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    Morning Nerds! :) I have the best part of 2...

    Morning Nerds!

    I have the best part of 2 and a half articles written, it's just a matter of figuring out the structure & order of content for the next few. Would appreciate some feedback about what people are interested in. Right Now Part 2 is Role Balance, which will surely be a more contentious topic

    This first article is pretty simple, but it made sense as a stopping point for part 1. It's aimed at total design newbs so i tried to add a lot of detail/examples that might be overkill for some

    To the people who learned something new from this (hopefully someone!?), let me know if the examples were easy to follow, we can update/improve the article based on feedback.

    Thanks
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    Ya more than anything else, the most important...

    Quote Originally Posted by mhsmith0 (#6)
    PS I think that "what % of non-clears do wolves need to mislynch" is an excellent way to look at game balance, though I'm not sure that 50% is necessarily the correct number (I think figuring out a "normal" % is probably an EXCELLENT way of trying to understand balancing standards for a given community though)
    Ya more than anything else, the most important take away is finding a number that works for you and using that as your benchmark
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    It doesn't really matter how many wolves there...

    Quote Originally Posted by kaempfer13 (#11)
    Assuming you were to step away from the formula for the number of wolves, how would that affect the game balance (naturally, more wolves means more wolfsided, but whats the formula)? Especially wrt the nonclear villas.
    It doesn't really matter how many wolves there are, but adding more will generally mean less mislynches.

    Your formula is:
    Number of Non-Clears / Number of Mislynches = %
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    There an example at the end comparing 15v2 & 13v4...

    There an example at the end comparing 15v2 & 13v4

    It's kind of the reverse of what you're asking
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    There's a big difference between 15v2 and 13v4...

    Quote Originally Posted by kaempfer13 (#14)
    But that would imply that 1vs10 is just as balanced as 3vs10. That doesn't strike me as realistic. There is no way to gain towncred through bussing and you can just die randomly.
    There's a big difference between 15v2 and 13v4 compared to 10v1 and 10v3

    Besides, 15v2 required some tweaking to make it roughly similar to 13v4. Did you read the example?

    I wouldn't agree that anything i said indicates that 10v1 & 10v3 are the same...


    10v3 is normal mountainous. Wolves need to lynch 40% of non-clears. Slightly scum sided game.

    10v1 is barely even playing mafia anymore. But Scum need to lynch 50% of non-clears. Balanced game, but probably not very fun!


    Arguably there is no TMI in a 10v1 game, though some people still feel guilt even as a lone wolf and get caught anyway (even without awkward teammate interactions to analyze). In a game without TMI...lynching is probably just random guessing.
    If you randomly lynch 5 people from 11, town wins 45% of the time, which is good enough balance for most setups! (Again, that doesn't mean it's a fun setup)

    This feels like a weird math proof for my preferred non-clear percentage of 50%

    QED?



    That was fun. I don't think we learned anything tbh...but I'm sure @LordQuas enjoyed all the numbers and percentages!
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    Anyway! Let's talk "Number of correct lynches". ...

    Anyway! Let's talk "Number of correct lynches".

    Quote Originally Posted by kaempfer13 (#14)
    I think the number of times town has to lynch correctly is completely ignored here.
    It's not ignored at all.

    Number of Correct Lynches is just the "Number of Mafia" (see: Team Sizes). Too few mafia and it's not really a game of mafia anymore. Too many and it becomes really difficult for town to win. I felt like this idea was obvious enough that it wasn't really worth more than the couple of lines I gave it in the article.

    You can also look at Correct Lynches as one definition of a "Town Win Condition". My article focuses almost exclusively on the Wolf Win Condition. I think i explained why well enough, but let's go over it a bit more

    I focus on Wolf Win Condition because:
    - Designers never overlook the village win condition (case in point: you! )
    - Designers regularly overlook the wolf win condition
    - imo, the wolf win condition captures the whole game and is a useful indicator of balance
    - imo, the town win condition does not!


    Number of correct lynches inherently seems like a useful metric for game balance...but it's actually quite useless.

    Consider our Mountainous 13er
    Correct Lynches to win (for town): 3
    Non-clears to lynch (for wolves): 40%


    Now let's add 8 innocent children!
    The setup is 3 scum and 8 innocent children and 2 vanilla town.

