Conditional Matrix16

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> *We must become more comfortable with probability and uncertainty.*
>
>

Semi-open where most slots are fixed, but the variant slots are all conditionally interdependent

### Town Roles

Idol Hunter, Patsy, Sleepwalker, Villager (x5), Cop/Vanilla Cop/Lazy Tracker/Templar, Medic/Bulletproof/Nurse/Alcoholic/Templar, Revenant/Phantom/Tourist/Agoraphobe

### Mafia Roles

Anarchist, Godfather, Ninja, Mafia/Jaywalker/Quack/Jekyll

### Non-Default Settings

Informed Daystart, Hide Setup, Alignment Reveal

## Description

Most of the slots for both alignments are fixed, but the presence of each role in a slot will imply that other slots are more likely. Once mafia knows which investigative role they are dealing with, then they will also know the other 2 PR slots. The symmetry within the role distributions within variants provides for both direct CCs within a slot, as well as indirect CCs across slots when combinations of role claims are not possible within a single variant.

Alignment reveal prevents town from knowing which variation is being played off of an investigative claim and mafia indicator flip.

Each of the variable PRs knows they are in a handful of possible variations (excluding Alcoholic/Tourist). The same is also true for mafia.

As with most matrix setups, all combinations of roles are not possible, so when fake claiming as either alignment, be aware that there are the possibility of less obvious "gotcha" claims. For example, Templar and Tourist are strictly incompatible claims.

## Algorithm

Direct players to this wiki page and use random.org to generate a number from 1-16. Then, expand the table below and use the setup listed for the number generated.

Alternatively:

1. Add all the base slots (roles in the image above in the blue cell on the left and red cell at the top).
2. Select a number 1-4. Add the town role(s) in the corresponding light blue cell in the row header.
3. Select a letter A-D. Add the mafia role in the corresponding light red cell in the column header.
4. Add the role(s) in the intersection of the selected row and column.

## Optimal play

### Town

Town needs to balance figuring out the setup via claims and PR impact. If an investigative takes too long to claim, then they might die without giving notes. If they claim too early, there might not actually be a protective to save them.

#### Idol Hunter

A base PR common to all variants. While traditionally an Innocent Child role, alignment reveal plus the delayed, limited nature of its power means that claiming the slot alone is not typically enough to self-confirm (outside of day 1 claims).

Anarchist may interfere with your ability to hand out items to confirm yourself, or it might just be granted to a mafia that denies that they were given an item in the first place as an indirect counterclaim.

#### N Slot: Investigative

Protectives are equally from the perspective of investigatives, but the wildcard slot likelihood is affected the investigative slot. In general one wildcard is not possible for each investigative, and another is twice as likely.

##### Cop

Indicates the **1 Row** of variants. The wildcard slot has:

* 50% chance of Revenant
* 25% chance of Agoraphobe
* 25% chance of Tourist
	+ Tourists always come in pairs.

##### Vanilla Cop

Indicates the **2 Row** of variants. The wildcard slot has:

* 75% chance of Tourist/Alcoholic
	+ There is only one Tourist claim possible.
* 25% chance of Phantom
* 25% chance of Revenant

Generally functions as a Neapolitan (hard clearing vanilla results) except when in **2A**, which has no Tourist claims.

##### Lazy Tracker

Indicates the **3 Row** of variants. The wildcard slot has:

* 50% chance of Phantom
* 25% chance of Agoraphobe
* 25% chance of Tourist
	+ Tourists always come in pairs.

##### Templar

Indicates the **4 Row** of variants. The wildcard slot has:

* 50% chance of Agoraphobe
* 25% chance of Phantom
* 25% chance of Revenant
* 0% chance of Tourist/Alcoholic

As Templars come in pairs, they occupy both the investigative and protective slots. Softing is necessary for town to fully believe your claim in case your partner is night killed.

#### L Slot: Protective

Each protective slot (with the exception of Alcoholic), only occurs in two columns in the setup, but does necessitate the presence of an investigative when Templars aren't involved. Mafia are aware of the likelihood of specific protective roles, and thus you can leverage that perception to your advantage.

##### Medic

Occurs in **1A**, **2A**, and **3B**. Which means:

* 66% of the time mafia will correctly anticipate Medic
* 33% of the time mafia will erroneously anticipate Bulletproof
* 0% chance of Tourist

##### Bulletproof

Occurs in **1B**, **2B**, and **3C**. Which means:

* 66% of the time mafia will correctly anticipate Bulletproof
* 33% of the time mafia will erroneously anticipate Nurse
* 0% chance of Agoraphobe

##### Nurse

Occurs in **1C**, **2C**, and **3D**. Which means:

* 66% of the time mafia will correctly anticipate Medic
* 33% of the time mafia will erroneously anticipate Bulletproof
* 0% chance of Revenant

#### R Slot: Wildcard

Each wildcard slot (with the exception of Tourist), has 1 investigative that does not appear in any variations, and 1 investigative that is twice as likely to occur. This is also generally the town slot that is also the **most informed** about the setup possibilities and implications. Surviving until mid-game will reap huge information benefits, and possibly even catch out scum with an incompatible claim.

##### Revenant

Occurs in **1A**, **1B**, **2D**, and **4C**. Which means:

* 50% chance of Cop
* 0% chance of Lazy Tracker
* 0% chance of Nurse
* 0% chance of Tourist
	+ Thus Tourist and Alcoholic claims are equivalent.

