Ended Small Vanilla Mafia: Mafia Victory

Colonel Thunder

Renowned Blunderer & Dishonorary Czech
Member
Will insert generic OP later.

1 mafia, 1 town power role, 3 townies.

A small game, for players who are willing to make posts of some substance at least once every few days. Anatrons need not apply ;)


Players:
Jeroth - Townie
FD
Dunsparce
Andy
 
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Colonel Thunder

Renowned Blunderer & Dishonorary Czech
Member
I'm thinking 4 man game, 1 mafia, 1 doctor. If the doctor is lynched gg. If mafia is lynched gg. If a Townie is lynched, then the mafia has a 50 percent chance of being blocked and the game continuing to day 2 high alert mode.
 

AndyM03

Well-Known Member
Member
I'm thinking 4 man game, 1 mafia, 1 doctor. If the doctor is lynched gg. If mafia is lynched gg. If a Townie is lynched, then the mafia has a 50 percent chance of being blocked and the game continuing to day 2 high alert mode.
I like the sound of that!
 

Colonel Thunder

Renowned Blunderer & Dishonorary Czech
Member
Roles have been sent out! The game is now live!

There is 1 mafia, 1 doctor, and 2 townies. Vanilla rules apply.

It will take 3 votes to lynch a player.

Y'all have exactly one week from this post to lynch someone, otherwise it's a no-lynch.

Good luck!
 

Firedemon

Well-Known Member
Member
So I'm gonna go ahead and lay this out now. Frequently in this situation, it makes more sense to no lynch, go down from 3v1 to 2v1 over the night, and improve your odds of correctly lynching scum. Here's our RNGesus chances if we don't do that.

Day 1 outcomes:
Hit scum - 1/4 - Town victory gg
Hit the doctor - 1/4 - Mafia victory
Hit a townie - 1/2 - Proceed to night 1

Night 1*:
Townie/doctor dies - 3/4 - Mafia victory
No one dies - 1/4 - Proceed to day 2

Day 2 sub optimal:
Hit mafia - 1/3 - Town victory
Hit town - 2/3 - Mafia victory

OR

Day 2 where everyone claims like last game to be a bunch of cheeky bastards:
Hit mafia - 1/2 - Town victory
Hit town - 1/2 - Mafia victory

So playing "sub optimal" we have a (1/4) + (1/2 * 1/4 * 1/3) = 7/24 = ~29.2% chance to win
And with claiming we have a (1/4) + (1/2 * 1/4 * 1/2) = 5/16 = ~31.2% chance to win
Assuming we are all incompetent and RNGesus everything.

*Assuming no self protection, the doctor could mistakenly protect the mafia, so only 1/2 chance of even protecting the townie, then a 1/2 chance mafia tries to hit the townie instead of the doctor. Of course if the doctor can protect themself they could just self protect and turn this into a 50/50 chance overall, which brings up town success odds by a few percentage points. This brings up our chances of winning to 1/3 and 3/8 for each strategy.

So, I'm actually going to propose we not do that, specifically because this is day 1 and someone is likely going to just not get to even attempt to play the game in that scenario. We'd only get a tiny benefit from doing that, at the cost of 1/4 players not getting to play the game. And under optimal doctor mechanics we get the same odds or better anyways. I could totally factor in a 1/2 chance of getting optimal doctor mechanics, but I'm done doing math.

OH WAIT SHIT NO THERE IS A COMPLICATION IN THE NO LYNCH STRATEGY.

Day 1 - No lynch

Night 1*:
Doctor:
Protect scum - 1/3 - Somebody dies
Protect not scum - 2/3 - Somebody maybe dies
Mafia:
Hit doctor - 1/3 - Double townie day 2
Hit unprotected townie - 1/3 - Role claim BS opportunity
Hit protected townie - 1/3 - Doctor gets info?
If protected scum, hit either townie - 2/3 - Role claim BS opportunity
Total:
Double townie outcome - (1/3 * 1/3) + (2/3 * 1/3) = 1/3
Role claim BS - (1/3 * 2/3) + (2/3 * 1/3) = 4/9
Doctor info - (2/3 * 1/3) = 2/9

Double townie (or forgo BS - only thing that matters if planning on forgoing BS):
Hit scum - 1/3 - Town victory
Hit town - 2/3 - Mafia victory
Total - (1/3 * 1/3) = 1/9 = ~11.1% town victory by this path

Role claim BS:
Hit scum - 1/2 - Town victory
Hit town - 1/2 - Mafia victory
Total - (4/9 * 1/2) = 2/9 = ~22.2% town victory by this path

Oh god, the branching, why am I doing this?

