The EV Project

This experiment by Vi might go somewhere; who knows.

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%.

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

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.

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

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

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

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

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

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