The EV Project

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 is intended to be more realistic and focus on players trying to optimize their chances, even though lynches 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 230/693, or 33.2%.
  • Changing the setup to 11:2 Mountainous increases the expected Town win rate to 1088/3003, or 36.2%.
• 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%.

Mountainous Setups

• Premise: At even numbers, Town is assumed to No Lynch to raise their lynch 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 lynch 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 (33.3% 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 (33.3% 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 (46.7% Town win)

(1/7 + 6/7*7/15 = 19/35) 53.3% 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 = 152/315) 48.3% Town win
(163/315) 51.7% 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 (152/315 Town win)

(1/11 + 10/11*152/315 = 367/693) 53.0% Town win
(326/693) 47.0% Scum win

11P 9 - 2

(2/11) 18.2% GOTO 9P: 8 - 1 (152/315 Town win)
(9/11) 81.8% GOTO 9P: 7 - 2 (94/315 Town win)

(2/11*152/315 + 9/11*94/315 = 230/693) 33.2% Town win
(463/693) 66.8% 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*367/693 + 11/13*230/693 = 1088/3003) 36.2% Town win
(1915/3003) 63.8% Scum win

13P 10 - 3

(3/13) 23.1% GOTO 11P 9 - 2 (230/693 Town win)
(10/13) 76.9% GOTO 11P 8 - 3 (38/231 Town win)

(3/13*230/693 + 10/13*38/231 = 610/3003) 20.3% Town win
(2393/3003) 79.7% Scum win

Plus Innocent

• Premise: There is one confirmed innocent in the player list. This player cannot be lynched, but will be killed during the next Night. No Lynch 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 lynched; Town loses.

5P 4 - 1

(1/4) 25.0% Town win
(3/4) 75.0% Town will be lynched. 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% Town win
(3/4) 50.0% Scum win

6P 5 - 1

(1/5) 20.0% Town win
(4/5) 80.0% Town will be lynched. No Lynch 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 lynched. 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 lynched. ConfTown will die overNight. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(4/6) 66.7% Town will be lynched. 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 lynch, No Lynch; 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 lynch; No Lynch; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(5/7) 71.4% Town lynch; No Lynch; 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 lynch; No Lynch; 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 lynch; 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 lynched. ConfTown will die overNight. GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(6/8) 75.0% Town will be lynched. 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 lynched. ConfTown will die overNight. GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(5/8) 62.5% Town will be lynched. 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 lynch; 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 lynch; No Lynch; 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 lynch; No Lynch; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(7/9) 77.8% Town lynch; No Lynch; 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 lynch; No Lynch; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(6/9) 66.7% Town lynch; No Lynch; 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 lynch; No Lynch; 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 lynch; GOTO ~Mountainous~ 9P 8 - 1 (152/315 Town win)

(1/10 + 9/10*152/315 = 187/350) 53.4% Town win
(163/350) 46.6% Scum win

11P 9 - 2

(2/10) 20.0% Scum lynch; GOTO ~Mountainous~ 8 - 1 (152/315 Town win)
(8/10) 80.0% Town lynch; GOTO ~Mountainous~ 7 - 2 (94/315 Town win)

(2/10*152/315 + 8/10*94/315 = 176/525) 33.5% Town win
(349/525) 66.5% Scum win

11P 8 - 3

(3/10) 30.0% Scum will be lynched. ConfTown will die overNight. GOTO ~Mountainous~ 9P 7 - 2 (94/315 Town win)
(7/10) 70.0% Town will be lynched. 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 lynch; GOTO ~Mountainous~ 9P 6 - 3 (4/35 Town win)
(6/10) 60.0% Town lynch; 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 lynched, 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 lynched. 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

6P 5 - 1

(1/4) 25.0% Town win
(3/4) 75.0% Town will be lynched. 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 lynched. 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

9P 7 - 2

(2/7) 28.6% Scum will be lynched. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 7P 6 - 1 (5/9 Town win)
(5/7) 71.4% Town will be lynched. 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 lynched. ConfTown 1 will die overNight. GOTO ~Plus Innocent~ 9P 7 - 2.
(6/9) 66.7% Town will be lynched. 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

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

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