The EV Project: Difference between revisions

Revision as of 07:15, 13 July 2020

Purpose

The goal of the EV project is to establish a table of expected probabilities for a given faction winning a given Open game. Unlike "traditional" analyses, the philosophy behind the actions here (eventually) is intended to be more realistic and focus on players trying to optimize their chances, even though eliminations and kills are still realistically random.

These probabilities are calculated by attempting to reduce games to basic scenarios that have already had their probabilities found. Thus, this guide starts small and builds itself up to larger games. Even games such as Basic Twelve Player, with a breaking strategy, are tedious and time-consuming to analyze without a basis for calculations. (Ask me how I know.)

All of these are assumed to be Day Start unless otherwise specified, unlike pages like Numbers, Part 1.

Selected Results

These are some results from the table that are highlighted for easy reading. If the result you are looking for is not here, but you think it may be, consider the table of contents.

10:2 Mountainous, supposedly a "fair" setup, has an expected Town win rate of 244/693, or 35.2%.
- Changing the setup to 11:2 Mountainous increases the expected Town win rate to 1186/3003, or 39.5%.
The Open Setup Polygamist has an expected Town win rate of 3/5, or 60.0%.
- A smaller 6:2 version of Polygamist has an expected Town win rate of 1/2, or 50.0%.
The Open Setup Lovers Mafia has an expected Town win rate of 3/5, or 60.0%.
- However, any modifications to the setup that do not start in LyLo are even more Town-favored.
The Open Setup White Flag has an expected Town win rate of 1436/3003, or 47.8%.
- The number of additional players to make four scum work in this format is not known, but considerably higher.
The Nightless Expectation Rule, which states that balanced Nightless games are comprised of 1/4 scum.
The True Love Expectation Rule, which states that True Love-style games are balanced when scum comprise 1/4 of the players (controlling 1/2 of the pairs).
That Even/ Odd C9 has an expected Town win rate of 547/1680, or 32.6%.
The Open Setup SCIENCE! has an expected Town win rate of 781/2100, or 37.2%.

Mountainous Setups

Premise: At even numbers, Town is assumed to No Eliminate to raise their elimination accuracy. With no power roles, this is a dominant strategy. In practice, this is not a good idea, as the scum will kill off the strongest Townie. However, if there IS a strongest Townie, then why not just choose not to eliminate them and continue as if it were the odd-numbered setup?

3P: 2 - 1

(1/3) 33.3% Town win
(2/3) 66.7% Scum win

5P: 4 - 1

(1/5) 20.0% Town win
(4/5) 80.0% GOTO 3P: 2 - 1 (1/3 Town win)

(1/5 + 4/15 = 7/15) 46.7% Town win
(8/15) 53.3% Scum win

5P: 3 - 2

(2/5) 40.0% GOTO 3P: 2 - 1 (1/3 Town win)
(3/5) 60.0% Scum win

(2/5*1/3 = 2/15) 13.3% Town win
(13/15) = 86.7% Scum win

7P: 6 - 1

(1/7) 14.3% Town win
(6/7) 85.7% GOTO 5P: 4 - 1 (7/15 Town win)

(1/7 + 6/7*7/15 = 19/35) 54.3% Town win
(16/35) 47.7% Scum win

7P: 5 - 2

(2/7) 28.6% GOTO 5P: 4 - 1 (7/15 Town win)
(5/7) 71.4% GOTO 5P: 3 - 2 (2/15 Town win)

(2/7*7/15 + 5/7*2/15 = 8/35) 22.9% Town win
(27/35) 77.1% Scum win

7P: 4 - 3

(3/7) 42.9% GOTO 5P: 3 - 2 (2/15 Town win)
(4/7) Scum win

(3/7*2/15 = 2/35) 5.7% Town win
(33/35) 94.3% Scum win

9P: 8 - 1

(1/9) 11.1% Town win
(8/9) 88.9% GOTO 7P: 6 - 1 (19/35 Town win)

(1/9 + 8/9*19/35 = 187/315) 59.4% Town win
(128/315) 40.6% Scum win

9P 7 - 2

(2/9) 22.2% GOTO 7P: 6 - 1 (19/35 Town win)
(7/9) 77.8% GOTO 7P: 5 - 2 (8/35 Town win)

(2/9*19/35 + 7/9*8/35 = 94/315) 29.8% Town win
(221/315) 70.2% Scum win

9P 6 - 3

(3/9) 33.3% GOTO 7P: 5 - 2 (8/35 Town win)
(6/9) 66.7% GOTO 7P: 4 - 3 (2/35 Town win)

(3/9*8/35 + 6/9*2/35 = 4/35) 11.4% Town win
(31/35) 88.6% Scum win

9P 5 - 4

(4/9) 44.4% GOTO 7P: 4 - 3 (2/35 Town win)
(5/9) 55.6% Scum win

(4/9*2/35 = 8/315) 2.5% Town win
(307/315) 97.5% Scum win

11P 10 - 1

(1/11) 9.1% Town win
(10/11) 90.9% GOTO 9P: 8 - 1 (187/315 Town win)

(1/11 + 10/11*187/315 = 437/695) 63.0% Town win
(256/693) 37.0% Scum win

11P 9 - 2

(2/11) 18.2% GOTO 9P: 8 - 1 (187/315 Town win)
(9/11) 81.8% GOTO 9P: 7 - 2 (94/315 Town win)

(2/11*187/315 + 9/11*94/315 = 244/693) 35.2% Town win
(447/693) 64.8% Scum win

11P 8 - 3

(3/11) 27.3% GOTO 9P: 7 - 2 (94/315 Town win)
(8/11) 72.7% GOTO 9P: 6 - 3 (4/35 Town win)

(3/11*94/315 + 8/11*4/35 = 38/231) 16.4% Town win
(193/231) 83.5% Scum win

11P 7 - 4

(4/11) 36.4% GOTO 9P 6 - 3 (4/35 Town win)
(7/11) 63.6% GOTO 9P 5 - 4 (8/315 Town win)

(4/11*4/35 + 7/11*8/315 = 40/693) 5.8% Town win
(653/693) 94.2% Scum win

13P 11 - 2

(2/13) 15.4% GOTO 11P 10 - 1 (367/693 Town win)
(11/13) 84.6% GOTO 11P 9 - 2 (230/693 Town win)

(2/13*437/693 + 11/13*244/693 = 1186/3003) 39.5% Town win
(1817/3003) 60.5% Scum win

13P 10 - 3

(3/13) 23.1% GOTO 11P 9 - 2 (244/693 Town win)
(10/13) 76.9% GOTO 11P 8 - 3 (38/231 Town win)

(3/13*244/693 + 10/13*38/231 = 16/77) 20.8% Town win
(61/77) 79.2% Scum win

Plus Innocent

Premise: There is one confirmed innocent in the player list. This player cannot be eliminated, but will be killed during the next Night. No Elimination is not acceptable in this case, as the scum will simply kill off the confirmed Townie and there will be no improvement.

3P 2 - 1

(1/2) 50.0% Town win
(1/2) 50.0% Scum win

4P 3 - 1

(1/3) 33.3% Town win
(2/3) 66.7% Town will be eliminated; Town loses.

5P 4 - 1

(1/4) 25.0% Town win
(3/4) 75.0% Town will be eliminated. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)

(1/4 + 3/4*1/3 = 1/2) 50.0% Town win
(1/2) 50.0% Scum win

5P 3 - 2

(2/4) 50.0% GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(2/4) 50.0% Scum win

(2/4*1/3 = 1/6) 16.7% Town win
(5/6) 83.3% Scum win

6P 5 - 1

(1/5) 20.0% Town win
(4/5) 80.0% Town will be eliminated. No Elimination follows. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)

(1/5 + 4/5*1/3 = 7/15) 46.7% Town win
(8/15) 53.3% Scum win

6P 4 - 2

(2/5) 40.0% GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5) 60.0% Scum win

(2/5*1/3 = 2/15) 13.3% Town win
(13/15) 86.7% Scum win

7P 6 - 1

(1/6) 16.7% Town win
(5/6) 83.3% Town will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)

(1/6 + 5/6*7/15 = 5/9) 55.6% Town win
(4/9) 44.4% Scum win

7P 5 - 2

(2/6) 33.3% Scum will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(4/6) 66.7% Town will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)

(2/6*7/15 + 4/6*2/15 = 11/45) 24.4% Town win
(34/45) 75.6% Scum win

7P 4 - 3

(3/6) 50.0% GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(3/6) 50.0% Scum win

(3/6*2/15 = 1/15) 6.7% Town win
(14/15) 93.3% Scum win

8P 7 - 1

(1/7) 14.3% Town win
(6/7) 85.7% Town elimination, No Elimination; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)

(1/7 + 6/7*7/15 = 19/35) 54.3% Town win
(16/35) 45.7% Scum win

8P 6 - 2

(2/7) 28.6% Scum elimination; No Elimination; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(5/7) 71.4% Town elimination; No Elimination; GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)

(2/7*7/15 + 5/7*2/15 = 8/35) 22.8% Town win
(27/35) 77.1% Scum win

8P 5 - 3

(3/7) 42.9% Scum elimination; No Elimination; GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(4/7) 57.1% Scum win

(3/7*2/15 = 2/35) 5.7% Town win
(33/35) 94.3% Scum win

9P 8 - 1

(1/8) 12.5% Town win
(7/8) 87.5% Town elimination; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)

(1/8 + 7/8*19/35 = 3/5) 60.0% Town win
(2/5) 40.0% Scum win

9P 7 - 2

(2/8) 25.0% Scum will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(6/8) 75.0% Town will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)

(2/8*19/35 + 6/8*8/35 = 43/140) 30.7% Town win
(97/140) 69.3% Scum win

9P 6 - 3

(3/8) 37.5% Scum will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(5/8) 62.5% Town will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)

