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I'm with Shadow, I don't think the calculation is quite accurate. I think Bb's system is a great guideline for beginner hosts, but I don't think it accurately represents all the factors that go into mafia game balance.

Some of the major things I think are not completely represented:

1) Interaction factors (I believe this is the statistical term), i.e. the interplay between certain roles that makes them stronger or weaker in the presence of certain other roles than they would be alone. The kind of 'mafia game balance is more (or less) than the sum of its parts' thing.

2) Hosting styles/rules. Different hosts have different opinions about what goes into Posts, what takes precedence over what, etc, and this often affects the 'strength' of some roles/role combinations.

3) The Law of sheer numbers. As far as I can tell, the system doesn't give any weight to numbers (in terms of # of players), but many mafias come down to voting in the end, which is very much about the numbers. I.e. a game with 3 mafia and 6 'active' innocent roles would have the same calculation as if the game had 3 mafia, 6 'active' roles, and 10 "vanilla" villagers, but I think everyone would agree that the latter is far more in favor of the innocents ;). Also, generally a player with two different abilities is not as strong as 2 players each with one of those abilities, due to the possibility of blocks/redirect/manipulate as well as voting.

Just to point out a few places these factors come into play:

The fact that kills are not blocking in my hosting style is usually an advantage for the side that does less killing and has more members killed, so in this case, the innocents.

The fact that there is no innocent redirect and the mafia one is shown allows the information roles to be more confident in their information. Additionally, in a game with more information roles, this has more of an effect, in a game with less, this has less. MikeD (Artemis) could trust Vommack's info on Aaryan (unless Vommack himself was mafia/indie and playing something sneaky, of course ;)) b/c he knew he was not redirected.

The Independent role is a lot stronger than the calculations would suggest, for many reasons, some of the main ones being:

-The small size of the game, due to the Law of sheer numbers, as well as the ability to narrow down roles faster. Also, the small size allows the indie manipulate to control a larger proportion of the game earlier, and it's a lot more about proportion than number of players controlled.

-The fact that the target does not know they are manipulated, no one does except the indie (and me, of course ;P), and my vague style of information reporting, i.e. "Your target is Miss Martian" rather than "Vommack is Miss Martian."

-The ability to control the mafia NK and a lynch swap or a lynch save, effectively making themselves invincible once they had enough info. Combine this with the aforementioned effects of a small size game, and I think its pretty apparent that the indie is a lot more powerful than Bb's system might think (speaking of which, I had a huge speech prepared about underestimating Lex Luthor, in terms of the mythology as well as the game...damb...soooo close, lol ;P)

Maybe the innocents were slightly under-powered, I'm not sure, but the mafia was ridiculously lucky in terms of killing off the block and both killing roles by Night 2. The numbers in this game were 7 to 3 mafia, a greater than 2:1 ratio, and the indie role did not have an inherent kill, and was designed to be best played waiting and gathering info (as Shadow did so well B)) ), rather than to start randomly trying to fish for killing roles, so I do not think the balance was too much off. If I did a repeat, I might give Artemis the choice of blocking/redirecting as well as the original RD, but everything else I'd leave pretty much as is.

I think it might be fun to play with Bb's system and add some variables to compensate for some of these factors, but overall I like the 'holistic' approach...I feel comfortable enough with my mafia experience, my game theoretical knowledge/intuition, and my general competence that if my over-analytic 'gut' tells me differently than what the basic calculation does, I would lay odds on myself ;P.

Edit: Thank you all for the feedback though...as much as I am loath to admit it, I do get a 'spring in my step' from knowing ppl enjoyed my games ^_^

Edited by Yoruichi-san
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Y-san is a legendary host as far as I am concerned, it is hard to imagine anyone not enjoying one of her games.

The balance sheet does not take into account number of players, that is something that a host has to figure on their own. I find it useful but think its calculations for this game are off, as goodies would have won I think if not for the lynch switching. So the balance sheet is not perfect, but it is handy.