##### Phantom

Occurs in **2A**, **3C**, **3D**, and **4B**. Which means:

* 50% chance of Lazy Tracker
* 0% chance of Cop
* 0% chance of Tourist or Alcoholic
	+ Tourist claims are either baiting town or scum. Feel free to pick them as a target if you believe the latter.

##### Tourist

If you see yourself as Tourist, you are either Tourist or Alcoholic and in **1D**, **2B**, **2C**, **2D**, or **3A** (but not equally likely). With alignment reveal, town will be unable to determine whether you are Alcoholic or Tourist based on your death alone.

Always target with the intent to roleblock as if you are Alcoholic, but be aware you may falsely clear mafia from a Lazy Tracker investigation.

Most of the time town will be playing without a proper protective so you cannot rely on someone else to prevent mafia from night killing you. In exchange, you might end up being Alcoholic that can clutch out against last mafia, making Tourist/Alcoholic notes very valuable.

For the investigative slot this means:

* 28% chance of Cop
* 43% chance of Vanilla Cop
	+ It's worth noting that Mafia only occurs in **2A** which is not possible, thus Vanilla Cop functions as a Neapolitan (fully clears vanilla results).
* 28% chance of Lazy Tracker
* 0% chance of Templar

For the protective slot this means:

* **57%** chance there is another slot that sees themselves as Tourist, and thus no proper protective role (or wildcard role).
* 14% chance of Bulletproof
	+ Decreased to 0% if you are Alcoholic
* 14% chance of Nurse
	+ Decreased to 0% if you are Alcoholic

For the wildcard slot this means:

* 14% chance of Revenant
	+ Decreased to 0% if you are **not** Alcoholic
	+ Increased to 33% if you are Alcoholic
* 0% chance of Phantom
* 0% chance of Agoraphobe

##### Agoraphobe

Occurs in **1C**, **3B**, **4A**, and **4D**. Which means:

* 50% chance of Templar
* 0% chance of Vanilla Cop
* 0% chance of Bulletproof
* 0% chance of Tourist or Alcoholic

#### Villager/Patsy/Sleepwalker

Standard gameplay. Be aware you could be Patsy or Sleepwalker and investigate unfavorably to most of the investigative roles.

Villager fake claims are inherently going to be less valuable due to the possibility mafia knows you are fake claiming Patsy, on top of alignment reveal hiding your real role if you do get night killed.

### Mafia

Pay attention to which mafia is in the in the indicator slot. This helps to inform mafia of which roles are possible and more likely in the protective slot. Each of the indicators has a respective protective role that is twice as likely in the slot.

Mafia powers are generally on the weaker side given that mafia will have more knowledge about the setup than town generally, as well as being able to take advantage of town's potentially lost information due alignment reveal. Mafia needs to use their information advantage to manipulate days in their favor.

Consider coordinating fake claims so that a mid-/late-game mass claim does not immediately out mafia due to an incompatible claim.

There are 4 general claim strategies:

* Claim within the known column to be more consistent with town claims.
* Claim outside of the known column to confuse town.
* Claim Templar (possibly with dead partner) to force both an investigative and protective counterclaim.
* Delay claiming a protective in case of Templar's indirect counterclaim.

Read about a slot's section in this wiki page for more perspective on how a role sees the game and should behave in order to better understand and sell your fake claims. Understanding that that town PR slots will view the game in drastically different ways may also help you figure out PRs based on how they react to and share information.

#### Anarchist

Only active PR of the mafia team.

Use the rolecop action on the first night to try and gain more information about the setup.

The item-related actions can be used to interfere with Bulletproof and Idol Hunter.

The roleblock action can be used to support a Nurse or Alcoholic fake claim, or to just neutralize a town PR.

#### Ninja

Serves as a false negative against Lazy Tracker.

#### Z Slot: Indicator

The role in this slot serves to indicate to mafia which of of the four possible variants they are in. Due to Alignment Reveal, this information will not be known to town.

##### Mafia

Indicates the **A Column** of variants. The protective slot has:

* 50% chance of Medic
* 25% chance of Alcoholic
* 25% chance of Templar

Unlike the other options for this slot, this interacts *specifically* with Vanilla Cop in **2A**, but that is at least excusable as **2A** is the most town-sided out of the **2 Row** variants. Ideally, there could be some other role in this slot that doesn't interact meaningfully with the rest of the setup, but such a role does not exist at time of writing.

##### Jaywalker

Indicates the **B Column** of variants. The protective slot has:

* 50% chance of Bulletproof
* 25% chance of Medic
* 25% chance of Templar

##### Quack

Indicates the **C Column** of variants. The protective slot has:

* 50% chance of Nurse
* 25% chance of Bulletproof
* 25% chance of Templar

##### Jekyll

Indicates the **D Column** of variants. The protective slot has:

* 50% chance of Alcoholic
* 25% chance of Nurse
* 25% chance of Templar

## Trivia

The setup is named after the 4x4 matrix of possibilities, not the number of slots in the setup.

The setup is designed as an exercise in conditional probability.

The slots are named as such:

* N: **N**umber of the row
* L: **L**eft side of the supercell
* R: **R**ight side of the supercell
* Z: Alphabet of the column, but **Z** is chosen as a letter related to the alphabet