(3/8*8/35 + 5/8*2/35 = 17/140) 12.1% Town win
(123/140) 87.8% Scum win

9P 5 - 4

(4/8) 50.0% Scum elimination; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)
(4/8) 50.0% Scum win

(4/8*2/35 = 1/35) 2.8% Town win
(34/35) 97.1% Scum win

10P 9 - 1

(1/9) 11.1% Town win
(8/9) Town elimination; No Elimination; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)

(1/9 + 8/9*19/35 = 187/315) 59.4% Town win
(128/315) 40.6% Scum win

10P 8 - 2

(2/9) 22.2% Scum elimination; No Elimination; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(7/9) 77.8% Town elimination; No Elimination; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)

(2/9*19/35 + 7/9*8/35 = 94/315) 29.8% Town win
(221/315) 70.2% Scum win

10P 7 - 3

(3/9) 33.3% Scum elimination; No Elimination; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(6/9) 66.7% Town elimination; No Elimination; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)

(3/9*8/35 + 6/9*2/35 = 4/35) 11.4% Town win
(31/35) 88.6% Scum win

10P 6 - 4

(4/9) 44.4% Scum elimination; No Elimination; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)
(5/9) 55.6% Scum win

(4/9*2/35 = 8/315) 2.5% Town win
(307/315) 97.5% Scum win

11P 10 - 1

(1/10) 10.0% Town win
(9/10) 90.0% Town elimination; GOTO ~Mountainous~ 9P 8 - 1 (187/315 Town win)

(1/10 + 9/10*187/315 = 111/175) 63.4% Town win
(64/175) 36.6% Scum win

11P 9 - 2

(2/10) 20.0% Scum elimination; GOTO ~Mountainous~ 8 - 1 (187/315 Town win)
(8/10) 80.0% Town elimination; GOTO ~Mountainous~ 7 - 2 (94/315 Town win)

(2/10*187/315 + 8/10*94/315 = 563/1575) 35.7% Town win
(1012/1575) 64.2% Scum win

11P 8 - 3

(3/10) 30.0% Scum will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 9P 7 - 2 (94/315 Town win)
(7/10) 70.0% Town will be eliminated. ConfTown will die overNight. GOTO ~Mountainous~ 9P 6 - 3 (4/35 Town win)

(3/10*94/315 + 7/10*4/35 = 89/525) 16.9% Town win
(436/525) 83.9% Scum win

11P 7 - 4

(4/10) 40.0% Scum elimination; GOTO ~Mountainous~ 9P 6 - 3 (4/35 Town win)
(6/10) 60.0% Town elimination; GOTO ~Mountainous~ 9P 5 - 4 (8/315 Town win)

(4/10*4/35 + 6/10*8/315 = 32/525) 6.1% Town win
(493/525) 93.9% Scum win

Plus 2xInnocent

Premise: There are two confirmed innocents in the player list. These players cannot be eliminated, but will be killed during the Night as soon as possible.

5P 4 - 1

(1/3) 33.3% Town win
(2/3) 66.7% Town will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)

(1/3 + 2/3*1/2 = 2/3) 66.7% Town win
(1/3) 33.3% Scum win

5P 3 - 2

(2/3) 66.7% Scum gets eliminated; GOTO ~Plus Innocent~ 2 - 1 (1/2 Town win)
(1/3) 33.3% Scum win

(2/3*1/2 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

6P 5 - 1

(1/4) 25.0% Town win
(3/4) 75.0% Town will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 4P 3 - 1 (1/3 Town win)

(1/4 + 3/4*1/3 = 1/2) 50.0% Town win
(1/2) 50.0% Scum win

7P 6 - 1

(1/5) 20.0% Town win
(4/5) 80.0% Town will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)

(1/5+4/5*1/2 = 3/5) 60.0% Town win
(2/5) 40.0% Scum win

7P 5 - 2

(2/5) Scum elimination; ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(3/5) Town elimination; ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)

(2/5*1/2 + 3/5*1/6 = 3/10) 30% Town win
(7/10) 70% Scum win

9P 7 - 2

(2/7) 28.6% Scum will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 7P 6 - 1 (5/9 Town win)
(5/7) 71.4% Town will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 7P 5 - 2 (11/45 Town win)

(2/7*5/9 + 5/7*11/45 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

11P 8 - 3

(3/9) 33.3% Scum will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 9P 7 - 2.
(6/9) 66.7% Town will be eliminated. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 9P 6 - 3.

(3/9*43/140 + 6/9*17/140 = 11/60) 18.3% Town win
(49/60) 81.7% Scum win

Nightless

Premise: The scum do not have a night-kill. They win when they equal the Town's numbers.
Refer to the Nightless Expectation Rule for these probabilities when Mountainous.

Multiball

Premise: There are multiple scum groups. Scum will not kill members of their own group. Kill-immunity is not considered.
Premise: Scum cannot automatically win without killing off all other members of the scum team.
Premise: Depending on the moderator, if only an even number of scum are alive, either both teams will win or they will draw. Here, it is considered a draw.
Premise: It is generally advantageous for Town to No Elimination until only one scumgroup remains. This is NOT taken into account (yet) in probability calculations. Otherwise, this will affect all probabilities from 7P on up.

2P 0 - 1 - 1

Premise: This is a draw.

3P 1 - 1 - 1

Premise: This is a Dilemma. This is assumed to be a Draw.

However, if none of the scum are known and the game goes to No Elimination, then: (1/4) Town win
(1/4) Scum A win
(1/4) Scum B win
(1/4) Draw

4P 2 - 1 - 1

Premise: This is also a Dilemma. Town is assumed to win 100% of the time here.

4P 1 - 2 - 1

Premise: Since these games are Open, it is assumed that the number of players alive in each faction will always be known. Thus, since Scum A has veto power over any elimination that would harm them and both other factions are doomed if they elimination, all players No Elimination and the game goes to Night (2/3 Scum A win; 1/3 Draw).

4P 2 - 1 - 1 (Night)

(1/3*1/3 = 1/9) 11.1% Scum A and Scum B crosskill. Town win.
(1/3*2/3 = 2/9) 22.2% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(2/3*1/3 = 2/9) 22.2% As above, but swap scum. 1/3 Town win.
(2/3*1/3 = 2/9) 22.2% Scum A and Scum B kill same Townie. GOTO 3P 1 - 1 - 1 (Draw)
(2/3*1/3 = 2/9) 22.2% Scum A and Scum B kill different Townies. GOTO 2P 0 - 1 - 1 (Draw)

(1/9 + 2/9 + 2*2/9*1/3 = 7/27) 25.9% Town win
(2/9*2/3 = 4/27) 14.8% Scum A win
(2/9*2/3 = 4/27) 14.8% Scum B win
(2*2/9 = 4/9) 44.4% Draw between Scum A and Scum B

4P 1 - 2 - 1 (Night)

(1/2*1/3 = 1/6) 16.7% Scum A and Scum B both target Townie. Scum A win.
(1/2*2/3 = 1/3) 33.3% Scum A targets Townie; Scum B targets Scum A. GOTO 2P 0 - 1 - 1 (Draw)
(1/2*1/3 = 1/6) 16.7% Scum A targets Scum B; Scum B targets Townie. Scum A win.
(1/2*2/3 = 1/3) 33.3% Scum A targets Scum B; Scum B targets Scum A. Scum A win.

(1/6 + 1/6 + 1/3 = 2/3) 66.7% Scum A win
(1/3) Draw

5P 3 - 1 - 1

(1/5) 20.0% Scum A eliminated. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/5) 20.0% Scum B eliminated. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5) 60.0% Town eliminated. GOTO 4P 2 - 1 - 1 (Night) (7/27 Town win; 4/27 either Scum win; 4/9 Draw)

(2*1/5*1/3 + 3/5*7/27 = 13/45) 28.9% Town win
(1/5*2/3 + 3/5*4/27 = 2/9) 22.2% Scum A win
(2/9) 22.2% Scum B win
(3/5*4/9 = 4/15) 26.6% Draw between Scum A and Scum B

5P 2 - 2 - 1

(2/5) 40.0% Scum A eliminated. GOTO 4P 2 - 1 - 1 (Night) (7/27 Town win; 4/27 either Scum win; 4/9 Draw)
(1/5) 20.0% Scum B eliminated. Scum A win.
(2/5) 40.0% Town eliminated. GOTO 4P 1 - 2 - 1 (Night) (2/3 Scum A win; 1/3 Draw)

(2/5*7/27 = 14/135) 10.4% Town win
(2/5*4/27 + 1/5 + 2/5*2/3 = 71/135) 52.6% Scum A win
(2/5*4/27 = 8/135) 5.9% Scum B win
(2/5*4/9 + 2/5*1/3 = 14/45) 31.1% Draw

5P 1 - 2 - 2

Premise: This is a Dilemma. The scum Draw by collaboratively eliminationing the Townie.

5P 1 - 3 - 1

This is a guaranteed Scum A win.

5P 3 - 1 - 1 (Night)

(1/4*1/4 = 1/16) 6.2% Scum A and Scum B crosskill each other. Town win.
(1/4*3/4 = 3/16) 18.8% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/4*1/4 = 3/16) 18.8% As above, but swap scum. 1/3 Town win.
(3/4*1/4 = 3/16) 18.8% Scum A and Scum B kill same Townie. GOTO 4P 2 - 1 - 1 (Town win)
(3/4*2/4 = 3/8) 37.5% Scum A and Scum B kill different Townies. GOTO 3P 1 - 1 - 1 (Draw)

(1/16 + 2*3/16*1/3 + 3/16 = 3/8) 37.5% Town win
(3/16*1/3 = 1/8) 12.5% Scum A win
(1/8) 12.5% Scum B win (3/8) 37.5% Draw

5P 2 - 2 - 1 (Night)

(1/3*2/4 = 1/6) 16.7% Scum A kills Scum B; Scum B kills Scum A. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win; 2/3 Scum A win)
(1/3*2/4 = 1/6) 16.7% Scum A kills Scum B; Scum B kills Town. Scum A win.
(2/3*2/4 = 1/3) 33.3% Scum A kills Town; Scum B kills Scum A. GOTO 3P 1 - 1 - 1 (Draw).
(2/3*1/4 = 1/6) 16.7% Scum A and Scum B kill same Townie. GOTO 4P 1 - 2 - 1 (2/3 Scum A win; 1/3 Draw).
(2/3*1/4 = 1/6) 16.7% Scum A and Scum B kill different Townies. Scum A win.

