Mini 1167 - iPod Mafia - Game Over

[GreyICE]

AHEM

There is a STARTINGLY HUGE difference between a game that can end BEFORE DAY 2 starts and this one. The EARLIEST THIS GAME COULD END WOULD BE –

Day 1 – Lynch Town (8:3:1)
Night 1 – Weak Doc dies protecting, Mafia and SK both hit Town, Inventor is motivated and gives a Gun to Town who Shoots Town (4:3:1)
Day 2 – Lynch SK (4:3)
Night 2 – Mafia kills Town and Wins.

So the ABSOLUTE earliest the game could end would be N2, not N1. Furthermore I can run the statistics if want me to quantify ( on a pure random chance model anyway ) the difference in probabilities between this game and Cupcake Mafia.

By the way, I got bored and did this. Cupcake:

* Scum lynch (3/13)
* Vig shoots scum (2/12)
* Scum Night Kill Bomb (1/10)
* Scum NKing bomb is different than scum being vigged (1/2)

Total: 1/520 (0.19%)

Odds your game:
* Town is lynched (9/13)
* WD protects scum (4/11)
* Scum NK non-WD town (7/9)
* SK NKs other town (non-WD, non-NK) (6/11)
* Inventor gives gun (1/4)
* To scum (3/11) - (Shot Odds 5/9)
* To town or SK (8/11) - (5/11)

Total odds: 1.29%
Or 7350/570999 (oh adding complex fractions, what won't you do...)

Around 6.5 times more likely for yours to have the 'worst possible' case than Cupcake.

Lets face it, percents that low HAVE to be thrown out.

Because I can, Brotherhood, multicase:
Day 1 cases, two kills:


*Dayvig N-bulletproof scum (1/12)
*Lynch Scum (2/10)

*dayvig other scum (2/12)
*lynch bulletproof scum (1/11)

(assuming that the dayvig is unlynchable day 1)

N1 Cases, 1 scum death:
*Vig scum (1/10)

*Redirect scum (1/10) onto themselves (only logical redirect target)

Day 1 case, bulletproof dies:
Vigged (1/12) or lynched (1/11)

N1, two deaths:
Redirector redirects scum submitting NK (1/10)
Vig vigs other scum (1/10)


Total chances of ending on day 1:
19/6000 (2 scum dead day 1, 1 dead night 1) + 1/600 (bulletproof dies day 1 + 2 dead scum N1) = 29/6000

So summarize:

I-Pod, worse case: 1.29%
Brotherhood, ends day 1: 0.48%
Cupcake, ends day 1: 0.19%

[MagnaofIllusion]

Grey when I have time I'll dissect this to show you how completely bad you are at arranging probabilities.

[Fate]

PWNT

[GreyICE]

That should be fun.

Suffice to say that the calculation for cupcake (3/13*1/12*1/10) is fairly simple and very hard to argue with. The others are more complex because there's compound probabilities that occur in both (IPod compounds when you have the inventor giving either town or scum the gun, Brotherhood compounds because there's 4 possible ways that scum die).

[Fate]

I want to make a MoI fan page and have those statisics RIGHT next to his postgame post in Cupcake

[GreyICE]

Also for cupcake it's a tad higher than I said because the vig never vigs themself, so that's 1/11, so you can raise it to 0.21%.

Yeah so percentages on the orders of 1% or less are called miracle-shots, and can't be accounted for in swingy games.

[Fate]

(Course your math IS wrong because the chance Fate will draw the NK as bomb is 75% N1, 100% if scum was lynched that day)

[GreyICE]

(These are all blank roulette wheel odds with MINOR common sense (scum don't night kill scum, vig doesn't vig themselves, etc.), observed odds say that a day 1 scumlynch is a good deal higher than 3/13)

[MagnaofIllusion]

That should be fun.

Suffice to say that the calculation for cupcake (3/13*1/12*1/10) is fairly simple and very hard to argue with. The others are more complex because there's compound probabilities that occur in both (IPod compounds when you have the inventor giving either town or scum the gun, Brotherhood compounds because there's 4 possible ways that scum die).

Of course it will be fun. Slapping down horribly put together statastics done only to support a grudge based on ‘Lulz Buddies’ is always fun.

And let me say again these are based on pure random chance. No scum-hunting involved.

Chances Cupcake Mafia ends BEFORE Day 2

–

Scum are lynched Day 1 - (3/13)

Scum chooses to kill Bomb – (1/10) remember, scum will only be killing from living 10 Town players.

Town Vig chooses to shoot scum NOT killing Bomb – (1/11) Vig will not consider self as target

Chances game ends before Day 2 – (3/13) * (1/10) * (1/11) = 0.2098%

Chances IPod Mafia ends BEFORE Day 2

–

Zero. No chance at all.

