work if you know for sure that anyone else would have perfectly understood you. So, for Meeko, who has trouble with that, it is not a scum tell, unless the majority of people say they understood.
I had a thought that perhaps pointing for scum should be non-constant. Currently, the pointing model assigns 4.5 points for each vanilla scum. As Chronos stated, the game does not scale linearly.
I think it makes more sense to point something like:
3 points for first scum.
4 points for second scum.
5 points for third scum.
6 points for fourth scum.
7 points for fifth scum.
Then add bonuses for powers.
Chronos, does that fit in with your findings?
I’m pretty sure this means the current game is unbalanced.
Would it be better to base points on the ratio of town to scum? That allows you to scale for game size, as 4 scum would be strong in 15 player game but weaker in a 30 player.
(Also, there are extreme cases where having fewer scum is stronger - 2 scum in a game of 25 would be almost impossible to find, and run the risk of causing a mass inexplicable suicide.)
Well that’s kind of the point of the points. 4 scum corresponds to 3+4+5+6 = 18. So Town should have a number of players and powers that add up to 18 to be ‘balanced.’ Does that make sense? In other words, choosing the number of scum sets the size of the game, not the other way around.
And I’m not even sure if the numbers 3, 4, 5, 6 are correct. For all I know it should be 3, 5, 7, 9, 11…
As for 2 scum vs 23 Town: Such a game is very slanted to Town, but is poorly constructed for a gameplay/fun point of view. Town will most likely find both scum… eventually. But the long process would make the game much less fun.
Ah, I follow you now.
I think there might be a point where extra scum have limited value, so the sixth scum, for example, doesn’t add as much as the third. In fact the third and fourth scum almost certainly add the most incremental value to the point total, and the first scum is probably worth 0.
Still assuming an all-vanilla game (since I haven’t yet incorporated power roles into my analysis), the number of Town as a function of number of Scum for the game to be as close to balanced as possible:
1 Scum: 4 Townies
2 Scum: 8 Townies
3 Scum: 19 Townies
4 Scum: 34 Townies
5 Scum: 53 Townies
I’m not sure precisely what the asymptotic form of the progression is, but it’s pretty clear that you can’t reasonably balance a game larger than 10 with just vanilla (nobody would be insane enough to make a 38-player game).
Another interesting point is that it makes a big difference whether the number of players is even or odd. For instance, with 8 Town vs. 2 Scum, Town has a 0.507812 chance of winning, but with 9 Town vs. 2 Scum, that chance drops to 0.352092 . This holds generally: If you have a game with an even number of players, and you add a single Townie, it significantly hurts the Town. This is because it doesn’t change the number of mislynches, but does change the probability of each mislynch, since there are more innocent bystanders. Mind you, this is assuming exactly one death per cycle, and can be thrown off by Vigs, Doctors, players dropping out, or factions being allowed to voluntarily forgo their kill.
I actually just played an all-vanilla game with 2 scum out of 34, two kills a night (irrespective of number of scum standing), and no death reveals. (Also, dead people were allowed to still participate.)
As it turns out, we the town got a lucky lynch on day two, and won with about ten players left.
Not sure what this proves, except to note that it worked well as a game. Though it’s unbalanced in favor of the town – apparently the mafia have only pulled it off one time in nine chances.
NAF… you reading this?
Quiet you. That was the best game in SDMB mafia history*. (Maybe second best. Seekham was pretty good too.)
*from a fun standpoint
Excellent. This is exactly what I wanted… All-vanilla, just to get a baseline.
So, based on Chronos’s numbers the point values are:
first scum: 4 points
second scum: 4 points
third scum: 11 points
fourth scum: 15 points
fifth scum: 19 points
Wow. That’s surprising! And much steeper than I would have expected. Though the strength of 5 scum in the recent games kind of makes sense.
A smoother, less eye-popping version would be something like:
first scum: 3 points
second scum: 5 points
third scum: 8 points
fourth scum: 12 points
fifth scum: 17 points
Yes. I had noticed that as well. The dynamic program has two independent sets.
I think we did the same analysis. Only I didn’t shoot for a .5 to .5 split to determine “fairness.” 3-handed is a well-accepted game which, by the numbers yields a 33% chance for Town to win. I think when I looked at it I went for a 30-35% value for Town winning. The balance comes from the interaction and history of the game. That is, the random model does not account for the non-random selection of lynch choices.
Either way, I’m convinced now of a progressive pointing for each additional scum.
I’m not sure we are looking at the game the same way.
The way I’m looking at it is that each additional scum adds more power than the previous one because by sheer numbers the coordinated group is more powerful. In other words, 6 scum have a powerful voting block that is more powerful than a 5 scum voting block, and that 6th scum is a greater addition than 5th was over 4th.
Yeah. I’m confusing like that.
I’m very much liking this discovery.
Edit: Let’s do it Fibonacci style!
1 scum: 3 points
2 scum: 5 points
3 scum: 8 points
4 scum: 13 points
5 scum: 21 points
Okay, maybe not, but that would be cool.
Actually, I think that introducing strategy into the gameplay can only help the Scum even more. The model I was using assumed that each day’s lynch is chosen completely at random from among all the living players. This is what would happen, effectively, if the Town had no information at all about who’s Scum. But it’s up to the Scum to decide whether to give Town that information: The Scum can always choose to play exactly as if they were Town, and ignore the extra information they have, so they can always force the numbers to be what the model predicts. On the other hand, though, it’s surely sometimes advantageous for the Scum to act in at least a somewhat coordinated way, even if it does potentially provide information to Town. The classic example is the last-minute vote switch at LyLo, like we saw in Crimson Glyph.