(1/6*1/3 = 1/18) 5.6% Town win
(1/6*2/3 + 1/6 + 1/6*2/3 + 1/6 = 5/9) 55.6% Scum A win
(1/6*1/3 + 1/3 = 7/18) 38.9% Draw

Note that in this situation, Scum B is playing exclusively for the Draw unless the identities of the scum are not revealed during the last Day.

5P 1 - 2 - 2 (Night)

(2/3*2/3 = 4/9) 44.4% Scum A and Scum B crosskill. GOTO 3P 1 - 1 - 1 (Draw)
(2/3*1/3 = 2/9) 22.2% Scum A kills Scum B; Scum B kills Townie. Scum A win.
(1/3*2/3 = 2/9) 22.2% As above, but reverse scum. Scum B win.
(1/3*1/3 = 1/9) 11.1% Scum A and Scum B kill Townie. Draw.

(2/9) 22.2% Scum A win
(2/9) 22.2% Scum B win
(4/9+1/9) 55.6% Draw

6P 4 - 1 - 1

(1/6) 16.7% Scum A eliminated. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/6) 16.7% Scum B eliminated; 1/3 Town win.
(4/6) 66.7% Town eliminated; GOTO 5P 3 - 1 - 1 (Night) (3/8 Town win; 1/8 either scum win; 3/8 Draw)

(2*1/6*1/3 + 2/3*3/8 = 13/36) 36.1% Town win
(1/6*2/3 + 2/3*1/8 = 7/36) 19.4% Scum A win
(7/36) 19.4% Scum B win (2/3*3/8 = 1/4) 25.0% Draw

6P 3 - 2 - 1

(2/6) 33.3% Scum A eliminated. GOTO 5P 3 - 1 - 1 (Night). (3/8 Town win; 1/8 either scum win; 3/8 Draw)
(1/6) 16.7% Scum B eliminated. Scum A win.
(3/6) 50.0% Town eliminated. GOTO 5P 2 - 2 - 1 (Night). (1/18 Town win; 5/9 Scum A win; 7/18 Draw)

(2/6*3/8 + 1/2*1/18 = 11/72) 15.3% Town win
(2/6*1/8 + 1/6 + 3/6*5/9 = 35/72) 48.6% Scum A win
(2/6*1/8 = 1/24) 4.2% Scum B win
(2/6*3/8 + 3/6*7/18 = 23/72) 31.9% Draw

6P 2 - 3 - 1

Premise: This Day will end in No Elimination. GOTO 6P 2 - 3 - 1 (Night).

6P 2 - 2 - 2

(2/6) 33.3% Scum A eliminated. GOTO 5P 2 - 2 - 1 (1/18 Town win; 5/9 Scum B win; 7/18 Draw)
(2/6) 33.3% Scum B eliminated. As above, but with reversed scum.
(2/6) 33.3% Townie eliminated. GOTO 5P 1 - 2 - 2 (Draw)

(2*1/3*1/18 = 1/27) 3.7% Town win
(1/3*5/9 = 5/27) 18.5% Scum A win
(1/3*5/9 = 5/27) 18.5% Scum B win
(2*1/3*7/18 + 1/3 = 16/27) 59.2% Draw

6P 4 - 1 - 1 (Night)

(1/5*1/5 = 1/25) 4.0% Scum A and Scum B crosskill; Town win.
(1/5*4/5 = 4/25) 16.0% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win; 2/3 Scum A win)
(4/5*1/5 = 4/25) 16.0% As above, but swap scum. (1/3 Town win; 2/3 Scum B win)
(4/5*1/5 = 4/25) 16.0% Scum A and Scum B kill same Townie. GOTO 5P 3 - 1 - 1 (13/45 Town win; 2/9 either scum win; 4/15 Draw)
(4/5*3/5 = 12/25) 48.0% Scum A and Scum B kill different Townies. GOTO 4P 2 - 1 - 1 (Town win)

(1/25 + 2*4/25*1/3 + 4/25*13/45 + 12/25 = 757/1125) 67.3% Town win
(4/25*2/3 + 4/25*2/9 = 32/225) 14.2% Scum A win
(32/225) 14.2% Scum B win
(4/25*4/15 = 16/375) 4.3% Draw

6P 3 - 2 - 1 (Night)

(1/4*2/5 = 1/10) 10.0% Scum A and Scum B crosskill; GOTO ~Mountainous~ 2 - 1 (1/3 Town win; 2/3 Scum A win)
(1/4*3/5 = 3/20) 15.0% Scum A kills Scum B; Scum B kills Townie. Scum A win.
(3/4*2/5 = 3/10) 30.0% Scum A kills Townie; Scum B kills Scum A. GOTO 4P 2 - 1 - 1 (Town win)
(3/4*1/5 = 3/20) 15.0% Scum A and Scum B kill same Townie. GOTO 5P 2 - 2 - 1 (14/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 14/45 Draw)
(3/4*2/5 = 3/10) 30.0% Scum A and Scum B kill different Townies. GOTO 4P 1 - 2 - 1 (2/3 Scum A win; 1/3 Draw)

(1/10*1/3 + 3/10 + 3/20*14/135 = 157/450) 34.9% Town win
(1/10*2/3 + 3/20 + 3/20*71/135 + 3/10*2/3 = 223/450) 49.6% Scum A win
(3/20*8/135 = 2/225) 0.9% Scum B win
(3/20*14/45 + 3/10*1/3 = 11/75) 14.7% Draw

6P 2 - 3 - 1 (Night)

(1/3) 33.3% Scum A kills Scum B overNight; Scum B's kill is irrelevant. Scum A win.
(2/3*3/5 = 2/5) 40.0% Scum A kills a Townie; Scum B kills Scum A. GOTO 4P 1 - 2 - 1 (2/3 Scum A win; 1/3 Draw)
(2/3*1/5 = 2/15) 13.3% Scum A and Scum B kill same Townie. Scum A win.
(2/3*1/5 = 2/15) 13.3% Scum A and Scum B kill different Townies. Scum A win.

(1/3 + 2/5*2/3 + 2*2/15 = 13/15) 86.7% Scum A win
(2/15) Draw

6P 2 - 2 - 2 (Night)

(2/4*2/4 = 1/4) 25.0% Scum A and Scum B crosskill. GOTO 4P 2 - 1 - 1 (Town win) (2/4*2/4 = 1/4) 25.0% Scum A kills Scum B; Scum B kills Townie. GOTO 4P 1 - 2 - 1 (2/3 Scum A win; 1/3 Draw)
(2/4*2/4 = 1/4) 25.0% As above, but with reversed scum.
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill same Townie. GOTO 5P 1 - 2 - 2 (Draw)
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill different Townies. Draw.

(1/4) 25.0% Town win
(1/4*2/3 = 1/6) 16.7% Scum A win
(1/4*2/3 = 1/6) 16.7% Scum B win
(2*1/4*1/3 + 2*1/8 = 5/12) 41.7% Draw

7P 5 - 1 - 1

(1/7) 14.3% Scum A elimination; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)
(1/7) 14.3% Scum B elimination; same as above (7/15 Town win; 8/15 Scum A win)
(5/7) 71.4% Town elimination; GOTO 6P 4 - 1 - 1 (Night). (757/1125 Town win; 32/225 either scum win; 16/375 Draw)

(2*1/7*7/15 + 5/7*757/1125 = 967/1575) 61.3% Town win
(1/7*8/15 + 5/7*32/225 = 8/45) 17.8% Scum A win
(8/45) 17.8% Scum B win
(5/7*16/375 = 16/525) 3.0% Draw

7P 4 - 2 - 1

(2/7) 28.6% Scum A elimination; GOTO 6P 4 - 1 - 1 (Night) (757/1125 Town win; 32/225 either scum win; 16/375 Draw)
(1/7) 14.3% Scum B elimination; GOTO ~Mountainous~ 3 - 2 (2/15 Town win; 13/15 Scum A win)
(4/7) 57.1% Town elimination; GOTO 6P 3 - 2 - 1 (Night) (157/450 Town win; 223/450 Scum A win; 2/225 Scum B win; 11/75 Draw)

(2/7*757/1125 + 1/7*2/15 + 4/7*157/450 = 154/375) 41.1% Town win
(2/7*32/225 + 1/7*13/15 + 4/7*223/450 = 47/105) 44.8% Scum A win
(2/7*32/225 + 4/7*2/225 = 8/175) 4.6% Scum B win
(2/7*16/375 + 4/7*11/75 = 12/125) 9.6% Draw

7P 3 - 3 - 1

(3/7) 42.8% Scum A elimination; GOTO 6P 3 - 2 - 1 (Night) (157/450 Town win; 223/450 Scum A win; 2/225 Scum B win; 11/75 Draw)
(1/7) 14.3% Scum B elimination. Scum A win.
(3/7) 42.8% Town elimination; GOTO 6P 2 - 3 - 1 (Night) (13/15 Scum A win; 2/15 Draw)

(3/7*157/450 = 157/1050) 15.0% Town win
(3/7*223/450 + 1/7 + 3/7*13/15 = 109/150) 72.7% Scum A win
(3/7*2/225 = 2/525) 0.4% Scum B win
(3/7*11/75 + 3/7*2/15 = 3/25) 12.0% Draw

