Mini 2320: Smuggler's Port II [Endgame]

[Gamma Emerald]

I'm pretty sure the breaking strategy here is to just give ourselves triple Masons

I think Kyouko's plan comes from town though

How does this plan work?

[ssbm_Kyouko]

I used a binomial calculator to get these numbers on the probability of these shipment configurations occurring (only counting the town players because this is the POV that scum will have if we follow this strat):
0L-5C: 0.03125
1L-4C: 0.15625
2L-3C: 0.3125
3L-2C: 0.3125
4L-1C: 0.15625
5L-0C: 0.03125

Treat these configurations as distinct rather than collapsing them and consider the Linen to be inspected every time (in actuality this will be random, but you could reverse the L and C and the numbers are the same. Scum are guessing the PA from amongst the off-wagon players (the Copper number plus 2) and if they are correct they gain a nightkill to POE their TD guess down to the Copper Number (if they guess the PA then the PA is removed from the denominator and the NK removes one more, or in the case of 5-0 wagon, scum just win due to the PA guess + the TD guess).

Here are the odds of scum guessing the TD in each configuration

if we mislim on D2

, which includes their ability to POE by guessing the PA:
0L-5C: 100% (If we mislim with 5 clears it means we killed a PR so there is only 1 potential PR left for scum to guess)
1L-4C: (1/6 guess * (1/5 NK TD + (4/5 miss NK * 1/4 guess TD))) + (5/6 fail * 1/6 guess TD) = 20.5%
2L-3C: (1/5 guess * (1/4 NK TD + (3/4 miss NK * 1/3 guess TD))) + (4/5 fail * 1/5 guess TD) = 26.0%
3L-2C: (1/4 guess * (1/3 NK TD + (2/3 miss NK * 1/2 guess TD))) + (3/4 fail * 1/4 guess TD) = 35.4%
4L-1C: (1/3 guess * (1/2 NK TD + (1/2 miss NK * 1/1 guess TD))) + (2/3 fail * 1/3 guess TD) = 55.6%
5L-0C: 100% (If we mislim with 5 clears it means we killed a PR so there is only 1 potential PR left for scum to guess)

Multiply the odds of each configuration occurring by scum's chance to guess the TD and we get scum's EV in the D2 mislim scenario. Note that if we eliminate scum on D2 that they do not get to know if their PA guess was correct because we move straight to their guessing game before N2, which is when they would learn whether they guess correctly.

0L-5C: (0.03125 * 1) +
1L-4C: (0.15625 * .205) +
2L-3C: (0.3125 * .26) +
3L-2C: (0.3125 * .354) +
4L-1C: (0.15625 * .556) +
5L-0C: (0.03125 * 1) = 37.3% chance to have guessed or killed the TD by the end of D3 if we fail to eliminate scum on D1 or D2

I need to run some additional numbers on the distribution of wagons if all the townies randomly choose between all 3 products instead of between 2 - the distributions may end up being more favorable that way. I won't have time to do this until tomorrow though.

[Roden]

I'm pretty sure the breaking strategy here is to just give ourselves triple Masons

I think Kyouko's plan comes from town though

How does this plan work?

Before we vote someone out today, we should each nominate three people who we think are the towniest slots. Once we agree on a top three consensus, those three should choose Linen, and everyone else picks Copper, except Tomboy Daughter who picks Wheat if they were not nominated. What happens next is one of two options:

-Port Authority checks Linen if neither the Tomboy Daughter or themself are nominated. If we all read the nominations correctly, then we now have three conf towns who can lead Day 2. But if Tea is detected and scum somehow snuck into our consensus town reads, then we have at least a 2 in 3 shot of killing scum by the end of Day 3.

-Port Authority checks Copper if one or both of Tomboy Daughter or themself are nominated. In this case, we have to hunt through a pool of five players if we detect Tea, which we would've had to do anyway in Scenario 1.

Scenario 1 is obviously the better outcome, and I think we can do it if town just generally plays well. This also gives us twice as much data to analyze, since we can look at votes

and

nominations to find scum.

[Dunnstral]

>Leash everyone in game to 2 products
>leave the third product for the Tomboy Daughter to ship
>Town individually and randomly chooses which of the 2 leashed products to ship
>Port Authority individually and randomly chooses which of the 2 leashed products to inspect
>Expected 2.5 town per product: (10 players total -2 for PRs -2 for scum -1 for D1 elimination)/2 = 2.5
>Note that if scum are eliminated D1 we move straight to their guessing game

Scenario 1: The shipment is free of tea. 2 smugglers are off shipment amongst the other (expected) 6.5 players, and scum has a 1/3.5 chance of guessing the Tomboy Daughter if we mislim on D2 from amongst the expected 6.5.

Scenario 2: The shipment contains tea.
>1 scum on the shipment means 1/3.5 players are scum on the shipment. The odds of finding the TD for scum are still 1/3.5 here (3.5 on shipment means 5.5 off, one of which is scum and one of which may be mislimmed on D2.
>2 scum on the shipment means 2/4.5 players are scum on the shipment. The odds of finding the TD for scum are the same as in scenario 1.

I think this produces good expected results without risking revealing the TD in any way

Sure, we can do this

[SirCakez]

VOTE: kyouko bc i cannot understand 26 at all lmao

[SirCakez]

maybe i should read the setup

[Dunnstral]

Trying to get 3 town in a group likely ends up with 2 town and 1 mafia. And 1 in 3 is not very impressive odds compared to the size of the game and amount of eliminations we have to work with.

[Celebloki]

Smugglers are notoriously bad at math, 26 was clearly a ploy to confuse them.

