MAFIA GUIDE; HOSTING, SUGGESTIONS, AND DISCUSSION
Posts
I could host my Pokemon Mafia if anyone would be interested.
I am tempted to make a small game. Kloe's is dead. accept it.
Nothing was happening, so I went ahead and made a warm up thread:
Y's Mafia
It lacks detail, but I want people in it first.
Y's Mafia
It lacks detail, but I want people in it first.
I've changed my mind about the mafia I'm going to host when it's my turn. It's not going to be Spy v. Mafia 2. It's going to be something completely different! Inspired by previous events, and my own original story!
I will still eventually do Spy v. Mafia 2, but it's going on a backburner for now.
I will still eventually do Spy v. Mafia 2, but it's going on a backburner for now.
Jeroen_Sol
Nothing reveals Humanity so well as the games it plays. A game of betrayal, where the most suspicious person is brutally murdered? How savage.
3885
I posted this in WAYTARN, but I spent so long on it I think it deserves to be in this thread too.
Lynching vs Nolynching Day 1 - An analysis:
Maybe I should turn this into an article and get me some sweet makerscore for it as well. I can still shave it up here and there, but I spent a lot of time crunching those numbers so I don't want it to get lost.
Lynching vs Nolynching Day 1 - An analysis:
Abstract: lynching on day 1 is a good idea (almost)* always.
Some people like to argue that lynching on day 1 is a bad idea because it lowers town's numbers. However, random lynching on day 1 nets you mafia about 1/4 of the time. The actual probability is s/(s+t), where s denotes the amount of scum players, and t denotes the amount of town players. For most games, this is close to 1/4 on day 1. So you're indeed about 3 times more likely to hit a townie than you are to hit a scum day 1 if you guess randomly. However, the value of hitting scum is far higher than the value of losing a townie, so this alone isn't enough to discourage nolynching day 1! After all, on each day, the amount of townies will be greater than the amount of scum, so random guessing will always hit scum less than 50% of the town.
Luckily, scumhunting can help our success rate.
Scumhunting is definitely possible on day 1, especially if new scum are involved, making that chance even higher. New scum tend to look really bad in their first post. (Think Adon with his: "Just a starter lynch" post.)
Let's assume a standard 7 town, 2 scum game for an example:
Nolynch worst possible scenario (0% accuracy):
D1: 7-2
D2: 6-2
D3: 4-2 MYLO
D4: 2-2 mafia win.
Lynch worst possible scenario (0% accuracy):
D1: 7-2
D2: 5-2
D3: 3-2 LYLO
D4: 1-2 mafia win.
So in the worst possible scenario, mislynching day 1 makes you lose just as fast as nolynching day 1 does. You don't lose faster if you lynch.
Now let's assume lynching has a 50% accuracy:
Nolynch:
D1: 7-2
D2: 6-2
D3: 0.5 5-1 + 0.5 4-2 (50% MYLO)
D4: 0.25 4-0 + 0.5 3-1 + 0.25 2-2 (25% town win, 50% MYLO, 25% scum win)
D5: 0.25 4-0 + 0.25 2-0 + 0.25 1-1 +0.25 2-2 (50% town win, 50% scum win)
Lynch:
D1: 7-2
D2: 0.5 6-1 + 0.5 5-2
D3: 0.25 5-0 + 0.5 4-1 + 0.25 3-2 (25% town win, 25% LYLO)
D4: 0.25 5-0 + 0.25 3-0 + 0.375 2-1 + 0.125 1-2 (50% town win, 37.5% LYLO, 12.5% scum win)
D5: 0.25 5-0 + 0.25 3-0 + 0.1875 1-0 + 0.1875 0-1 + 0.125 1-2 (68.75% town win, 31.25% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 50% to 68.75%.
But town can't lynch with 50% accuracy, you might interject. Let's look at a 1/3 accuracy then.
Noynch:
D1: 7-2
D2: 6-2
D3: 1/3 5-1 + 2/3 4-2 (66.7% MYLO)
D4: 1/9 4-0 + 4/9 3-1 + 4/9 2-2 (11.1% town win, 44.4% MYLO, 44.4% scum win)
D5: 1/9 4-0 + 4/27 2-0 + 8/27 1-1 + 4/9 2-2 (25.9% town win, 74.1% scum win)
Lynch:
D1: 7-2
D2: 1/3 6-1 + 2/3 5-2
D3: 1/9 5-0 + 4/9 4-1 + 4/9 3-2 (11.1% town win, 44.4% LYLO)
D4: 1/9 5-0 + 4/27 3-0 + 12/27 2-1 + 8/27 1-2 (25.9% town win, 44.4% LYLO, 29.6% scum win)
D5: 1/9 5-0 + 4/27 3-0 + 4/27 1-0 + 24/81 0-1 + 8/27 1-2 (40.7% town win, 59.3% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 25.9% to 40.7%.