7P 3 - 2 - 2

(2/7) 28.6% Scum A elimination. GOTO 6P 3 - 2 - 1 (Night) (157/450 Town win; 223/450 Scum B win; 2/225 Scum A win; 11/75 Draw)
(2/7) 28.6% Scum B elimination. As above, but with scum teams swapped.
(3/7) 42.8% Town elimination. GOTO 6P 2 - 2 - 2 (Night). (1/4 Town win; 1/6 either scum win; 5/12 Draw)

(2*2/7*157/450 + 3/7*1/4 = 1931/6300) 30.6% Town win
(2/7*223/450 + 2/7*2/225 + 3/7*1/6 = 97/450) 21.5% Scum A win
(97/450) 21.5% Scum B win
(2*2/7*11/75 + 3/7*5/12 = 551/2100) 26.2% Draw

7P 5 - 1 - 1 (Night)

(1/6*1/6 = 1/36) 2.8% Scum A and Scum B crosskill. Town win.
(1/6*5/6 = 5/36) 13.4% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)
(5/6*1/6 = 5/36) 13.4% As above, but reverse scum. 7/15 Town win; 8/15 Scum A win.
(5/6*1/6 = 5/36) 13.4% Scum A and Scum B kill same Townie. GOTO 6P 4 - 1 - 1 (13/36 Town win; 7/36 either scum win; 1/4 Draw)
(5/6*4/6 = 5/9) 55.6% Scum A and Scum B kill different Townies. GOTO 5P 3 - 1 - 1 (13/45 Town win; 2/9 either scum win; 4/15 Draw)

(1/36 + 2*5/36*7/15 + 5/36*13/36 + 5/9*13/45 = 53/144) 36.8% Town win
(5/36*8/15 + 5/36*7/36 + 5/9*2/9 = 97/432) 22.4% Scum A win
(97/432) 22.4% Scum B win
(5/36*1/4 + 5/9*4/15 = 79/432) 18.3% Draw

7P 4 - 2 - 1 (Night)

(1/5*2/6 = 1/15) 6.7% Scum A and Scum B crosskill each other. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum A win)
(1/5*4/6 = 2/15) 13.3% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)
(4/5*2/6 = 4/15) 26.6% Scum A kills Townie; Scum B kills Scum A. GOTO 5P 3 - 1 - 1 (13/45 Town win; 2/9 either scum win, 4/15 Draw)
(4/5*1/6 = 2/15) 13.3% Scum A and Scum B kill same Townie. GOTO 6P 3 - 2 - 1 (11/72 Town win; 35/72 Scum A win; 1/24 Scum B win; 23/72 Draw)
(4/5*3/6 = 2/5) 40.0% Scum A and Scum B kill different Townies. GOTO 5P 2 - 2 - 1 (14/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 14/45 Draw)

(1/15*7/15 + 2/15*1/6 + 4/15*13/45 + 2/15*11/72 + 2/5*14/135 = 173/900) 19.2% Town win
(1/15*8/15 + 2/15*5/6 + 4/15*2/9 + 2/15*35/72 + 2/5*71/135 = 433/900) 48.1% Scum A win
(4/15*2/9 + 2/15*1/24 + 2/5*8/135 = 239/2700) 8.8% Scum B win
(4/15*4/15 + 2/15*23/72 + 2/5*14/45 = 643/2700) 23.8% Draw

7P 3 - 3 - 1 (Night)

(1/4*3/6 = 1/8) 12.5% Scum A and Scum B crosskill. GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)
(1/4*3/6 = 1/8) 12.5% Scum A kills Scum B; Scum B kills Townie. Scum A win.
(3/4*3/6 = 3/8) 37.5% Scum A kills Townie; Scum B kills Scum A. GOTO 5P 2 - 2 - 1 (14/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 14/45 Draw)
(3/4*1/6 = 1/8) 12.5% Scum A and Scum B kill same Townie. GOTO 6P 2 - 3 - 1 (13/15 Scum A win; 2/15 Draw) (3/4*2/6 = 1/4) 25.0% Scum A and Scum B kill different Townies. GOTO 5P 1 - 3 - 1 (Scum A win).

(1/8*1/6 + 3/8*14/135 = 43/720) 6.0% Town win
(1/8*5/6 + 1/8 + 3/8*71/135 + 1/8*13/15 + 1/4 = 113/144) 78.5% Scum A win
(3/8*8/135 = 1/45) 2.2% Scum B win
(3/8*14/45 + 1/8*2/15 = 2/15) 13.3% Draw

7P 3 - 2 - 2 (Night)

(2/5*2/5 = 4/25) 16.0% Scum A and Scum B crosskill. GOTO 5P 3 - 1 - 1 (13/45 Town win; 2/9 either scum win; 4/15 Draw)
(2/5*3/5 = 6/25) 24.0% Scum A kills Scum B; Scum B kills Townie. GOTO 5P 2 - 2 - 1 (14/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 14/45 Draw)
(3/5*2/5 = 6/25) 24.0% As above, but with reversed scum.
(3/5*1/5 = 3/25) 12.0% Scum A and Scum B kill same Townie. GOTO 6P 2 - 2 - 2 (1/27 Town win; 5/27 either scum win; 16/27 Draw) (3/5*2/5 = 6/25) 24.0% Scum A and Scum B kill different Townies. GOTO 5P 1 - 2 - 2 (Draw)

(4/25*13/45 + 2*6/25*14/135 + 3/25*1/27 = 113/1125) 10.0% Town win
(4/25*2/9 + 6/25*71/135 + 6/25*8/135 + 3/25*5/27 = 223/1125) 19.8% Scum A win
(223/1125) 19.8% Scum B win
(4/25*4/15 + 2*6/25*14/45 + 3/25*16/27 + 6/25 = 566/1125) 50.3% Draw

8P 6 - 1 - 1

(1/8) 12.5% Scum A elimination. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)
(1/8) 12.5% Scum B elimination; 7/15 Town win; 8/15 Scum A win.
(6/8) 75.0% Town elimination; GOTO 7P 5 - 1 - 1 (Night) (2593/6480 Town win; 97/432 either scum win; 109/1296 Draw)

(2*1/8*7/15 + 6/8*2593/6480 = 3601/8640) 41.7% Town win
(1/8*8/15 + 6/8*97/432 = 677/2880) 23.5% Scum A win
(677/2880) 23.5% Scum B win
(6/8*109/1296 = 109/1728) 6.3% Draw

8P 5 - 2 - 1

(2/8) 25.0% Scum A elimination. GOTO 7P 5 - 1 - 1 (Night) (53/144 Town win; 97/432 either scum win; 79/432 Draw)
(1/8) 12.5% Scum B elimination. GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)
(5/8) 62.5% Town elimination. GOTO 7P 4 - 2 - 1 (Night) (173/900 Town win; 433/900 Scum A win; 239/2700 Scum B win; 643/2700 Draw)

(2/8*53/144 + 1/8*1/6 + 5/8*173/900 = 671/2880) 23.3% Town win
(2/8*97/432 + 1/8*5/6 + 5/8*433/900 = 3983/8640) 46.1% Scum A win
(2/8*97/432 + 5/8*239/2700 = 107/960) 11.1% Scum B win
(2/8*79/432 + 5/8*643/2700 = 1681/8640) 19.4% Draw

8P 4 - 3 - 1

(3/8) 37.5% Scum A elimination. GOTO 7P 4 - 2 - 1 (Night) (173/900 Town win; 433/900 Scum A win; 239/2700 Scum B win; 643/2700 Draw)
(1/8) 12.5% Scum B elimination. Scum A win.
(4/8) 50.0% Town elimination. GOTO 7P 3 - 3 - 1 (Night) (43/720 Town win; 113/144 Scum A win; 1/45 Scum B win; 2/15 Draw)

(3/8*173/900 + 4/8*43/720 = 367/3600) 10.2% Town win
(3/8*433/900 + 1/8 + 4/8*113/144 = 157/225) 69.8% Scum A win
(3/8*239/2700 + 4/8*1/45 = 319/7200) 4.4% Scum B win
(3/8*643/2700 + 4/8*2/15 = 1123/7200) 15.6% Draw

8P 4 - 2 - 2

(2/8) 25.0% Scum A elimination. GOTO 7P 4 - 2 - 1 (Night) (173/900 Town win; 433/900 Scum B win; 239/2700 Scum A win; 643/2700 Draw)
(2/8) 25.0% As above, but with scum reversed.
(4/8) 50.0% Town elimination. GOTO 7P 3 - 2 - 2 (Night) (113/1125 Town win; 223/1125 either scum win; 566/1125 Draw)

(2*2/8*173/900 + 4/8*113/1125 = 439/3000) 14.6% Town win
(2/8*433/900 + 2/8*239/2700 + 4/8*223/1125) 24.152% Scum A win
24.152% Scum B win
(2*2/8*643/2700 + 4/8*566/1125) 37.063% Draw

8P 6 - 1 - 1 (Night)

(1/7*1/7 = 1/49) 2.0% Scum A and Scum B crosskill each other. Town win.
(1/7*6/7 = 6/49) 12.2% Scum A kills Scum B; Scum B kills Townie. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum A win)
(6/7*1/7 = 6/49) 12.2% As above, but reverse scum. 7/15 Town win; 8/15 Scum B win.
(6/7*1/7 = 6/49) 12.2% Scum A and Scum B kill same Townie. GOTO 7P 5 - 1 - 1 (967/1575 Town win; 8/45 either scum win; 16/525 Draw)
(6/7*5/7 = 30/49) 61.2% Scum A and Scum B kill different Townies. GOTO 6P 4 - 1 - 1 (13/36 Town win; 7/36 either scum win; 1/4 Draw)

(1/49 + 2*6/49*7/15 + 6/49*967/1575 + 30/49*13/36) 43.0962% Town win
(6/49*8/15 + 6/49*8/45 + 30/49*7/36 = 101/490) 20.6 Scum A win
(101/490) 20.6% Scum B win
(6/49*16/525 + 30/49*1/4) 15.6793% Draw

