People are sick of Closed Setups. I am, so whoever opposes. I don't care.
I'm sure you all know this by now but let's play the first ever osu! True Lovers Mafia. For those of you who don't know it's been proven that this mafia setup is a 50% chance of either faction winning. This is proven by this simple formula.
There are few things we need to clarify first.
Rules:
Day 1 Start!
Night 1 / Day 2 Start!
Night 2 Start!
Day 3 Start!
Notes:
Oh right, to also prevent bias, I will not be the person who will allocate the roles. It will be my brother who doesn't know anyone here or what Mafia is. It will be chosen by the order of which you signup, the number will then be taken and I will say "Choose two numbers who will be Mafia." The Mafia and Town Lovers will be linked together by whatever number he decides to link together.
I'm sure you all know this by now but let's play the first ever osu! True Lovers Mafia. For those of you who don't know it's been proven that this mafia setup is a 50% chance of either faction winning. This is proven by this simple formula.
"Courtesy of Mafiascum.net"
*Let S be scum pairings and
*Let Pa be total pairings
P(Town win) = 1 - S/Pa = (Pa-S)/Pa
If given the reverse.
P(Mafia win) = S/Pa
Base Case: Given a 1 - 1 LyLo (two pairs of Lovers, one of which has scum in it), the chance that Town will win is the chance of lynching a member of the scum pair, or 1/2.
This is 1 - 1/2 = 1/2.
Given that the rule holds for S scum and PA players, it is necessary to show that it holds for S scum and PA+1.
P(Town win,S,PA+1) = (S/(Pa+1))(P(Town win,S-1,Pa)) + ((Pa+1-S)/(Pa+1))(P(Town win,S,Pa))
=(S/(Pa+1))(Pa-(S-1))/(Pa) + ((Pa+1-S)/(Pa+1))((Pa-S)/Pa)
=(SPa - S2 + S + Pa2 - SPa + Pa - S - SPa + S2)/(Pa(Pa+1))
=(Pa2 + Pa - SPa)/(Pa(Pa+1))
=(Pa+1-S)/(Pa+1)
...which is precisely the original formula, with (Pa+1) swapped in for Pa. Thus completes the proof.
Letting P(Town win) = 1/2), this means:
1/2 = (Pa-S)/Pa
Pa/2 = Pa - S
S = Pa/2
Hence, this setup has a 50% chance of either side winning.
*Let Pa be total pairings
P(Town win) = 1 - S/Pa = (Pa-S)/Pa
If given the reverse.
P(Mafia win) = S/Pa
Base Case: Given a 1 - 1 LyLo (two pairs of Lovers, one of which has scum in it), the chance that Town will win is the chance of lynching a member of the scum pair, or 1/2.
This is 1 - 1/2 = 1/2.
Given that the rule holds for S scum and PA players, it is necessary to show that it holds for S scum and PA+1.
P(Town win,S,PA+1) = (S/(Pa+1))(P(Town win,S-1,Pa)) + ((Pa+1-S)/(Pa+1))(P(Town win,S,Pa))
=(S/(Pa+1))(Pa-(S-1))/(Pa) + ((Pa+1-S)/(Pa+1))((Pa-S)/Pa)
=(SPa - S2 + S + Pa2 - SPa + Pa - S - SPa + S2)/(Pa(Pa+1))
=(Pa2 + Pa - SPa)/(Pa(Pa+1))
=(Pa+1-S)/(Pa+1)
...which is precisely the original formula, with (Pa+1) swapped in for Pa. Thus completes the proof.
Letting P(Town win) = 1/2), this means:
1/2 = (Pa-S)/Pa
Pa/2 = Pa - S
S = Pa/2
Hence, this setup has a 50% chance of either side winning.
There are few things we need to clarify first.
Rules:
- All former rules that applied in LS games are said hard rules. A violation of them, however, will end with the game to be terminated as it will not prove the above rule correctly. I will also make sure that it is enforced that you will not be able to play ANY games of osu! Mafia for a pretty long time. I mean it.
- This is an Open Setup game. It will consist of 2 Mafia Lovers and 6 Town Lovers. Lovers are divided into four pairs. Both scum are individually paired with a town player.
- This is a Nightless setup. There is no night phase so there is no fear that town will be killed at night. However, I'll will give a certain time break once day ends. This may range from an hour to a day.
- Mafia will get a QuickTopic with both of them and Lovers will get a QuickTopic. Also Town Lovers will not know their Lovers alignment.
Mafia Lover
Welcome, [Player Name]. You are a Mafia Lover, along with your mafia partner, [Player Name]. You are also a Lover with [Player Name].
Abilities:
Factional communication: At any time during the game you may talk with your partner here [QuickTopic link].
Lover's Angst: If you or your Lover partner is lynched at any point in the game, the other will automatically suicide.
Lover chat: You may talk anytime during the game with your Lover here [Quicktopic link].
Win condition:
You win when you control 50% of the town.
Town LoverPlayers:
Welcome, [Player Name], you are a Town Lover.
Abilities:
Lover's Angst: If you or your Lover partner is lynched at any point in the game, the other will automatically suicide.
You do not know your partner's alignment.
Lover chat: You may talk anytime during the game with your Lover here [Quicktopic link].
Win condition:
You win when all threats to the town have been eliminated.
- LunaticMara
FisHie- Revenged killed D2.JInxyjem- Lynched D1.- Rantai
- Backfire
KRZY- Lynched D3.animask- Lynched D2.DeathxShinigami- Suicide D1.
Day 1 Start!
Night 1 / Day 2 Start!
Night 2 Start!
Day 3 Start!
Notes:
Oh right, to also prevent bias, I will not be the person who will allocate the roles. It will be my brother who doesn't know anyone here or what Mafia is. It will be chosen by the order of which you signup, the number will then be taken and I will say "Choose two numbers who will be Mafia." The Mafia and Town Lovers will be linked together by whatever number he decides to link together.