Finally, let's assume town guesses completely randomly. accuracy = s/(s+t). (These calculations are going to suck a lot, but here I go...)
Nolynch:
D1: 7-2
D2: 6-2
D3: 1/4 5-1 + 3/4 4-2 (66.7% MYLO)
D4: 1/20 4-0 + 9/20 3-1 + 1/2 2-2 (5% town win, 45% MYLO, 50% scum win)
D5: 1/20 4-0 + 9/80 2-0 + 27/80 1-1 + 1/2 2-2 (16.25% town win, 83.75% scum win)
Lynch:
D1: 7-2
D2: 2/9 6-1 + 7/9 5-2
D3: 2/63 5-0 + 26/63 4-1 + 35/63 3-2 (55.5% LYLO)
D4: 2/63 5-0 + 26/315 3-0 + 174/315 2-1 + 105/315 1-2 (11.4% town win, 55.2% LYLO, 33.3% scum win)
D5: 2/63 5-0 + 26/315 3-0 + 58/315 1-0 + 116/315 0-1 + 105/315 1-2 (29.8% town win, 70.2% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 16.25% to 29.8%.
Now random guessing has the lowest possible accuracy of all lynching methods. The only strategies that have lower accuracies are strategies that in some way intentionally lynch town over scum, which town obviously should never do. Even for this lowest possible accuracy, it's still better to lynch day 1 than nolynch. It almost doubles town's win chances in fact!
So, in conclusion, bath math tells us that lynching on day 1 is (almost)* always the correct option for town.
* Footnote: It has to be noted that power roles and neutral roles are not taken into account here. If not all townies are valued the same, or non town/scum players exist, results may differ. But running through the math on these examples alone took me far too long already.
Some people like to argue that lynching on day 1 is a bad idea because it lowers town's numbers. However, random lynching on day 1 nets you mafia about 1/4 of the time. The actual probability is s/(s+t), where s denotes the amount of scum players, and t denotes the amount of town players. For most games, this is close to 1/4 on day 1. So you're indeed about 3 times more likely to hit a townie than you are to hit a scum day 1 if you guess randomly. However, the value of hitting scum is far higher than the value of losing a townie, so this alone isn't enough to discourage nolynching day 1! After all, on each day, the amount of townies will be greater than the amount of scum, so random guessing will always hit scum less than 50% of the town.
Luckily, scumhunting can help our success rate.
Scumhunting is definitely possible on day 1, especially if new scum are involved, making that chance even higher. New scum tend to look really bad in their first post. (Think Adon with his: "Just a starter lynch" post.)
Let's assume a standard 7 town, 2 scum game for an example:
Nolynch worst possible scenario (0% accuracy):
D1: 7-2
D2: 6-2
D3: 4-2 MYLO
D4: 2-2 mafia win.
Lynch worst possible scenario (0% accuracy):
D1: 7-2
D2: 5-2
D3: 3-2 LYLO
D4: 1-2 mafia win.
So in the worst possible scenario, mislynching day 1 makes you lose just as fast as nolynching day 1 does. You don't lose faster if you lynch.
Now let's assume lynching has a 50% accuracy:
Nolynch:
D1: 7-2
D2: 6-2
D3: 0.5 5-1 + 0.5 4-2 (50% MYLO)
D4: 0.25 4-0 + 0.5 3-1 + 0.25 2-2 (25% town win, 50% MYLO, 25% scum win)
D5: 0.25 4-0 + 0.25 2-0 + 0.25 1-1 +0.25 2-2 (50% town win, 50% scum win)
Lynch:
D1: 7-2
D2: 0.5 6-1 + 0.5 5-2
D3: 0.25 5-0 + 0.5 4-1 + 0.25 3-2 (25% town win, 25% LYLO)
D4: 0.25 5-0 + 0.25 3-0 + 0.375 2-1 + 0.125 1-2 (50% town win, 37.5% LYLO, 12.5% scum win)
D5: 0.25 5-0 + 0.25 3-0 + 0.1875 1-0 + 0.1875 0-1 + 0.125 1-2 (68.75% town win, 31.25% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 50% to 68.75%.
But town can't lynch with 50% accuracy, you might interject. Let's look at a 1/3 accuracy then.