[Roden]

Trying to get 3 town in a group likely ends up with 2 town and 1 mafia. And 1 in 3 is not very impressive odds compared to the size of the game and amount of eliminations we have to work with.

We have three days to eliminate one scum, that's typical for 10p.

[ssbm_Kyouko]

The problem is if we put a PR in top 3 it is obvious to scum, if the PA reveals the group of 5, where the PA and where the TD are. If TD is in top 3 and PA is not, PA reveals themself by flipping copper. If they're both in top 3 then that is also confirmed by flipping copper

[Dunnstral]

Your plan puts us in a possibly game losing situation if a smuggler and tomboy's daughter are both in the list of 3 people. And a tricky but less fatal situation if the port authority and tom boy's daughter are in the list of 3 people.

[Roden]

I mean, yes, that's a worst case scenario. I'm assuming the risk is minimal though, because the majority of the town have to play badly for that to happen. Maybe it's just me then but I think this player list is kinda stacked.

[Gamma Emerald]

I think kyouko’s plan might be the best idea rn, it feels pretty concrete
Anyway, now down to meat and potatoes

VOTE: SirCakez
Something about that kyouko vote bothers me. It might be that post after.

[Hu Tao]

Hi.

[Celebloki]

Ahoy, what are your opinions on tea?

[Hu Tao]

I used a binomial calculator to get these numbers on the probability of these shipment configurations occurring (only counting the town players because this is the POV that scum will have if we follow this strat):
0L-5C: 0.03125
1L-4C: 0.15625
2L-3C: 0.3125
3L-2C: 0.3125
4L-1C: 0.15625
5L-0C: 0.03125

Treat these configurations as distinct rather than collapsing them and consider the Linen to be inspected every time (in actuality this will be random, but you could reverse the L and C and the numbers are the same. Scum are guessing the PA from amongst the off-wagon players (the Copper number plus 2) and if they are correct they gain a nightkill to POE their TD guess down to the Copper Number (if they guess the PA then the PA is removed from the denominator and the NK removes one more, or in the case of 5-0 wagon, scum just win due to the PA guess + the TD guess).

Here are the odds of scum guessing the TD in each configuration

if we mislim on D2

, which includes their ability to POE by guessing the PA:
0L-5C: 100% (If we mislim with 5 clears it means we killed a PR so there is only 1 potential PR left for scum to guess)
1L-4C: (1/6 guess * (1/5 NK TD + (4/5 miss NK * 1/4 guess TD))) + (5/6 fail * 1/6 guess TD) = 20.5%
2L-3C: (1/5 guess * (1/4 NK TD + (3/4 miss NK * 1/3 guess TD))) + (4/5 fail * 1/5 guess TD) = 26.0%
3L-2C: (1/4 guess * (1/3 NK TD + (2/3 miss NK * 1/2 guess TD))) + (3/4 fail * 1/4 guess TD) = 35.4%
4L-1C: (1/3 guess * (1/2 NK TD + (1/2 miss NK * 1/1 guess TD))) + (2/3 fail * 1/3 guess TD) = 55.6%
5L-0C: 100% (If we mislim with 5 clears it means we killed a PR so there is only 1 potential PR left for scum to guess)

Multiply the odds of each configuration occurring by scum's chance to guess the TD and we get scum's EV in the D2 mislim scenario. Note that if we eliminate scum on D2 that they do not get to know if their PA guess was correct because we move straight to their guessing game before N2, which is when they would learn whether they guess correctly.

0L-5C: (0.03125 * 1) +
1L-4C: (0.15625 * .205) +
2L-3C: (0.3125 * .26) +
3L-2C: (0.3125 * .354) +
4L-1C: (0.15625 * .556) +
5L-0C: (0.03125 * 1) = 37.3% chance to have guessed or killed the TD by the end of D3 if we fail to eliminate scum on D1 or D2

I need to run some additional numbers on the distribution of wagons if all the townies randomly choose between all 3 products instead of between 2 - the distributions may end up being more favorable that way. I won't have time to do this until tomorrow though.

I didn't know I signed up for math class

[Hu Tao]

Ahoy, what are your opinions on tea?

I like tea

[HighPrincessErinys]

VOTE: kyouko bc i cannot understand 26 at all lmao

anti-town fr

[HighPrincessErinys]

This one likes it's RVS vote on Cakez now.

[Dunnstral]

I mean, yes, that's a worst case scenario. I'm assuming the risk is minimal though, because the majority of the town have to play badly for that to happen. Maybe it's just me then but I think this player list is kinda stacked.

Right... your plan is good if everything goes well, but if it doesn't go well it puts us in a bad spot.

Kyouko's plan always takes the tomboy out of the equation, so we never run into a scenario where the plan goes bad like that.

[HighPrincessErinys]

To me the main danger of the plan is just... the smugglers narrowing down the tomboy after a night or two of inspecting the copper and linen and seeing who's not showing up.

[Dunnstral]

But alternatively, with no plan they could potentially see tea being sent in a shipment they were not a part of and narrow things down that way instead

[ssbm_Kyouko]

To me the main danger of the plan is just... the smugglers narrowing down the tomboy after a night or two of inspecting the copper and linen and seeing who's not showing up.

We dont do random shipments on D2 I think. Probably we re-send the same shipments/investigation

[HighPrincessErinys]

But alternatively, with no plan they could potentially see tea being sent in a shipment they were not a part of and narrow things down that way instead

Yeah, never said the plan wasn't better because this

is

an instant game over if the tomboy is caught like that, but still.

[Gamma Emerald]

But alternatively, with no plan they could potentially see tea being sent in a shipment they were not a part of and narrow things down that way instead

Now I’m confused
What exactly are you saying here?