8P 5 - 2 - 1 (Night)

(1/6*2/7 = 1/21) 4.8% Scum A and Scum B crosskill. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum A win)
(1/6*5/7 = 5/42) 11.9% Scum A kills Scum B; Scum B kills Townie. GOTO 5P 3 - 2 (2/15 Town win; 13/15 Scum A win)
(5/6*2/7 = 5/21) 23.8% Scum A kills Townie; Scum B kills Scum A. GOTO 6P 4 - 1 - 1 (13/36 Town win; 7/36 either scum win; 1/4 Draw)
(5/6*1/7 = 5/42) 11.9% Scum A and Scum B kill same Townie. GOTO 7P 4 - 2 - 1 (154/375 Town win; 47/105 Scum A win; 8/175 Scum B win; 12/125 Draw)
(5/6*4/7 = 10/21) 47.6% Scum A and Scum B kill Townies. GOTO 6P 3 - 2 - 1 (11/72 Town win; 35/72 Scum A win; 1/24 Scum B win; 23/72 Draw)

(1/21*7/15 + 5/42*2/15 + 5/21*13/36 + 5/42*154/375 + 10/21*11/72 = 43/175) 24.6% Town win
(1/21*8/15 + 5/42*13/15 + 5/21*7/36 + 5/42*47/105 + 10/21*35/72 = 2027/4410) 46.0% Scum A win
(5/21*7/36 + 5/42*8/175 + 10/21*1/24) 7.1580% Scum B win
(5/21*1/4 + 5/42*12/125 + 10/21*23/72 = 1054/4725) 22.3% Draw

9P 7 - 1 - 1

(1/9) 11.1% Scum A elimination. GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win; 16/35 Scum B win)
(1/9) 11.1% Scum B elimination. 19/35 Town win; 16/35 Scum A win.
(7/9) 77.8% Town elimination. GOTO 8P 6 - 1 - 1 (Night) (43.0962% Town win; 101/490 either scum win; 15.6793% Draw)

(2*1/9*19/35 + 7/9*0.430962) 45.5828% Town win
(1/9*16/35 + 7/9*101/490 = 19/90) 21.1% Scum A win
(19/90) 21.1% Scum B win
(7/9*0.156793) 12.1950% Draw

9P 6 - 2 - 1

(1/9) 11.1% Scum B elimination. GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win; 27/35 Scum A win)
(2/9) 22.2% Scum A elimination. GOTO 8P 6 - 1 - 1 (Night) (43.0962% Town win; 101/490 either scum win; 15.6793% Draw)
(6/9) 66.7% Town elimination. GOTO 8P 5 - 2 - 1 (Night) (43/175 Town win; 2027/4410 Scum A win; 7.1580% Scum B win; 1054/4725 Draw)

(1/9*8/35 + 2/9*0.430962 + 6/9*43/175) 28.4976% Town win
(1/9*27/35 + 2/9*101/490 + 6/9*2027/4410 = 2897/6615) 43.8% Scum A win
(2/9*101/490 + 6/9*0.07158) 9.3525% Scum B win
(2/9*0.156793 + 6/9*1054/4725) 18.3555% Draw

Mafia Lovers

Premise: All of the Mafia are Lovers. If one dies, the rest commit suicide and Town wins.

5P 3 - 2

(2/5) 40% Town win
(3/5) 60% Scum win

7P 5 - 2

(2/7) 28.6% Town win
(5/7) 71.4% GOTO 5P 3 - 2

(2/7 + 5/7*2/5 = 4/7) 57.1% Town win
(3/7) 42.9% Scum win

7P 4 - 3

(3/7) 42.9% Town win
(4/7) 57.1% Scum win

9P 7 - 2

(2/9) 22.2% Town win
(7/9) 77.8% GOTO 7P 5 - 2 (4/7 Town win)

(2/9 + 7/9*4/7 = 2/3) 66.7% Town win
(1/3) 33.3% Scum win

9P 6 - 3

(3/9) 33.3% Town win
(6/9) 66.7% GOTO 7P 4 - 3 (3/7 Town win)

(3/9 + 6/9*3/7 = 13/21) 61.9% Town win
(8/21) 38.1% Scum win

9P 5 - 4

(4/9) 44.4% Town win
(5/9) 55.6% Scum win

11P 9 - 2

(2/11) 18.2% Town win
(9/11) 81.8% GOTO 9P 7 - 2 (2/3 Town win)

(2/11 + 9/11*2/3 = 8/11) 72.7% Town win
(3/11) 27.3% Scum win

11P 8 - 3

(3/11) 27.3% Town win
(8/11) 72.7% GOTO 9P 6 - 3 (13/21 Town win)

(3/11 + 8/11*13/21 = 167/231) 72.3% Town win
(64/231) 27.7% Scum win

11P 7 - 4

(4/11) 36.4% Town win
(7/11) 63.6% GOTO 9P 5 - 4 (4/9 Town win)

(4/11 + 7/11*4/9 = 64/99) 64.6% Town win
(35/99) 35.4% Scum win

11P 6 - 5

(5/11) 45.4% Town win
(6/11) 54.5% Scum win

Lovers Mafia

Premise: Mafia are Lovers; if one dies, they all die.
Premise: The game is Nightless; scum do not have a kill.

5P 3 - 2

(2/5) 40.0% Town win
(3/5) 60.0% Scum win

6P 4 - 2

(2/6) 33.3% Town win
(4/6) 66.7% GOTO 5P 3 - 2 (2/5 Town win)

(2/6 + 4/6*2/5 = 3/5) 60.0% Town win
(2/5) 40.0% Scum win

7P 5 - 2

(2/7) 28.6% Town win
(5/7) 71.4% GOTO 6P 4 - 2 (3/5 Town win)

(2/7 + 5/7*3/5 = 5/7) 71.4% Town win
(2/7) 28.6% Scum win

7P 4 - 3

(3/7) 42.8% Town win
(4/7) 57.1% Scum win

8P 6 - 2

(2/8) 25.0% Town win
(6/8) 75.0% GOTO 7P 5 - 2 (5/7 Town win)

(2/8 + 6/8*5/7 = 11/14) 78.6% Town win
(3/14) 21.4% Scum win

8P 5 - 3

(3/8) 37.5% Town win
(5/8) 62.5% GOTO 7P 4 - 3 (3/7 Town win)

(3/8 + 5/8*3/7 = 9/14) 64.3% Town win
(5/14) 35.7% Scum win

True Love

Premise: All players are in two-person Lover bonds. The Mafia are not Lovers with each other.
Premise: The game is Nightless.

Refer to the True Love Expectation Rule when Mountainous.

Polygamist

Premise: All Town players are in two-person Lover bonds. All scum players are Lovers with each other. Nightless.
- With an odd number of scum, the probabilities are identical to Mafia Lovers above.

6P 4 - 2

(2/6) 33.3% Town win
(4/6) 66.7% Scum win

8P 6 - 2

(2/8) 25.0% Town win
(6/8) 75.0% GOTO 6P 4 - 2 (2/6 Town win)

(2/8 + 6/8*2/6 = 1/2) 50.0% Town win
(1/2) 50.0% Scum win

10P 8 - 2

(2/10) 20.0% Town win
(8/10) 80.0% GOTO 8P 6 - 2 (1/2 Town win)

(2/10 + 8/10*1/2 = 3/5) 60.0% Town win
(2/5) 40.0% Scum win

10P 6 - 4

(4/10) 40.0% Town win
(6/10) 60.0% Scum win

12P 10 - 2

(2/12) 16.7% Town win
(10/12) 83.3% GOTO 10P 8 - 2 (3/5 Town win)

(2/12 + 10/12*3/5 = 2/3) 66.7% Town win
(1/3) 33.3% Scum win

12P 8 - 4

(4/12) 33.3% Town win
(8/12) 66.7% GOTO 10P 6 - 4 (2/5 Town win)

(4/12 + 8/12*2/5 = 3/5) 60.0% Town win
(2/5) 40.0% Scum win

White Flag

Premise: If there is only one Mafioso remaining, the Town immediately wins.
All scenarios with two Mafiosi alive are identical to Mafia Lovers above.

7P: 4 - 3

(3/7) 42.9% GOTO ~Mafia Lovers~ 5P: 3 - 2 (2/5 Town win)
(4/7) 57.1% Scum win

(3/7*2/5 = 6/35) 17.1% Town win
(29/35) 82.8% Scum win

9P: 6 - 3

(3/9) 33.3% GOTO ~Mafia Lovers~ 7P: 5 - 2 (4/7 Town win)
(6/9) 66.7% GOTO 7P 4 - 3 (6/35 Town win)

(3/9*4/7 + 6/9*6/35 = 32/105) 30.5% Town win
(73/105) 69.5% Scum win

9P: 5 - 4

(4/9) GOTO 7P 4 - 3 (6/35 Town win)
(5/9) Scum win

(4/9*6/35 = 8/105) 7.6% Town win
(97/105) 92.4% Scum win

11P: 8 - 3

(3/11) 27.3% GOTO ~Mafia Lovers~ 9P: 7 - 2 (2/3 Town win)
(8/11) 72.7% GOTO 9P 6 - 3 (32/105 Town win)

(3/11*2/3 + 8/11*32/105 = 466/1155) 40.3% Town win
(689/1155) 59.6% Scum win

11P: 7 - 4

(4/11) 36.4% GOTO 9P: 6 - 3 (32/105 Town win)
(7/11) 63.6% GOTO 9P: 5 - 4 (8/105 Town win)

(4/11*32/105 + 7/11*8/105 = 184/1155) 15.9% Town win
(971/1155) 84.1% Scum win

13P: 10 - 3

(3/13) 23.1% GOTO ~Mafia Lovers~ 11P: 9 - 2 (8/11 Town win)
(10/13) 76.9% GOTO 11P: 8 - 3 (466/1155 Town win)

(3/13*8/11 + 10/13*466/1155 = 1436/3003) 47.8% Town win
(1567/3003) 52.2% Scum win

13P: 9 - 4

(4/13) 30.8% GOTO 11P: 8 - 3 (466/1155 Town win)
(9/13) 69.2% GOTO 11P: 7 - 4 (184/1155 Town win)

(4/13*466/1155 + 9/13*184/1155 = 64/273) 23.4% Town win
(209/273) 76.6% Scum win

Plus Named

Premise: There exists a Named Townie. This Named Townie is known to be Town. Scum will fakeclaim this Named Townie if run up.
It is always suboptimal for scum to counterclaim Named.
It is always optimal for Named to counterclaim scum.
At LyLo, Named will claim. Thus, the LyLo probabilities are the same as in Plus Innocent.