I also think the lynch switch would have become op with or without any goodie outting, since by the third day the baddies should have a pretty good idea of who several of the goodies are. Even a goodie should be able to figure out at least one or two roles by paying attention. I like new roles like the rid lynch switch but I think it works better as an indie power since baddies become invincible once they figure out a few roles.

Looking back at what the balance sheet says of this game, if the lynch switch had been just a normal rid kill, and the restrictions on goodie roles were lifted, the balance sheet would show this as a pretty balanced game (indy notwithstanding)

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Thanks, nana, I hope you'll be around if I decide to do a sequel to When the Mafia Cry or try the utter insanity that would be Suzumafia ;)

Having the 'bird's eye view', I know that the only role the mafia was guessing at before mass outing was Vommack, and had that incorrect (and hence would have ended up dying if they tried), so I disagree that the lynch switch would of been OP in the end without mass outing, since the mafia do not have a spy, and no innocent roles are announced when killed, not even Red Arrow. If the killing roles had not been killed off by Night 2, they could of easily taken out the lynch switch.

Having thought about it a little bit, here are two preliminary suggestions for what I will henceforth refer to as Bb's Model ;). (Btw, I was present when he first created the model, and then, as well as now, I commend him on creating a great and easy to use system. It took a lot of effort, and he did an amazing job, and I have the utmost mafia-tist respect for him...it's a lot easy to critique than to create ;P)

The simple suggestion:

The mafia BTSC (x2) factor should not apply to passive skills. As I understand it, the (x2) is due to the ability of the mafia to powerplay and to avoid 'friendly-fire', neither of which applies to passive skills.

For example, the mafia get (+6) for a player being invincible at Night, whereas the innocents only get (+3), which seems kind of backwards to me, since an innocent is generally more likely to get killed at Night then a mafia, and the innocents can fall victim to their own friendly-fire. In my mafia experience, I'd say at least 1/2 of innocents die at Night, whereas less than 1/3 of mafia do.

Which brings me to my second, more complicated suggestion:

Weigh each ability by a proportionality factor that represents the likelihood to actually be useful. Admittedly, this is pretty complex, since it involves both taking into account what other roles there are, what the general host rules are, and the proportion of the factions against each other, but that's exactly why I like it...it factors in all three of the issues I mentioned earlier.

I don't think there's a simple formula for how to do this for all roles, but I think I would divide it into two parts, one for 'information potential' and the other for 'action potential'. For example, a killing role, in a game in which kills are not blocking and there are no invincible roles that are outed if attacked, is pretty much all 'action potential', and the proportionality factor is would probably be equal to the (probability of killing a mafia)-(probability of killing an innocent) or some such. A straight spy probably has the most straightforward proportionality factor, since it's pure 'information potential', but if there are roles that can 'disguise' themselves or others, then that would have to be factored in. A block is both info and action potential, more or less so info depending on whether the hosts show blocks in the Posts, and what other actions are shown in the Posts.

As for general host rules, it's a lot more complicated for complicated setups. For example, this little piece of insanity I dug up from my mad mafia-tist days:

The Suzumafia: During the first Night, must choose who to kill for each of 13 Nights.

The Schizo: Aims to be an useful member of the Suzumafia, but is paralyzed by his own paranoia. Every Night, chooses a person to kill, but will not be able to carry through unless he is under the protection of the Doctor.

The Copycat: Each Night, chooses a player, and if she can correctly identify the role of the player, she gets to copy and use the player's ability for the Night. May not copy the same player two Nights in a row.

The DITE: A humanoid interface that can control her own surroundings. Each Night she may choose a player and any actions targeted at her will be redirected at that player.

The (More-or-less) Innocents:

The Bad Dog: A quick learner, he quickly mastered all the tricks his owner taught him...but he also learned that how to pretend not to. After all, why would he want to perform tricks on command to entertain the silly shallow humans? May choose to use one of his tricks each Night. May not use the same trick two Nights in a row.

Sit: Choose a player, sits on that player. That player cannot act for the Night.

Roll Over: Any action targeted on him rolls right off. If targeted by an information role, it is reflected back at the player.