Doctor info:
Doctor or protected townie is targeted for lynch - 1/2 - Doctor claims
Hit scum immediately - 1/4 - Town victory
Hit other townie immediately - 1/4 - Mafia victory
Doctor claims (Mafia counter claim is irrelevant, counter or not it's now a 1v1 situation with two confirmed town spectators):
Hit scum - 1/2 - Town victory
Hit town - 1/2 - Mafia victory
Total - (2/9) * (1/4 + (1/2 * 1/2)) = 1/9 = ~11.1% town victory by this path

*If doctor can self protect, this could force the role claim BS scenario, where the doctor only self protects every night until the mafia hits someone else (technically we could be assholes and have an endless game this way?), giving us a guaranteed 1/2 chance right from the get go if we're willing to do role claim BS. This just feels extremely cheesy though, so I hope the doctor doesn't try to force this situation if we go this route. Alternatively, the doctor self protects until a townie dies and we just play the "double townie" scenario without BS claiming, in which case total town victory odds are still just 1/3.

Overall (with no conscientious objection to the role claim BS where everyone claims) - 1/9 + 2/9 + 1/9 = 4/9 = ~44.4% town victory

So actually, if we're willing to do cheesy role claim BS, we improve our odds from ~31.2% or 37.5% (depending on doctor mechanics) to ~44.4% or 50% by doing a no lynch today. I don't really know how I feel about that revelation and this just got SO MUCH MORE META than I set out for this to be.
 

Firedemon

Well-Known Member
Member
WAIT! I MADE A MISTAKE!

Doctor info:
Doctor or protected townie is targeted for lynch - 1/2 - Doctor claims
Hit scum immediately - 1/4 - Town victory
Hit other townie immediately - 1/4 - Mafia victory
Doctor claims (Mafia counter claim is irrelevant, counter or not it's now a 1v1 situation with two confirmed town spectators):
Hit scum - 1/2 - Town victory
Hit town - 1/2 - Mafia victory
Total - (2/9) * (1/4 + (1/2 * 1/2)) = 1/9 = ~11.1% town victory by this path
Optimal move here is for doctor to just claim immediately and identify the protected townie. Mafia counter claim is irrelevant, the day reduces to a 1v1. So this day's total is actually 2/9 * 1/2 = 1/9... Wait, really? Huh. That doesn't seem right? But it is... Interesting.
 

Dunsparce

Well-Known Member
Member
My objection to no-lynching Day One is usually that it limits information, but that really doesn't apply in a game this small. Tomorrow, if somebody gets night killed, we'll have exactly as much info as we could ever have, if not, we still maintain our numbers. I support the no-lynch idea, but I'm not gonna vote on it 'till we get close to the end of the day.
 

AndyM03

Well-Known Member
Member
Now do I trust this dark magic called "Maths" or do I go with my gut?
Just kidding, obviously don't have any gut reads at this point. Most of FD's post seems to check out, but I don't understand the correction post. If Mafia jumps in before the doc and says they protected X person, and then the Doc counter claims, how on earth do we know who the Doc is? It's not like the mafia would have to wager whether or not some other power role stopped the kill.

I think regardless self save is the top thing for the doctor to do, especially with these numbers. Are you sure that's wrong? Your assumptions rely on the counter claim being irrelevant but from the perspective of a vanilla boi I don't think we'd have the info to reliably detect the mafia counter claim. Obviously things will be crystal clear to the doctor, but that 'revelation' can be faked by scum as well, especially if they manage to post first. Though for that to happen, I think they'd have to make a guess as to who the doc is?

Arrgh, how dare you bring maths into the first post. Anyway, besides that, pretty happy with the no lynch strat overall.
 

Firedemon

Well-Known Member
Member
So the reason counter claiming is irrelevant is you have one of two situations

Doctor claims and identifies protected townie
Mafia counter claims and has to identify a protected townie as well

So now we have two confirmed townies and two remaining uncertainties. Alternatively,

Doctor claims and identifies protected townie
Mafia doesn't counter claim

Now the doctor and protected townie are confirmed, and there are two remaining uncertainties.

If the mafia preempts the real doctor and claims, the doctor will just counter claim and we go into the first situation.
 
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