5P 4 - 1

(1/5) Scum gets counterclaimed for the Town win.
(1/5*1/4 = 1/20) Named claims; Scum eliminated for the Town win.
(1/5*3/4 = 3/20) Named claims; Town eliminated; Named killed overNight. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5*2/3 = 2/5) Town elimination; Town kill. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(3/5*1/3 = 1/5) Town elimination; Named kill. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)

(1/5 + 1/20 + 3/20*1/3 + 2/5*1/2 + 1/5*1/3 = 17/30) 56.7% Town win
(13/30) 43.3% Scum win

5P 3 - 2

(2/5) 40.0% Scum gets counterclaimed by Named; GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/5*2/4 = 1/10) 10.0% Named claims; scum eliminated; GOTO ~Mountanous~ 3P 2 - 1 (1/3 Town win)
(1/5*2/4 = 1/10) 10.0% Named claims; Town eliminated; scum win.
(2/5) 40.0% Town elimination; scum win.

(2/5*1/3 + 1/10*1/3 = 1/6) 16.7% Town win
(5/6) 83.3% Scum win

7P 6 - 1

(1/7) Scum gets counterclaimed for the Town win.
(1/7*1/6 = 1/42) Named claims; Scum eliminated for the Town win.
(1/7*5/6 = 5/42) Named claims; Town eliminated; Named killed overNight. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(5/7*4/5 = 4/7) Town elimination; Town kill. GOTO 5P 4 - 1 (17/30 Town win)
(5/7*1/5 = 1/7) Town elimination; Named kill. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)

(1/7 + 1/42 + 5/42*7/15 + 4/7*17/30 + 1/7*7/15 = 193/315) 61.3% Town win
(122/315) 38.7% Scum win

7P 5 - 2

(2/7) Scum gets countereliminated; Named dies; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(1/7*2/6 = 1/21) Named claims; Scum eliminated; Named dies; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(1/7*4/6 = 2/21) Named claims; Town eliminated; Named dies; GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(4/7*3/4 = 3/7) Town elimination; Town kill. GOTO 5P 3 - 2 (1/6 Town win)
(4/7*1/4 = 1/7) Town elimination; Named kill. GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)

(2/7*7/15 + 1/21*7/15 + 2/21*2/15 + 3/7*1/6 + 1/7*2/15 = 163/630) 25.9% Town win
(53/90) 58.9% Scum win

9P 8 - 1

(1/9) Scum gets counterclaimed for the Town win.
(1/9*1/8 = 1/72) Named claims; Scum eliminated for the Town win.
(1/9*7/8 = 7/72) Named claims; Town eliminated; Named killed; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(7/9*6/7 = 2/3) Town elimination; Town kill; GOTO 7P 6 - 1 (193/315 Town win)
(7/9*1/7 = 1/9) Town elimination; Named kill; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)

(1/9 + 1/72 + 7/72*19/35 + 2/3*193/315 + 1/9*19/35 = 611/945) 64.6% Town win
(334/945) 35.3% Scum win

9P 7 - 2

(2/9) Scum gets countereliminated; Named dies; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(1/9*2/8 = 1/36) Named claims; Scum eliminated; Named dies; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(1/9*6/8 = 1/12) Named claims; Town eliminated; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(6/9*5/6 = 5/9) Town elimination; Town kill; GOTO 7P 5 - 2 (163/630 Town win)
(6/9*1/6 = 1/9) Town elimination; Named kill; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)

(2/9*19/35 + 1/36*19/35 + 1/12*8/35 + 5/9*163/630 + 1/9*8/35) 32.38977072% Town win
67.6% Scum win

9P 6 - 3

(3/9) Scum gets countereliminated; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(1/9*3/8 = 1/24) Named claims; Scum eliminated; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(1/9*5/8 = 5/72) Named claims; Town eliminated; Named dies; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)
(5/9*4/5 = 4/9) Town elimination; Town kill; GOTO ~Plus Innocent~ 7P 4 - 3 (1/15 Town win)
(5/9*1/5 = 1/9) Town elimination; Named kill; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)

(3/9*8/35 + 1/24*8/35 + 5/72*2/35 + 4/9*1/15 + 1/9*2/35 = 95/756) 12.6% Town win
(661/756) 87.4% Scum win

Plus 2xMasons

Premise: There are two Masons. If run up to claim, they will not be eliminated, but killed overNight.
Premise: Scum will claim Mason, drawing a counterclaim.

5P 4 - 1

(1/5) 20.0% Scum claims Mason; gets counterclaimed; gets eliminated. Town win.
(2/5*1/4 = 1/10) 10.0% Mason claims; Scum claims Mason; gets counterclaimed; gets eliminated. Town win.
(2/5*1/4*1/3 = 1/30) 3.3% Mason claims; Mason claims; scum eliminated. Town win.
(2/5*1/4*2/3 = 1/15) 6.7% Mason claims; Mason claims; Town eliminated; Mason dies overNight; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*2/4 = 1/5) 20.0% Mason claims; Town eliminated; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*2/3 = 4/15) 26.7% Town eliminated; Mason dies; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*1/3 = 2/15) 13.3% Town eliminated; last Townie dies; Town wins by confirmed majority.

(1/5 + 2/5*1/4 + 2/5*1/4*1/3 + 2/5*1/4*2/3*1/2 + 2/5*1/2*1/2 + 2/5*2/3*1/2 + 2/5*1/3 = 11/15) 73.3% Town win
(4/15) 26.7% Scum win

--OR--

Any D1 Mason claim will be forced to claim a partner. (Modified from Empking's idea)
Scum will not claim Mason in this case, as it would cause them to lose.

(1/5) 20.0% Scum gets eliminated. Town win.
(2/5*1/3 = 2/15) Two Masons claim; Scum eliminated. Town win.
(2/5*2/3 = 4/15) Two Masons claim; Town eliminated; Mason dies overNight; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*2/3 = 4/15) 26.7% Town eliminated; Mason dies; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*1/3 = 2/15) 13.3% Town eliminated; last Townie dies; Town wins by confirmed majority.

(1/5 + 2/15 + 4/15*1/2 + 4/15*1/2 + 2/15 = 11/15) 73.3% Town win
(4/15) 26.7% Scum win

5P 3 - 2

(2/5) 40.0% Scum claims Mason; gets counterclaimed; gets eliminated. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*2/4) Mason claims; scum eliminated; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*1/4) Mason claims; Town eliminated; Scum win.
(2/5*1/4*2/3) Both Masons claim; scum eliminated; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/5*1/4*1/3) Both Masons claim; Town eliminated; Scum win.
(1/5) V. Townie eliminated. Scum win.

(2/5*1/2 + 2/5*1/2*1/2 + 2/5*1/4*2/3*1/2 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

--OR--

Masons claim. Scum do not counterclaim.

(2/3) Scum elimination; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(1/3) Town elimination; Scum win.

(2/3*1/2 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

--OR--

Masons claim. Scum counterclaim as a group.

(1/2) Town win
(1/2) Scum win

However, the scum are the ones who have to counterclaim, and they are not served by doing so.

7P 5 - 2

(2/7) 28.6% Scum claims Mason; Mason counterclaims; scum gets eliminated. GOTO ~Plus Named~ 5P 4 - 1 (17/30 Town win)
(2/7*2/6 = 2/21) 9.5% Mason claims; scum eliminated; GOTO ~Plus Named~ 5P 4 - 1 (17/30 Town win)
(2/7*3/6 = 1/7) 14.3% Mason claims; Town eliminated; GOTO ~Plus Named~ 5P 3 - 2 (1/6 Town win)
(2/7*1/6*2/5 = 2/105) 1.9% Both Masons claim; scum eliminated; GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(2/7*1/6*3/5 = 1/35) 2.9% Both Masons claim; Town eliminated; GOTO ~Plus Innocent~ 5P 3 - 2 (1/3 Town win)
(3/7*2/4 = 3/14) 21.4% Town elimination; Mason killed overNight; GOTO ~Plus Named~ 5P 3 - 2 (1/6 Town win)
(3/7*2/4 = 3/14) 21.4% Town elimination; Townie killed overNight; GOTO 5P 3 - 2 (1/3 Town win)

(2/7*17/30 + 2/21*17/30 + 1/7*1/6 + 2/105*1/2 + 1/35*1/3 + 3/14*1/6 + 3/14*1/3 = 461/1260) 36.6% Town win
(799/1260) 63.4% Scum win

--OR--

Any D1 Mason claim will be forced to claim a partner. (Modified from Empking's idea)
Scum will not claim Mason in this case, as it would cause them to lose.