    Correct Lynches to win (for town): 3
    Non-clears to lynch (for wolves): 200%


    The number of correct lynches didn't change, but the PoE is 5 people and town have 6 lynches!
    The game is unwinnable for scum..and yet your metric (correct lynches) didn't capture that at all.

    Percent of non-clears to lynch is 200% though, it's immediately obvious this setup is broken.


    Number of Correct Lynches doesn't say anything about number of PRs, Clears, Non-Clears, or overall game difficulty for town.

    It's more like a game rule than anything else.
    Score 3 goals to win, but how hard is it to score? We have no idea, because the number doesn't tell us anything about it.

    The Wolf Win Condition (as defined in the article) tells of everything, so that's the one to focus on.




    We could try to define a Town Win Condition based around percentage of correct reads in relation to non-clears or something...
    But i think we'd inevitably just come up with either the inverse of the formulas already in the article or some variation of what we already have?

    I'll probably give it a go later tbh, but now i gotta get back to work
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    For a 13er Towns win condition is lynch 3 scum...

    For a 13er

    Towns win condition is lynch 3 scum in 6 lynches.
    Or dont lynch more than 3 towns.
    Or townclear 7 towns.

    I dunno what makes the most sense.


    If town win condition is clearing 7/10 non-clears (70%), then the town loss condition (i.e. wolf win condition) is if they only clear 6/10 towns (& misclear 1 scum), which is 60%.

    This is just the inverse of "Number of Non-clears to mislynch" for wolf win condition: 40%.


    So you can look at balance from the point of view of correct lynches but it's just going to be the exact inverse of the Wolf Win Con (mislynches).
    As expected

    The important common denominator is that you are counting non-clears.
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    I'm going to start over. Number of times...

    I'm going to start over.

    Quote Originally Posted by kaempfer13 (#14)
    I think the number of times town has to lynch correctly is completely ignored here.
    Number of times to lynch correctly is just the exact opposite of number of times you can lynch incorrectly, i.e. mislynches.

    Number of Mislynches is covered pretty thoroughly in the article

    TY for your question
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    Gotcha :D That's ok i enjoy talking to myself...

    Quote Originally Posted by kaempfer13 (#19)
    Yh, my mistake was to not account for the additional nightkill that occurs after lynching scum. as such 8v1 would theoretically have the same balance as 10v3.
    Gotcha

    That's ok i enjoy talking to myself about balance
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    explain the math on this one this just doesn't...

    Quote Originally Posted by mhsmith0 (#23)
    10v1 mountainous with random lynching / mandatory night kills gives you a wolf win only 37% of the time.
    explain the math on this one

    this just doesn't seem intuitive, but sometimes math isn't?


    initially i was lazy and did 45% of all players are lynched. 55% chance the scum isn't one of them.


    Just now I tried:

    D1 = 10/11 (Odds of Town lynch)
    AND
    D2 = 8/9 (Odds of Town lynch)
    AND
    D3 = 6/7 (Odds of Town lynch)
    AND
    D4 = 4/5 (Odds of Town lynch)
    AND
    D5 = 2/3 (Odds of Town lynch)
    ---
    10/11 x 8/9 x 6/7 x 4/5 x 2/3 = 66.666% = Odds of scum never getting lynched?
    I forgot to click enter on the calculator. LOL.

    10/11 x 8/9 x 6/7 x 4/5 x 2/3 = 37% = Odds of scum never getting lynched?


    But then i did just ran through final 3 and I had:

    Odds of townie #1 voting right (50%) AND Odds of townie #2 voting right (50%)
    = Odds of both townies voting right (25%).

    75% in scums favour is a bit better than the above calculation of 66%...maybe the math needs to be a bit more complex


    @mhsmith0
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    I dunno if i did this right but the odds of...

    I dunno if i did this right but the odds of townies agreeing is far lower than the odds of choosing a player at random.


    Final 5
    5 players. Wolf always votes to save themself.
    3 need to vote the wolf to kill him...or 2-1-1 split works too (coinflip)...but a 2-2 split doesn't (wolf self pres). Let's just look at maj for now...