Noynch:
D1: 7-2
D2: 6-2
D3: 1/3 5-1 + 2/3 4-2 (66.7% MYLO)
D4: 1/9 4-0 + 4/9 3-1 + 4/9 2-2 (11.1% town win, 44.4% MYLO, 44.4% scum win)
D5: 1/9 4-0 + 4/27 2-0 + 8/27 1-1 + 4/9 2-2 (25.9% town win, 74.1% scum win)
Lynch:
D1: 7-2
D2: 1/3 6-1 + 2/3 5-2
D3: 1/9 5-0 + 4/9 4-1 + 4/9 3-2 (11.1% town win, 44.4% LYLO)
D4: 1/9 5-0 + 4/27 3-0 + 12/27 2-1 + 8/27 1-2 (25.9% town win, 44.4% LYLO, 29.6% scum win)
D5: 1/9 5-0 + 4/27 3-0 + 4/27 1-0 + 24/81 0-1 + 8/27 1-2 (40.7% town win, 59.3% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 25.9% to 40.7%.
Finally, let's assume town guesses completely randomly. accuracy = s/(s+t). (These calculations are going to suck a lot, but here I go...)
Nolynch:
D1: 7-2
D2: 6-2
D3: 1/4 5-1 + 3/4 4-2 (66.7% MYLO)
D4: 1/20 4-0 + 9/20 3-1 + 1/2 2-2 (5% town win, 45% MYLO, 50% scum win)
D5: 1/20 4-0 + 9/80 2-0 + 27/80 1-1 + 1/2 2-2 (16.25% town win, 83.75% scum win)
Lynch:
D1: 7-2
D2: 2/9 6-1 + 7/9 5-2
D3: 2/63 5-0 + 26/63 4-1 + 35/63 3-2 (55.5% LYLO)
D4: 2/63 5-0 + 26/315 3-0 + 174/315 2-1 + 105/315 1-2 (11.4% town win, 55.2% LYLO, 33.3% scum win)
D5: 2/63 5-0 + 26/315 3-0 + 58/315 1-0 + 116/315 0-1 + 105/315 1-2 (29.8% town win, 70.2% scum win)
As you can see, lynching instead of nolynching on day 1 makes town's win chance go up from 16.25% to 29.8%.
Now random guessing has the lowest possible accuracy of all lynching methods. The only strategies that have lower accuracies are strategies that in some way intentionally lynch town over scum, which town obviously should never do. Even for this lowest possible accuracy, it's still better to lynch day 1 than nolynch. It almost doubles town's win chances in fact!
So, in conclusion, bath math tells us that lynching on day 1 is (almost)* always the correct option for town.
* Footnote: It has to be noted that power roles and neutral roles are not taken into account here. If not all townies are valued the same, or non town/scum players exist, results may differ. But running through the math on these examples alone took me far too long already.
Maybe I should turn this into an article and get me some sweet makerscore for it as well. I can still shave it up here and there, but I spent a lot of time crunching those numbers so I don't want it to get lost.
i've exhaustively gone over it over and over again and rehashing the discussion is pointless now imo. nobody on either side of the fence is gonna change their mind.
I did some time ago.
The Question is, if there is a situation, which benefits from no-lynch?
I would say that it can only occur in a power madness setup. In vanilla flips are a sole source of info for town.
The Question is, if there is a situation, which benefits from no-lynch?
I would say that it can only occur in a power madness setup. In vanilla flips are a sole source of info for town.
if you basically know that you are in a situation that is "mislynch and lose" it is generally advantageous to not lynch
example: it's day and there's 3 townies alive, one scum alive. if you lynch incorrectly, it becomes 2 townies alive, and then the scum kill and win the game. no lynching in this scenario will narrow down the list of suspects if the scum kills. the scum can withhold their kill though unless there are rules in place to prevent the game stalling in some way.
example: it's day and there's 3 townies alive, one scum alive. if you lynch incorrectly, it becomes 2 townies alive, and then the scum kill and win the game. no lynching in this scenario will narrow down the list of suspects if the scum kills. the scum can withhold their kill though unless there are rules in place to prevent the game stalling in some way.
Who wants to host? If you have no idea mafiascum wiki is full of them.
If nobody is interested I can run a simple game.
If nobody is interested I can run a simple game.
Man, if you had only posted that a week ago haha -- while yes, I would, I also have a doc up for an Umineko theme that I was planning to post this weekend once I finish running the numbers on it.
Jeroen_Sol
Nothing reveals Humanity so well as the games it plays. A game of betrayal, where the most suspicious person is brutally murdered? How savage.
3885
Ooh, might have to join that one just for the theme then.
...Yes, I know that's a terrible reason.
...Yes, I know that's a terrible reason.