(2/7*2/5 = 4/35) Scum fails to claim Mason; scum eliminated. Mason killed overNight. GOTO ~Plus Named~ 5P 4 - 1 (17/30 Town win)
(2/7*3/5 = 6/35) Scum fails to claim Mason; scum eliminated. Townie killed overNight. GOTO 5P 4 - 1 (11/15 Town win)
(2/7*2/5 = 4/35) Masons claim; scum eliminated. GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(2/7*3/5 = 6/35) Masons claim; Town eliminated; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(3/7*2/4 = 3/14) Town eliminated; Mason killed overNight; GOTO ~Plus Named~ 5P 3 - 2 (1/6 Town win)
(3/7*2/4 = 3/14) Town eliminated; Townie killed overNight; GOTO 5P 3 - 2 (1/3 Town win)

(4/35*17/30 + 6/35*11/15 + 4/35*1/2 + 6/35*1/6 + 3/14*1/6 + 3/14*1/3 = 23/60) 38.3% Town win
(37/60) 61.7% Scum win

Town would force this second option.

Plus 2xMasons/1Known

Premise: There are two Masons. One of the Masons is known. If run up to claim, the other Mason will not be eliminated. One Mason will be killed overNight.
Premise: Scum cannot claim Mason.

5P 4 - 1

(1/4) 25.0% Scum gets eliminated. Town win.
(1/4*1/3 = 1/12) 8.3% Unknown Mason claims; Scum gets eliminated. Town win.
(1/4*2/3 = 1/6) 16.7% Unknown Mason claims; Town eliminated; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(2/4 = 1/2) 50% Town eliminated; Known Mason dies; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)

(1/4 + 1/12 + 1/6*1/2 + 1/2*1/2 = 2/3) 66.7% Town win
(1/3) 33.3% Scum win

--OR--

Both Masons claim. Scum do not counterclaim.

(1/3) 33.3% Scum elimination; Town win
(2/3) 66.7% Town will be eliminated. Known Mason dies overNight. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)

(1/3 + 2/3*1/2 = 2/3) 66.7% Town win
(1/3) 33.3% Scum win

5P 3 - 2

(2/4 = 1/2) 50.0% Scum gets eliminated. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(1/4*2/3 = 1/6) 16.7% Unknown Mason claims; Scum gets eliminated. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(1/4*1/3 = 1/12) 8.3% Unknown Mason claims; Town eliminated; Scum win.
(1/4) Townie eliminated. Scum win.

(1/2*1/2 + 1/6*1/2 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

--OR--

Both Masons claim. Scum do not counterclaim.

(2/3) Scum elimination; GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(1/3) Town elimination; Scum win.

(2/3*1/2 = 1/3) 33.3% Town win
(2/3) 66.7% Scum win

7P 5 - 2

(2/6 = 1/3) 33.3% Scum gets eliminated. GOTO ~Plus Named~ 5P 4 - 1 (17/30 Town win)
(1/6*2/5 = 1/15) 6.7% Unknown Mason claims; Scum eliminated; GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(1/6*3/5 = 1/10) 10% Unknown Mason claims; Town eliminated; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(3/6 = 1/2) 50% Town elimination; Mason killed overNight; GOTO ~Plus Named~ 5P 3 - 2 (1/6 Town win)

(2/6*17/30 + 1/15*1/2 + 1/10*1/6 + 1/2*1/6 = 29/90) 32.2% Town win
(61/90) 67.7% Scum win

Both Masons claiming causes this to become ~Plus 2xInnocent~ 7P 5 - 2 which has a lower EV

7P 4 - 3

(3/6 = 1/2) 50% Scum gets eliminated. GOTO ~Plus Named~ 5P 3 - 2 (1/6 Town win)
(1/6*3/5 = 1/10) 10% Unknown Mason claims; Scum eliminated; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(1/6*2/5 = 1/15) 6.7% Unknown Mason claims; Town eliminated; Scum win.
(2/6 = 1/3) 33.3% Town elimination; Scum win.

(1/2*1/6 + 1/10*1/6 = 1/10) 10% Town win
(9/10) 90% Scum win

--OR--

Both Masons claim. Scum do not counterclaim.

(3/5) Scum elimination; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(2/5) Town elimination; Scum win.

(3/5*1/6 = 1/10) 10% Town win
(9/10) 90% Scum win

Plus 3xMasons

Premise: There are three Masons. If run up to claim, they will not be eliminated, but killed overNight.
Premise: Scum will claim Mason, drawing a counterclaim.

7P 5 - 2

(2/7) 28.6% Scum claims Mason; Mason counterclaims; scum gets eliminated. GOTO ~Plus 2xMasons~ 5P 4 - 1 (11/15 Town win)
(3/7*2/6 = 1/7) 14.3% Mason claims; Scum eliminated; GOTO ~Plus 2xMasons~ 5P 4 - 1 (11/15 Town win)
(3/7*2/6 = 1/7) 14.3% Mason claims; Town eliminated; GOTO ~Plus 2xMasons~ 5P 3 - 2 (1/3 Town win)
(3/7*2/6*2/5 = 2/35) 5.7% Two Masons claim; Scum eliminated; GOTO ~Plus 2xMasons/1Known~ 5P 4 - 1 (2/3 Town win)
(3/7*2/6*2/5 = 2/35) 5.7% Two Masons claim; Town eliminated; GOTO ~Plus 2xMasons/1Known~ 5P 3 - 2 (1/3 Town win)
(3/7*2/6*1/5*2/4 = 1/70) 5.7% Three Masons claim; Scum eliminated; GOTO ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win)
(3/7*2/6*1/5*2/4 = 1/70) 5.7% Three Masons claim; Town eliminated; GOTO ~Plus 2xInnocent~ 5P 3 - 2 (1/3 Town win)
(2/7*3/4 = 3/14) 21.4% Town elimination; Mason killed overNight; GOTO ~Plus 2xMasons~ 5P 3 - 2 (1/3 Town win)
(2/7*1/4 = 1/14) 7.1% Town elimination; last Townie killed overNight; Town wins by confirmed majority.

(2/7*11/15 + 1/7*11/15 + 1/7*1/3 + 2/35*2/3 + 2/35*1/3 + 1/70*2/3 + 1/70*1/3 + 3/14*1/3 + 1/14 = 121/210) 57.6% Town win
(89/210) 42.4% Scum win

--OR--

Any D1 Mason claim will be forced to claim ONE partner. (Modified from Empking's idea)
Scum will not claim Mason in this case, as it would cause them to lose.

(2/7*3/5 = 6/35) 17.1% Scum eliminated. Mason killed overNight. GOTO ~Plus 2xMasons~ 5P 4 - 1 (11/15 Town win)
(2/7*2/5 = 4/35) Scum eliminated. Townie killed overNight. Town wins by confirmed majority.
(3/7*2/5 = 6/35) 17.1% Two Masons claim; Scum eliminated; GOTO ~Plus 2xMasons/1Known~ 5P 4 - 1 (2/3 Town win)
(3/7*2/5 = 6/35) 17.1% Two Masons claim; Town eliminated; GOTO ~Plus 2xMasons/1Known~ 5P 3 - 2 (1/3 Town win)
(3/7*1/5*2/4 = 3/70) Three Masons claim; Scum eliminated; GOTO ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win)
(3/7*1/5*2/4 = 3/70) Three Masons claim; Town eliminated; GOTO ~Plus 2xInnocent~ 5P 3 - 2 (1/3 Town win)
(2/7*3/4 = 3/14) 21.4% Town elimination; Mason killed overNight; GOTO ~Plus 2xMasons~ 5P 3 - 2 (1/3 Town win)
(2/7*1/4 = 1/14) 7.1% Town elimination; last Townie killed overNight; Town wins by confirmed majority.

(6/35*11/15 + 4/35 + 6/35*2/3 + 6/35*1/3 + 3/70*2/3 + 3/70*1/3 + 3/14*1/3 + 1/14 = 209/350) 59.7% Town win
(141/350) 40.3% Scum win

Town would force this second option.

7P 4 - 3

(3/7) Scum claims Mason; gets counterclaimed; gets eliminated. GOTO ~Plus 2xMasons~ 5P 3 - 2 (1/3 Town win)
(3/7*3/6 = 3/14) Mason claims; Scum eliminated; GOTO ~Plus 2xMasons~ 5P 3 - 2 (1/3 Town win)
(3/7*1/6 = 1/14) Mason claims; Town eliminated; Scum win.
(3/7*2/6*3/5 = 3/35) 5.7% Two Masons claim; Scum eliminated; GOTO ~Plus 2xMasons/1Known~ 5P 3 - 2 (1/3 Town win)
(3/7*2/6*1/5 = 1/35) 5.7% Two Masons claim; Town eliminated; Scum win.
(3/7*2/6*1/5*3/4 = 3/140) 5.7% Three Masons claim; Scum eliminated; GOTO ~Plus 2xInnocent~ 5P 3 - 2 (1/3 Town win)
(3/7*2/6*1/5*1/4 = 1/140) 5.7% Three Masons claim; Town eliminated; Scum win.
(1/7) Town elimination; Scum win.

(3/7*1/3 + 1/14*1/3 + 3/35*1/3 + 3/140*1/3 = 17/84) 20.2% Town win
(67/84) 79.8% Scum win

--OR--

All Masons claim. Scum do not counterclaim.

(3/4) Scum elimination; GOTO ~Plus 2xInnocent~ 5P 3 - 2 (1/3 Town win)
(1/4) Town elimination; Scum win.

(3/4*1/3 = 1/4) 25% Town win
(3/4) 75% Scum win

Town would force this second option.

Even/Odd C9

Premise: There is one Cop that can only investigate on odd Nights. There is one Doctor that can only investigate on even Nights. All other players are Vanilla.
Premise: The Cop and Doctor will claim on D2 with their result, as the Cop is unlikely to get another investigation and the Doctor can protect them.
Premise: The Cop or Doctor will claim if they are run up. The scum will claim Cop D1 if run up (drawing a counterclaim) and Doc D2 (if both of them are alive).

Here two cases are considered: Even/Odd C9 and Alternating 9P. Because of the even/odd mechanic win rates cannot be calculated in reverse and extrapolated to other setups.