The game could only win under the following circumstances.

1. Town kills all the scum. Can’t happen. Town can only achieve 2 kills by Night 1 (via Lynch and Motivated Gun). No possible way all 4 scum (SK and 3 Mafia can) can die before Day 2. If they lynch the Serial Killer on 1 scum can be killed an Night. If they lynch a Mafia the Serial Killer can’t die at Night. If the Mafia Daykills the Serial Killer and Town lynches Scum the can’t kill both remaining scumm at Night.
2. Serial Killer kills everyone else. Obv can’t happen.
3. Mafia wins in a 3-3 or 3-2-1 endgame. Scum needs 7 dead bodies to achieve either one of these.

3-3 – This means the Serial Killer was either lynched or Daykilled Day 1. If lynched there are only 3 other kills that can happen – Mafia Kill, Motivated Inventor giving a Gun, and Weak Doc death. So we have a total of 4 dead bodies.

If Daykilled and assuming a Town lynch there are only 2 other kills that can happen – Motivated Inventor giving a Gun and Weak Doc death. Same case …only 4 dead bodies.

Worst case under this scenario we have a 3-6 set-up after Night 2.

If the Serial Killer is not Daykilled or Lynched there are the following possible deaths.

Lynch – SK Kill on Town – Mafia Kill on Town / Daykill on Town – Motivated Gun kill on Town – Weak Doc death.

That’s 5 kills. Worst case scenario we have 3-1-4.

In any case the scum can’t achieve their win-con BEFORE Night 2.

Changes game ends before Day 2 – 0%

Chances Brotherhood Mafia ends BEFORE Day 2

-

Daykill on Mafia – (3/12)

Lynch of Mafia - (1/12) : This is lower because for the game to end by Day 2 the Mafia Godmother has to die by either Lynch or Daykill. Making that the secondary target ups the odds.

Vig targets remaining Mafia – (1/10) Vig again will not consider self a target.

As with Cupcake this consider no other role interactions (like Role-blocks, etc)

Chances game ends before Day 2 – (3/12) * (1/12) * (1/10) = 0.2083%

--

To put them together for easy viewing –

Cupcake Mafia – 0.2098%
Brotherhood Mafia – 0.2083%
iPod Mafia – 0%

So in the end Cupcake and Brotherhood had pretty even chances of ending before Day 2. iPod has none.

[GreyICE]

*sigh*

No, wrong. The chances that the godmother dies day 1 is not 1/12. It's 1/12 she's shot by the vig, and assuming the vig is obvtown after the shot (which he was, even though it hit town), 1/11 to be lynched.

You have to add the two chances together, and you end up with a 23/132 chance that the godmother dies day 1.

Then assuming the godmother dies day 1, the chances that the other one hits scum are 2/11.

So the compounded chance is 23/132 * 2/11

Which ignores the redirector, but thems the breaks.

Basically, you've taken 46/1452 (3.07%) and simplified it to 1/48 (2.08%), which isn't even CLOSE to correct.

[MagnaofIllusion]

*sigh*

No, wrong. The chances that the godmother dies day 1 is not 1/12. It's 1/12 she's shot by the vig, and assuming the vig is obvtown after the shot (which he was, even though it hit town), 1/11 to be lynched.

You have to add the two chances together, and you end up with a 23/132 chance that the godmother dies day 1.

Then assuming the godmother dies day 1, the chances that the other one hits scum are 2/11.

So the compounded chance is 23/132 * 2/11

Which ignores the redirector, but thems the breaks.

Basically, you've taken 46/1452 (3.07%) and simplified it to 1/48 (2.08%), which isn't even CLOSE to correct.

Um, whut?

Either the Godmother is DayVigged (1/12) and then scum is lynched (2/12)

or

scum is Dayvigged (3/12) and then the Godmother is lynched (1/12).

Those are the two possible scenarios.

What you are doing above is calculating the chances that she is EITHER lynched or Dayvigged and then tacking on the chances of a scum lynch to that.

Fail.

Nice of you to dodge how incredibly bad your iPod Mafia calculation was Grey. Cudos!

[GreyICE]

Well what we're doing is hybredizing two different cases together.

Case 1: Godmother dayvig, scum lynch:
1/12*2/11

Case 2: Other scum dayvig, godmother lynch:
2/12*1/11

Since EITHER case one OR case 2 gets us the same result, the combined odds are really:

1/66 + 1/66, for a combined odds of 1/33, or around 3.03%. Which is more accurate, but mine was within spitting distance and I'm lazy.

