Mini 2320: Smuggler's Port II [Endgame]

[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.

I realized when trying to run the numbers on choosing between all 3 products, it's no longer binomial and it's been a long time since I did stats and I don't want to run all the permutations of like 0-0-5, 0-1-4, 0-2-3, 0-3-2, 0-4-1, 0-5-0, 1-0-4, 1-1-3, etc.

However, using the numbers from this post and combining with Roden's idea of triple masons and my idea of splitting the 9 living players at the end of D1 into 3 groups of 3, we can compare the 2 scenarios.

Scenario 1 [Town Random + TD Wheat]: Scum has a 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. This is not their EV because they also autowin if we fail to eliminate scum by the end of D3.

Scenario 2 [1-3Linen 4-6Copper 7-9Wheat]: This guarantees we either enter the 3-2 scenario from above, or catch scum:
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%

So scum have slightly worse odds if we just divide up the playerlist into groups of 3 and let the PA inspect one of the shipment(s) that contains neither the PA nor the TD. Furthermore, scum cannot deviate from this plan without autolosing if they should be in the shipment that the PA decides to inspect

Scenario 2a (Player is missing): If a player is missing from where they should be, they are obviously scum and can just be killed

Scenario 2b (Tea is found): if tea is found, we have a pool of 3 guaranteed to contain 1-2 scum. Let's assume it's one scum because it's easy to see that if there are 2 scum one will be found by D3. On D2 we choose which of the 3 to eliminate and before hammering we leash the surviving POEs to ship Linen and Copper (each ships one). Everyone else ships Wheat. The PA inspects either shipment (L/C) on N2 and if they find tea on a 1p shipment, that player is scum. If they don't find tea on a 1p shipment, the other player is scum. If they inspect a shipment that has 2 players for some reason, then the person that did not obey the leash is scum.

Scenario 2c (Tea is not found): We are in the 3-2 scenario from above where scum have a:

Spoiler: math

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% chance to guess the TD

In this case (2c) the D2 shipping plan maybe should be for everyone to ship wheat and for the PA to inspect either L or C

[ssbm_Kyouko]

Alive

1. Hu Tao
   
2. Roden
   
3. Dunnstral
   
4. atsi
   
5. HighPrincessErinys
   
6. SirCakez
   
7. Claptastik
   
8. Celebloki
   
9. ssbm_Kyouko
   
10. Gamma Emerald

So here's our list of 10 above. After someone dies, take me for example, re-number the list as though the dead player is gone and split the shipments as follows:

Alive after D1 elimination

1. Hu Tao
   
   
2. Roden
   
   
3. Dunnstral
   
   
4. atsi
   
   
5. HighPrincessErinys
   
   
6. SirCakez
   
   
7. Claptastik
   
   
8. Celebloki
   
   
9. Gamma Emerald

Ships Linen

Ships Copper

Ships Wheat

[ssbm_Kyouko]

We can also do it where once we think we know who we want to kill today, we can create 3 groups of 3 and then let the PA decide which to inspect independently. Creating one group of 3 just screws us over if the TD or the PA are inside.

[ssbm_Kyouko]

like create the groups and then finish hammering. And assume if there is a quickhammer or something that we go with the ordering in 76

[Gamma Emerald]

I like this

[Claptastik]

We can also do it where once we think we know who we want to kill today,

Do we:

Vote as usual? Risks hitting the TD, but possibility of hitting smuggler.

No eliminate?

A vanilla merchant takes the fall voluntarily to get us to three groups of three?

[Dunnstral]

No elimination is a bad move, I feel. Smugglers win if both are alive on day 3.

[Dunnstral]

And the PA never inspects themself or the TD

Quick note, there is no downside to the PA inspecting themselves. And the PA can reveal themselves on day 3.

[Dunnstral]

76 works for me as well

[Celebloki]

I think I like this newer plan better, it forces better odds. While the initial plan is still a longshot to out the TD, this one makes it at worst 1/3 I think. Assuming the PA inspects a shipment with no Tea, it gives the Scum a pool of 4 that the TD can be in, they can guess one as the PA and if are right they have a 1/3 to find the TD at that point. 1/4 if they don't guess the PA right. Then this plan also has the benefit of outing a Smuggler if they are on the inspected shipment or their name doesn't appear on the right shipment.