D1 5CD - 2 (no claims)

(2/7) Scum eliminated! GOTO N1 5CD - 1 (19/25 Town win)
(1/7) Cop eliminated. GOTO N1 4D - 2 (19/120 Town win)
(1/7) Doctor eliminated. GOTO N1 4C - 2 (11/60 Town win)
(3/7) V. Townie eliminated. GOTO N1 4CD - 2 (11/40 Town win)

(2/7*19/45 + 1/7*19/120 + 1/7*11/60 + 3/7*11/40 = 181/630) 28.7% Town win
(449/630) 71.3% Scum win

D1 5CD - 2

(2/7) Scum fakeclaims Cop; Cop counterclaims; scum gets eliminated; Cop dies overNight; GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(1/7*3/6 = 1/14) Cop claims; Town gets eliminated; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(1/7*2/6 = 1/21) Cop claims; scum claims Doctor; gets counterclaimed; scum dies; GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(2*1/7*1/6*3/5 = 1/35) Doctor claims; Cop claims; Town gets eliminated; GOTO N1 4(C)(D) - 2 (1/6 Town win)
(2*1/7*1/6*2/5 = 2/105) Doctor claims; Cop claims; scum gets eliminated; GOTO N1 5(C)(D) - 1 (2/3 Town win)
(1/7*2/6 = 1/21) Doctor claims; scum fakeclaims Cop; gets counterclaimed; scum eliminated; GOTO N1 5(C)(D) - 1 (1/2 Town win)
(1/7*3/6 = 1/14) Doctor claims; V. Townie eliminated; GOTO N1 4C(D) - 2 (5/24 Town win)
(3/7) V. Townie eliminated; GOTO N1 4CD - 2 (11/40 Town win)

(2/7*1/2 + 1/14*1/6 + 1/21*1/2 + 1/35*1/6 + 2/105*1/2 + 1/14*5/24 + 3/7*11/40 = 547/1680) 32.6% Town win
(1133/1680) 67.4% Scum win

IF Counterclaim (Cop) succeeds for scum: (1/4*1/3 + 3/4*4/9 = 5/12) 41.7% Town win rate
IF Counterclaim (Cop) fails for scum: 50.0% Town win rate
IF Counterclaim (Doc) succeeds for scum: (1/4*1/3 + 3/4*(1/4 + 3/4*1/2) = 53/96) 55.2% Town win rate
IF Counterclaim (Doc) fails for scum: GOTO N2 5C(D) - 1 (3/4) 75.0% Town win rate
Thus, the scum should counterclaim no Town roles.

N1 5CD - 1

(1/5) Cop dies. GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(1/5*4/5 = 4/25) Cop investigates scum and doesn't die. Town win.
(1/5*1/5 = 1/25) Cop investigates Doctor, who dies. GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(1/5*3/5 = 3/25) Cop investigates V. Townie; Doctor dies. GOTO ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win)
(3/5*1/5 = 3/25) Cop investigates V. Townie who dies. GOTO ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win)
(3/5*1/5 = 3/25) Cop investigates Doctor; V. Townie dies; GOTO ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win)
(3/5*2/5 = 6/25) Cop investigates V. Townie; scum kills different V. Townie. Town win by confirmed majority.

(1/5*1/2 + 4/25 + 1/25*1/2 + 3/25*2/3*3 + 6/25 = 19/25) 76.0% Town win
(6/25) 24.0% Scum win

N1 4D - 2

(1/4) 25.0% Doctor killed. GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(3/4) 75.0% V. Townie killed. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)

(1/4*2/15 + 3/4*1/6 = 19/120) 15.8% Town win
(101/120) 84.2% Scum win

N1 4C - 2

(1/4) 25.0% Cop killed. GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(3/4*1/5 = 3/20) Cop investigates dead V. Townie. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(3/4*2/5 = 3/10) Cop investigates scum; gets counterclaimed; GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(3/4*2/5 = 3/10) Cop investigates V. Townie who isn't killed; gets counterclaimed; 1/4 Town win.

(1/4*2/15 + 3/20*1/6 + 3/10*1/6 + 3/10*1/4 = 11/60) 18.3% Town win
(49/60) 81.7% Scum win

N1 5C(D) - 1

This poses a problem. If the scum shoots the Doctor, then:

(1/4) Cop investigates scum. Town win.
(3/4) Cop investigates Town. GOTO D2 4C(T) - 1 (2/3 Town win)

(1/4 + 3/4*2/3 = 3/4) 75.0% Town win
(1/4) 25.0% Scum win

If the scum tries to shoot the Cop, then:

(1/4) Hit Cop! GOTO ~Plus Innocent~ 5P 4 - 1 (1/2 Town win)
(3/4*1/4 = 3/16) Hit the Townie the Cop was investigating; GOTO D2 4CD - 1 (2/3 Town win)
(3/4*1/4 = 3/16) Hit a Townie, get investigated - Town win.
(3/4*2/4 = 3/8) Hit a Townie; Cop investigates another Townie; GOTO D2 4CD(T) - 1 - Town win.

(1/4*1/2 + 3/16*2/3 + 3/16 + 3/8 = 13/16) 81.2% Town win
(3/16) 18.8% Scum win

So the scum is best served trying to hit the Doctor if they don't know who the Cop is.

N1 4CD - 2

(1/4) 25.0% Scum kills Cop. GOTO D2 3D - 2 (1/6 Town win)
(1/4*2/5 = 1/10) 10.0% Scum kills Doctor; Cop investigates scum. Eventually winds up as ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/4*2/5 = 1/10) 10.0% Scum kills Doctor; Cop investigates Town. Cop needs to be counterclaimed for a 1/2*1/3 = 1/6 Town win rate.
(1/4*1/5 = 1/20) 5.0% Scum kills Doctor; Cop investigates Doctor. GOTO ~Plus Innocent~ 3 - 2 (1/6 Town win)
(2/4*2/5 = 1/5) 20.0% Scum kills V. Townie; Cop investigates scum. GOTO D2 3CD(S) - 2 (1/2 Town win)
(2/4*1/5 = 1/10) 10.0% Scum kills V. Townie; Cop investigates Townie that isn't killed. GOTO D2 3CD(T) - 2 (1/4 Town win)
(2/4*1/5 = 1/10) 10.0% Scum kills V. Townie; Cop investigates Townie that is killed. GOTO D2 3CD - 2 (5/12 Town win)
(2/4*1/5 = 1/10) 10.0% Scum kills V. Townie; Cop investigates Doctor. GOTO D2 3C(D) - 2 (1/4 Town win)

(1/4*1/6 + 1/10*1/3 + 1/10*1/6 + 1/20*1/6 + 1/5*1/2 + 3*1/10*1/4 = 11/40) 27.5% Town win
(29/40) 72.5% Scum win

N1 4C(D) - 2

Option 1: Scum kills Doctor.

(2/4) 50.0% Cop investigates scum. Counterclaim, 1/6 Town win.
(2/4) 50.0% Cop investigates Town. Counterclaims, 1/4 Town win.

(5/24) 20.8% Town win
(19/24) 79.2% Scum win

Option 2: Scum tries for Cop.

(1/3) 33.3% Scum kills Cop. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(2/3) 66.7% Scum kills V. Townie; Cop investigates someone. (1/4 Town win)

(2/9) 22.2% Town win
(7/9) 77.8% Scum win

So the scum are better served by killing the Cop.

N1 4(C)(D) - 2

Scum kills Cop. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)

N1 5(C)(D) - 1

Scum kills Cop. GOTO ~Plus Innocent~ 5P 4 - 1 (2/3 Town win).

D2 3D - 2

It doesn't matter whether the Doctor is counterclaimed or not. 1/6 Town win.

D2/N2 3 - 2(C)

Fakeclaiming Cop is immediately eliminated. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win).

D2/N2 3D - 2(C)

Fakeclaiming Cop is immediately eliminated. Doctor does not claim. Thus ends D2.

N2 3D - 1
(2/3*1/3 = 1/9) 22.2% Doctor protects kill target. Regardless of whether the remaining scum counterclaims Doctor, 1/2 Town win.
(1/3) 33.3% Scum kills Doctor. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(2/3*2/3 = 4/9) 44.4% Doctor fails to protect from kill. Regardless of whether the remaining scum counterclaims Doctor, 1/2 Town win.

(2/9*1/2 + 1/3*1/3 + 4/9*1/2 = 4/9) 44.4% Town win
(5/9) 55.6% Scum win

D2 3CD(any result) - 2

One scum must counterclaim Cop. If the Cop investigated the Doctor, the other scum must counterclaim Doctor.

No matter what, (1/4) Town win
(3/4) Scum win

D2 4CD(T) - 1

Cop and Doc claim. With three confirmed innocents it is impossible for the scum to win. Town win.

D2 4CD - 1

Cop and Doc claim. ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win).

D2 4C - 1

Cop claims with lack of result. ~Plus Innocent~ 5P 4 - 1 (1/2 Town win).

D2 4C(T) - 1

Cop claims with result. ~Plus 2xInnocent~ 5P 4 - 1 (2/3 Town win).

D2 4D - 1

(1/5) 20.0% Scum eliminated. Town win.
(1/5*1/4 = 1/20) 5.0% Doc claims. Scum eliminated. Town win.
(1/5*3/4 = 3/20) 15.0% Doc claims. Town eliminated. Doc dies overNight. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5) 60.0% Town eliminated. GOTO N2 3D - 1 (4/9 Town win)

(1/5 + 1/20 + 3/20*1/3 + 3/5*4/9 = 17/30) 56.7% Town win
(13/30) 43.3% Scum win

N2 3D - 1

(2/3*1/3 = 2/9) Doctor saves Townie from kill. Regardless of whether scum counterclaims Doc D3, 1/2 Town win. (1/3) Scum kills Doctor. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win) (2/3*2/3 = 4/9) Doctor fails to stop kill. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)

(2/9*1/2 + 1/3*1/3 + 4/9*1/2 = 4/9) 44.4% Town win
(5/9) 55.6% Scum win