Fetch: Chooses a player to fetch to safety for the Night.

Shake Hands: Chooses a player, and his identity is revealed to that player.

Play Dead: Any Night, but only once, may choose to pretend to be dead, until he chooses to stop the play-acting. While he is playing dead, he may not act or post on the thread, and has no vote. Also cannot be acted on. Once he posts, the play-acting is over.

The Doctor: May choose to protect any person from death. May not protect the same person two Nights in a row. The first time is free. The second time the Doctor protects a player, he learns that player's identity.

The Time Bunny: Travels through time on a killing spree while dressed in a bunny suit. On the first Night, choose a player to kill each Prime Night from 2-13. When the Night occurs in-game, may choose to call off the kill "at the last moment". Cannot call off the kill if she is dead.

The Emo: Travels through time stopping others from acting. On the first Night, chooses players to visit each even Night and make a scene in front of so that that player cannot act.

The Doppler Shift: Each Night, may choose a player whose action will be shifted one Night into the future.

The Channeler: Each Night, may choose to redirect the action of one player onto another player.

The Esper: Has the power to explore Closed Spaces. Each Night, chooses a player to find out the role identity of.

The Night Posts will be in random, non-chronological order. They will also be incomplete unless the Night in question has already occurred in-game. Incomplete Posts will show who the Suzumafia are attacking, who the Time Bunny is attacking, and who the Emo blocks. Results and secondary actions that effect the results will not be shown in Incomplete Posts (i.e. saves or if the TB calls off the kill or redirects/blocks/delays). After the Night occurs in-game, the Incomplete Post will be filled in.

The roles of Suzumafia aren't that complicated, but the general set-up has a huge effect on everything, especially game balance.

(Okay, rereading it, I really want to host it now lol...time traveling paradoxes aside...*whistling*)

Edit: Actually, this is kind of fun, if I have time between puzzle and game projects (and, oh yeah, that annoying thing called "real life" :rolleyes:), I might work on the Mathgirl Formula ;P)

Edited by Yoruichi-san
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Yup, real life gets in the way of a lot of stuff *sigh* Back on topic, yes the system is not foolproof, it still shouldn't be used in games with vanillas (though I still haven't won that argument past Bb) and all-in-one the system does not account for context-specific info. Including order of actions, interactions, other host rules, fact that abilities still can't be weighted the same for an uninformed / informed faction, etc. Her comes the but part. As we were in need of an easy-to-apply system, we've embraced it as a foundation and it's easy to teach to apprentice hosts. Much like newtonian physics. Nana even tried to make it as auto as possible to capture even the laziest hosts possible (and mass verification as required by an industrial boom). The idea is to use it in conjuction with open debates before the game is queued, to allow as much human/community contributions as possible. Back to this game, the goodie restrictions were not visible in this exact instance but could have made an impact. Redirects not being shown almost always disrupt balance thoughts from a host as it easily leads to incorrect assumptions which prove to be fatal in Mafia games. For the uniformed usually. I still think this was imbalanced i.e would show the baddies win more than 1/3 of games. However there is no way I can prove it without statistics/ large number of simulations. Which is not feasible, even if we have bots to host simple mafias we're far from simulating mafia players. I will only throw one more argument in: both minorities had abilities that grew in power (baddies unblockable lynch switch as goodies can be narrowed down or out, and indys no of actions which also benefits from info spreading and even previous trial and error attempts. Goodies did not have that. I would enjoy having a different system to chew at, but I am skeptical that an easy to use system is right around the corner. The goal is not to have a foolproof system but to make the overall balance judgement process starting from a reasonable scaffolding and adding pepper and salt to iron things out... I once dreamed of publishing a research paper on the subject, but obviously when I woke up, I did not find the page I had scribbled my lemmas. Been researching dreaming ever since, on a regular basis, with no luck so far.

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Lol...I think you misunderstand me...I agree with everything you've said about it being easy to use, useful, and widely applicable, especially for new hosts (I said as much in my first post on the topic). I'm not trying to, like, 'put it down', or anything, like I said, I respect Bb greatly for creating it and I think it's a great model overall.