Does this seem reasonable?

[atsi]

And the PA never inspects themself or the TD

Quick note, there is no downside to the PA inspecting themselves. And the PA can reveal themselves on day 3.

If PA inspects themself, won't that just give scum a free NK?

[SirCakez]

okay i actually read now and i am fine with this plan, 3x3 seems like the optimal division
and i agree with dunn that no elim would not be a good idea

[Claptastik]

No elimination is a bad move, I feel. Smugglers win if both are alive on day 3.

They also win if we kill/expose the TD.

[Celebloki]

PA inspecting the shipment they (would be) on outs them. PA picks the set that doesn't have them or the TD in it. If they happen to be on the same shipment as the TD, they can just pick one of the other two.

[Dunnstral]

And the PA never inspects themself or the TD

Quick note, there is no downside to the PA inspecting themselves. And the PA can reveal themselves on day 3.

If PA inspects themself, won't that just give scum a free NK?

Ah, you're right. The PA doesn't ship anything so they shouldn't inspect themselves.

[Dunnstral]

No elimination is a bad move, I feel. Smugglers win if both are alive on day 3.

They also win if we kill/expose the TD.

So do you think we would have better odds of winning by killing nobody today, and relying on the investigation results from tomorrow?

[Claptastik]

No elimination is a bad move, I feel. Smugglers win if both are alive on day 3.

They also win if we kill/expose the TD.

So do you think we would have better odds of winning by killing nobody today, and relying on the investigation results from tomorrow?

I don't know. That's why I'm asking ssbm, as she's better at setup analysis than I am.

[Celebloki]

You're saying the worry is that we might end up wagoning and elimming the TD D1, so is it better to not chance that D1?

Personally I'm inclined to say we still vote someone out D1.

[atsi]

VOTE: Claptastik

[Claptastik]

You're saying the worry is that we might end up wagoning and elimming the TD D1, so is it better to not chance that D1?

Yes, that's the issue.

Considering this:

If at end of Day 3, there are at least 2 Smugglers alive, then Smugglers win.

I doubt that no-kill is a good idea, but I want to make sure it's being considered. ssbm asked mod if no-kill is allowed, so the thought may have crossed her mind as well.

[Claptastik]

VOTE: Claptastik

Feels like a low-effort policy vote.

He discussed no-kill...I have a reason to vote someone!

[Gamma Emerald]

VOTE: Claptastik

Feels like a low-effort policy vote.

He discussed no-kill...I have a reason to vote someone!

I don’t know about policy but atsi dies feel quite uninvolved

[Celebloki]

If we are going to go with Kyouko's second plan, I want a very explicit and clear post made by someone pre-hammer pointing out the shipments and who should be on them. I just know we're gonna get someone claiming to not have understood the assignment D2.

@Mod:

I assume people have to send a shipment, and the someone not sending in an action (afk) results in prods or something?

[ssbm_Kyouko]

We can also do it where once we think we know who we want to kill today,

Do we:

Vote as usual? Risks hitting the TD, but possibility of hitting smuggler.

No eliminate?

A vanilla merchant takes the fall voluntarily to get us to three groups of three?

No elimination is a bad move, I feel. Smugglers win if both are alive on day 3.

No lim is bad yeah, I was asking about it in case it helped with Scenario 1 of [Town Random + TD Wheat], and maybe it does, but scenario 2 just feels better.

I think we vote as usual for now, maybe at some point a VT steps in and volunteers to die in place of the E-1 if one of their top townreads is about to be forced to claim. I think rather than asking for claims in this game we should ask if a VT wants to take their place, because once someone has to claim, if they are a PR, they either: (fakeclaim VT and die) (trueclaim PA and scum gets a nightkill) (trueclaim TD and we lose). TD could try fakeclaiming PA I guess but so could scum.

If every VT off the wagon says fuck you to the E-1 and they're a PR we just lose but that's unavoidable.

[ssbm_Kyouko]

atsi more like A True Smuggler In disguise as a merchant
VOTE: atsi