    25% percent chance town #1 votes correctly
    25% percent chance town #2 votes correctly
    25% percent chance town #3 votes correctly
    25% percent chance town #4 votes correctly


    all correct = 0.00390625
    1,2,3 correct = 0.01171875
    1,2,4 correct = 0.01171875
    1,3,4 correct = 0.01171875
    2,3,4 correct = 0.01171875
    =
    0.05859375


    ~6% chance enough randomly townies agree and vote scum

    ???

    odds of a random death hitting scum: 20%
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    random voting seems more valid than random...

    Quote Originally Posted by mhsmith0 (#25)
    You can complicate the math for sure, but the main thing is that "random player gets lynched" is a reasonable quick and dirty proxy for a game state in a bunch of site metas (MU lynches above rand, but not like insanely above it I don't think). Blindly voting gives you 3/4 mislynch in f3, but "random lynching" effectively assumes town is a LITTLE better than random voting, but the difference cancels the wolf info advantage to get at 2/3 (f3), 4/5 (f5), etc.

    I think random lynching is a mediocre balance metric overall but it can sometimes help with certain unusual structures.

    Or take it to a fully absurd level, 1000/1 is balanced by the standard of "what % of willagers do you need to mislynch" but not really balanced in pratice (you could make it 1000/3 to make it "mafia" with a "team" and the balance doen'st much change ).
    random voting seems more valid than random lynching

    in the same way that random lynching seems more valid that my original "quick and dirty" 5/11 players get lynched, therefore 55% chance scum survives


    My original idea doesn't account for narrowing lynch pool via NKs.
    Random lynching doesn't account for the teamwork/coordination required to actually lynch one person.
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    Bullet point 1 25% of players should be mafia...

    Quote Originally Posted by kaempfer13 (#29)
    Yh, I knew something was off when looking at only non-clear%

    Quote Originally Posted by Newcomb
    Core Design TL;DR
    • Around 25% of players are Werewolves
    • The number of mislynches wolves need to win should be 50% of all non-clear villagers
    • Both teams should control 50% of the game's kill power
    • All deviations should be compensated for in some way
    Bullet point 1

    25% of players should be mafia

    Kaemper's examples:
    - games with 8 to 12% mafia.

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    Based on Smith's posts I have spent the morning...

    Based on Smith's posts I have spent the morning comparing different metrics to see where they converge, and when each is most useful vs others

    It feels like a not small amount of work so it may take a while to actually figure it out (if that's even a thing that can be done!?)
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    Preliminary Results (assuming i mathed right) ...

    Preliminary Results (assuming i mathed right)

    Vanilla 9er
    Random lynch wolf win: 70.14%
    Non-clear percent: 42%

    Cop 9er (cop dies N1)
    Random Lynch wolf Win: 66.64%
    Non-clear percent: 60%

    Vanilla 13er
    Random Lynch Wolf Win: [@mhsmith0 probably knows this number by heart]%
    Non-clear percent: 40%

    Vanilla 17er
    Random Lynch Wolf Win: smith gimme this number too pls
    Non-clear percent: 38%


    Non-clear percent goes down with player count.
    I assume random lynching win % goes up with player count also.
    Seems like both agree with common consensus (more players is better for wolves)



    Random lynching doesn't seem to indicate a cop makes much difference in a 9er.
    Non-clears weights it as a decent sized difference.
    Maybe a second peek will change the results of this comparison (on the to-do list)



    Fun fact that when there are clears to be NKd (rather than non-clears) then you get this weird thing where randomly lynching exactly one wolf is as likely to happen on any given day.


    D1 wolf lynch: WTTT (2/7 x 5/6 x 4/5 x 2/3) = 0.126984126984127
    D2 wolf lynch: TWTT (5/7 x 2/6 x 4/5 x 2/3) = 0.126984126984127
    D3 wolf lynch: TTWT (5/7 x 4/6 x 2/5 x 2/3) = 0.126984126984127


    Normally it gets easier the more days you go without lynching a wolf:

    WTTT (2/9 x 6/7 x 4/5 x 2/3) = 0.1015873015873016
    TWTT (7/9 x 2/7 x 4/5 x 2/3) = 0.1185185185185185
    TTWT (7/9 x 5/7 x 2/5 x 2/3) = 0.1481481481481482


    #MathNerds
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