And I absolutely agree about the Newtonian physics part, I was actually thinking about that analogy as well :lol:. But using the same analogy, I, in my infinite Mathgirl-ness, can't help trying to develop Maxwell's laws... ;)

Araver, I sincerely apologize if you feel I was offending the system. That was not my intent...I admit, I tend be analytical rather than, like, 'tactful', although I did try to make clear my respect and support of the system as a general system (sorry I failed :(). One thing I learned the hard way about forum content: it doesn't show tone well...I write with an analytical tone much of the time, which can be wrongly read as an 'attacking tone' :/.

I am a scientist by trade (and by DNA, apparently *whistling*) and I look at Bb's system as an empirical model that is useful and clever, and hence, like most scientists who look at empirical models that they like, try to find places it could be improved. Science is about collaboration, and scientists are always critiquing and trying to improve on others' works. I am truly sorry if this aspect of my personality can cause conflict or seem insulting to some :(.

Again, I reiterate, I think Bb's Model is fantastic and I fully support using anyone's choice to use it as a tool to design games. Please don't mind my scientific/engineering curiosity if I try to build Maxwell's Mafia equations, tho ;).

Edited by Yoruichi-san
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Lol, posting from a phone really makes my posts come out worse than I thought :)) and yes, I am likewise analytical (and have been lynched many times b/c of the loss of tone meta-information in forum communication).

Sorry there were no paragraph marks in my post :(.

Trying to separate the threads again (from a computer this time):

1. There was no misunderstanding, I wasn't in any way against your future Maxwell equations and I did not feel you offended the system :P

I have only tried to compactly present (some of) the conclusions of some very long threads into one or two paragraphs just to get you up to speed to where / why we used it and what the overall opinion is after we've been using it for more than 1 year (fragmented opinions but with some common ground).

Especially the pressure of having multiple Hosts designing multiple Mafias (kinda mainstream) melded those opinions.

2. Re this game I have my own biased opinion on interactions which has nothing to do with the discussion about balance in general. Bias from playing (albeit not very long), bias from being a sore loser (half bias 'cause I just admitted it out loud, right? :) ) and most of all bias from being a host having personal preferences and inklings regarding interactions in Mafia games.

3. My last paragraph (lines actually) were actually designed to be a joke. E.g.

[off-topic parenthesis: I have been proud to call myself an (aspiring) scientist, until a mob of people convinced me that actually all of the results I proved follow the same pattern: something is either not true, utterly impossible or at least infeasible. So I became a manager, thinking it's a job where the inclination of discovering there is no way to do something will be very useful. Turns out it doesn't.]

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Lol...sorry, my mistake (compounded by a mild case of heat stroke and a painful internal sore on my foot...I should really stop doing 10 mile runs in the 85 degree heat and like 80% humidity ^_^)...it seemed that you were defending using the system, which I didn't think needed defending, unless you misunderstood my intent. I totally understand why Bb's model is a great one to use and I wasn't telling anyone not to use it for their games, but I do think that in the 'user-friendliness' of the model, it sacrifices some refinement. Having the engineering game theorist's soul that I do, I couldn't help (really O:)) analyzing it and trying to find places for improvement. To be honest, I don't expect anyone to actually use the 'Maxwell' version I am trying to come up it, since, well, as you can probably guess, it will be somewhat math-intense.

But I do think my suggestion for passive skills makes a lot of sense, and is not difficult to implement ;).

And I admit, I have a personal bias too...in my mafia player 'career' (or 'careers', I should say :ph34r:, *cough* *whistling*), the only games I lost as an innocent were the ones where I died the first Night/Day or that were probability based and we, like, lost 5 coin tosses in a row :lol:, so I tend to think the innocent 'strength' is under-estimated in general.

Speaking of which, I have a crazy little piece in the works: 7 players, no factions, free for all, individual win conditions. Keep an eye out for it.

Oh and if anyone wants to be a substitute in Liar Game, PM me :thumbsup: .

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