Open 65 - Mini Love (Over!) before 578

[Albert B. Rampage]

I have the urge to self-vote again.

Please do. You are a nuisance to the town.

[farside22]

You're all mathematically challenged retards who can't crunch numbers properly.

The lover plan is downright stupid. And armlx is making compelling points, even though Jex was scummy as fuck.

Unvote, vote Korts

FOS: armlx

because he replaced Jex.

Please explain how the numbers are faulty? Tell me oh wise one if Korts is lynched and comes up town how in the hell does the town learn anything about which lovers could be the right choice. If Korts comes up scum I withdraw my comments.

[Albert B. Rampage]

At least we'll get rid of one idiot leading the town astray.

[dahill1]

i'm pretty damn sure Korts is scum

[Albert B. Rampage]

Unvote

I REALLY want to lynch armlx.

Is there any support at all for this ?

[armlx]

Holy shit Jex was dumb this game.

I like where her vote was though. Looks a lot like another ongoing with KortS scum to say the least, plus the whole lover lynch push....

[kravhen]

IM STILL ALIVE.

I've been inactive in the past weeks do to RL issues but im all gewd now.
Moar posts coming up.

P.S.: Korts didn't I tell you self-voting is not cool or honorful in any way already?

[silence]

Ok, my attempt to crunch numbers (mathematically challenged). Rather quickly written and may well contain some errors or typos at least, and is probably difficult to read.


0. Introduction
---------------

Some of the main assumptions I make
- neither party has any reading skills, we have know idea who is scum and the mafia has no idea about the good lover pair, so all probabilites are just (favorable cases)/(all cases). Not too realistic but it would be rather difficult to come up with a realistic model of scumhunting accuracy

- mafia kills the doctor the following day

I compare only two strategies: executing the lover plan today vs. executing the lover plan tomorrow. Whether to keep lovers alive even tomorrow would warrant additional analysis, but this result already shows it is better to hunt today than execute the lover plan today, so the question whether some other future strategy would make hunting today even better is not relevant for deciding optimal actions for today.

Chapter 1 analyzes the lover plan, Chapter 2 the hunt-today-plan. Subsequent scenarios are analyzed in subchapters. In chapter 3 scenarios that occur in both plans are analyzed.

1. The lover plan
-----------------

Probability (1/2) of lynching the bad pair, after which we have tomorrow 4 townies, unknown loverpair and 1 goon - scenario 1.1. Value of this 0.5429

Probability (1/2) of lynching the good pair, after which we will lynch the bad pair, mafia kills townie, and day after tomorrow we have 3 townies and 1 goon. Value of this (1/3). (See chapter 3)

So, value of executing the lover plan today (1/2)*0.5429 + (1/2)*(1/3) = 0.4381

1.1. Scenario: 4 townies, unknown loverpair, 1 goon
-----------------------------------------------------
If we threaten a lover, they claim and we change target. So

Probability (1/5) of lynching the goon - we win.

Probability (2/7)(4/5) of outing the loverpair and then lynching a townie -> 2 townies, known loverpair, 1 goon
here we have (1/3) chance of lynching goon, mislynch leads to loss.

Probability (4/7) of lynching a townie without targeting a lover. -> 2 townies, unknown loverpair, 1 goon. This is analyzed in chapter 3.1. and has value 7/15

So value of this scenario (1/5)+(2/7)(4/5)(1/3)+(4/7)(7/15)=0.5429


2. Hunt today, execute lover plan tomorrow
--------------------------------------------

Probability (1/5) we lynch scum today - we win.

Probability (2/7)*(4/5)=(8/35) we out the unknown loverpair and lynch a townie -> starting tomorrow with 3 townies, 1 goon, lover pairs known. Scenario 2.1. Value of this is (1/3)

Probability (4/7) we lynch a townie without outing the unknown loverpair -> starting tomorrow with 3 townies, 1 goon, lover pair unknown. Scenario 2.2. Value of this is (28/75)

So total value of the plan of hunting today and executing lover plan tomorrow is (1/5) + (8/35)*(1/3) + (4/7)*(28/75) = 0.4895

2.1. Scenario: 3 townies, 1 goon, lover pair known, executing lover plan
-------------------------------------------------------------------------
With probability (1/2) we lynch the bad pair, after which mafia kills the good pair. We have 1 goon, 3 townies and thus value (1/3).

With probability (1/2) we lynch the good pair, after which mafia kills a townie. We have 1 goon, 2 townies, treacherous lover, good lover. This is a lynch or lose situation (otoh if we lynch the goon, we win). So value (1/3).

Both cases have a value of (1/3) so the value of the scenario is (1/3).