Your error was that you used a hybrid diddly case that made no sense

3/12 (odds scum is vigged... INCLUDING GODMOTHER SCUM)
1/12 (odds godmother is lynched)

This is clearly wrong, because in the circumstances where the vig shoots godmother, odds of scum lynch are 0%. So to hybrid it properly, you'd have to path it:

2/12 * 1/12
1/12 * 0

Then you realize that of course the town can lynch other scum if the godmother is shot, and you end up with what I have.

[MagnaofIllusion]

Then you realize that of course the town can lynch other scum if the godmother is shot, and you end up with what I have.

Here’s what you had –

No, wrong. The chances that the godmother dies day 1 is not 1/12. It's 1/12 she's shot by the vig, and assuming the vig is obvtown after the shot (which he was, even though it hit town), 1/11 to be lynched.

You have to add the two chances together, and you end up with a 23/132 chance that the godmother dies day 1.

Then assuming the godmother dies day 1, the chances that the other one hits scum are 2/11.

So the compounded chance is 23/132 * 2/11

So you were saying that the chances the Godmother died to either lynches or Dayvig was

23/132 and then you added on an additional scum lynch of 2/11.

So you were actually factoring two Day 1 lynches into your calculation.

In any event you aren’t arguing that my numbers are substantially wrong.

And once again – the percentage chance you pulled out of your ass for iPod were so obviously wrong I don’t even …

[GreyICE]

That was for your worse case '5 dead town by day 2' calculation (which, while not a certain scum victory, being in 4:3:1 on day 2 is pretty damn close to a certain town loss).

No I multiplied by 2/11. Not added. There's a small, tiny little difference. (2/11 * 2/11 being somewhat different from 2/11 + 2/11)

[Lady Lambdadelta]

Please refer to the above picture as a representation of this entire debate.

[MagnaofIllusion]

That was for your worse case '5 dead town by day 2' calculation (which, while not a certain scum victory, being in 4:3:1 on day 2 is pretty damn close to a certain town loss).

The point ... you are purposefully FUCKING MISSING IT.

It doesn't matter if it was a 'clear Town loss' or not. Cupcake Mafia ENDED BEFORE DAY 2 BEGAN. iPod Mafia COULD NOT DO SO BY ANY MEANS.

You pulled out some bullshit percentages in an attempt to attack me for my criticism of your dear pal Katsuki. I understand you cling to the notion that you are a member of the 'Cool Kids Club' and that anyone who dares to question one of your members must be bombed with pointless posts that don't stand up to logical sense.

I'll consider this conversation over since you've completely abandoned whatever it was you were trying to say and now are just throwing crap together.

[Surye]

Why are mommy and daddy fighting?

[Lady Lambdadelta]

Why are mommy and daddy fighting?

Because Popemobile McTurboCunt over here won't stop beating a dead horse, and just let sleeping dogs lay.

And because Godzilla won't ignore him, and feels the need to try and disprove his lolstatistics.

[GreyICE]

Sorry, mine are right, his are wrong. I didn't take four years of engineering in college including through Calc IV and Differential Equations to not know how to do a compounded probability. For pete's sake that's what any failure analysis of any sort comes down to.

[GreyICE]

Please refer to the above picture as a representation of this entire debate.

Also:


Honk honk, motherfucker

/obligatory

[Lady Lambdadelta]

I giggled.

[MagnaofIllusion]

Sorry, mine are right, his are wrong. I didn't take four years of engineering in college including through Calc IV and Differential Equations to not know how to do a compounded probability. For pete's sake that's what any failure analysis of any sort comes down to.

Hey look ... all classes I took also.

I was a Math Major before I was an Accountant.

And yet you, despite your grand education, have no clue what you are doing with your "Stats pulled out of your ass"

In summary

[Lady Lambdadelta]

There needs to be significantly less comparing of "credentials" in this thread.

I mean, boys will be boys, but still. You can do that somewhere private, right~?

[GreyICE]

Oh dun worry, math is so perfect that its proofs are the only proofs, anything considered 'proven' in a science is a pale shadow of a joke next to what math considers proof. It is used in every single science. There's no question that math has the largest breadth and spans the most subjects.

Engineering just taps a part of that, but we have all of the practical uses.

[ooba]

Read the game. Congrats Fate!

Just thought I should say that I disagree with the viewpoint that what nopoint did was right.
- Anything he said before he was lynched would have been fine as you can attribute it to him wanting to avoid a lynch
- He was already lynched AND he was the last mafia-ite. No help to his wincon by outing Fate at that point. Should have just shut up and died.

You don't out any other faction if you've already lost. Let them play it out .. Just because it's not in the rules doesn't mean it's right ..

For Reference:
http://mafiascum.net/wiki/index.php?tit ... t_not_scum.