2.2. Scenario: 3 townies, 1 goon, lover pair unknown, executing lover plan
------------------------------------------------------
With probability (1/2) we lynch the good pair, scum kills a townie, we are in a lynch or lose situation with value (1/3)

With probabiltiy (1/2) we kill the bad pair, go to scenario 2.2.1 that has value 31/75

So total value (1/2)*(1/3) + (1/2)*(31/75) = 28/75

2.2.1. Scenario : 3 townies, 1 goon, lover pair unknown, NIGHT
------------------------------------------------------------------
With probability (2/5) mafia kills the lovers, after which we are in a 1 vs. 3 situation, value (1/3)

With probability (3/5) mafia kills a townie, after which we have 2 townies, 1 goon, 1 unknown loverpair, scenario 3.1. with value of (7/15)

Total value (2/5)*(1/3) + (3/5)*(7/15) = (31/75)


3. Other subgames
-------------------

1 goon against 2 townies is obviously 1/3.
1 goon against 3 townies is also 1/3, as we get a 1 vs 2 by nolynching

3.1. Scenario: 2 townies, 1 goon, 1 unknown loverpair
-------------------------------------------------------
with probability (1/3) we lynch the goon and win

with probability (2/5)*(2/3) we out the lovers and lynch a townie and therefore lose

with probability (2/5) we don't out the lovers, but mislynch, in the night 1 townie, loverpair and the goon, so we win with probability (1/3)

So value of this scenario is (1/3)+(1/3)*(2/5) = 7/15.

4. Conclusion
--------------

Value of plan 2 is higher than value of plan 1, so based on this analysis we should hunt today. Intuitively I guess that having better-than-random scumhunting chances improves the hunt plan more, so in reality the value difference is probably even larger.

[Albert B. Rampage]

Thank you silence.

[armlx]

Thank you silence.

Defintely agree.

[Sethaniel]

ack, math again.

If: Dahill = scum and Korts= town

1.We lynch Dahill

Dahill dies, -1 scum
Eldarad dies, -1 town
Scum NK, -1 town
next day, we lynch a non-lover (because dahill was the treacherous lover) equal chance scum/town -1 scum/ -1 town
next night Scum NK -1 town
Total: Scum -1/-2 Town -3/-4

2.We lynch Korts

Korts dies, -1 town
Scum NK, -1 town
a. next day, we lynch dahill
dahill dies -1 scum
eldarad dies -1 town
next night Scum NK -1 town
Total: Scum -1 Town -4
b. next day, we lynch a non lover, equal chance scum/town -1 scum/ -1town
next night Scum NK -1 town
Total: Scum -1/-2 Town -5/-6


If: Dahill = town and Korts=scum

1. We lynch Dahill
Dahill dies, -1 town
Eldarad dies, -1 town
Scum NK, -1 town
a.next day, we lynch korts, -1 scum
next night scum NK -1 town
Total: Scum -1, Town -4
b. next day, we lynch the other pair of lovers, -1 scum, -1 town
next night, scum NK -1 town
Total: Scum -2, Town -5

2. We lynch Korts
korts dies, -1 scum
a. scum NK the lover pair, -2 town
next day, assume equal chance of scum/town lynch -1scum/-1 town
next night scum NK -1 town
Total: Scum -1/-2, Town -3/-4
b. scum NK someone else, -1 town
next day, assume equal chance of scum/town lynch -1 scum/-1town
next night scum NK -1 town
Total: Scum -1/-2, Town -2/-3

This is getting me nowhere. There's a lot of variables in here. I haven't even gotten doc protection figured into it.

Oh, I didn't even do if they're both town.

Anyway, seems like if one is scum and one is town, then it almost always comes down to trading 1 scum for 4 townies.

ABR, would you outline your case against armix/Jex?

[armlx]

Ah, but you fail to realize the scum have no incentive to kill the lover pair, especially if Korts is scum and is lynched.

[Sethaniel]

Um, no incentive? They get two townies instead of one.

Unless you're saying they're both scum?

[armlx]

Um, no incentive? They get two townies instead of one.

Unless you're saying they're both scum?

Except if Korts = scum and is dead and a double town lover pair dies, I wonder who the last scum is? Oh wait, traitorous lover....

[Korts]

I won't be deciding this one, so wake me when

september ends

you decided whether or not to lynch me.

[silence]

I wasn't convinced at all that Korts is the correct choice for hunting - don't think pushing the lover plan was obviously stupid/scummy even as I now believe the plan is not correct.

However, this tone of giving up in the latest post is pretty suggesting. I read it as that he isn't trying to find arguments that someone is more scummy, as he knows no-one is and the lover plan was his only hope.

So I currently plan to vote Korts. But I'll still do a reread+reconsideration before deadline.

[Korts]

I think my arguments would be in vain, anyway. My position is not really a defendable one.

[Korts]

Anyway,

Pinky Finger of Suspicion

Sethaniel for post 535. Making a point of trying to do the math and then failing, seems to me like a filler post.

[farside22]

I think you guys are wrong. If we lynch Korts and he is not scum at what point do you lynch the lovers to find out if one is scum?

[Albert B. Rampage]

NEVER.

[Coron]

I think you guys are wrong. If we lynch Korts and he is not scum at what point do you lynch the lovers to find out if one is scum?

When we've found the one hiding among the townies?

[Korts]

I think you guys are wrong. If we lynch Korts and he is not scum at what point do you lynch the lovers to find out if one is scum?

When we've found the one hiding among the townies?

And why would a lover hide among townies?

[armlx]

I think you guys are wrong. If we lynch Korts and he is not scum at what point do you lynch the lovers to find out if one is scum?

When we've found the one hiding among the townies?

And why would a lover hide among townies?

I'm trying to figure out if this is a joke or you didn't get that he was referring to mafia.

[Korts]

Yeah. Reading comprehension. Just bum-rape me already, I'm just lame this second day.

[Sethaniel]

Making a point of trying to do the math and then failing

Hey, I

said

mathyness was not my strong point. I'd rather vote based on whether I think Korts or dahill seems scummier, anyway.