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===3P 1 - 1 - 1===
===3P 1 - 1 - 1===
*Premise: This is a [[Dilemma]].  Town is assumed to win 100% of the time here.
*Premise: This is a [[Dilemma]].  This is assumed to be a Draw.


===4P 2 - 1 - 1===
===4P 2 - 1 - 1===
Line 364: Line 364:
(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)<br>
(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)<br>
(2/3*1/3 = 2/9) 22.2% As above, but swap scum.  1/3 Town win.<br>
(2/3*1/3 = 2/9) 22.2% As above, but swap scum.  1/3 Town win.<br>
(2/3*1/3 = 2/9) 22.2% Scum A and Scum B kill same Townie.  GOTO 3P 1 - 1 - 1 (Town win)<br>
(2/3*1/3 = 2/9) 22.2% Scum A and Scum B kill same Townie.  GOTO 3P 1 - 1 - 1 (Draw)<br>
(2/3*1/3 = 2/9) 22.2% Scum A and Scum B kill different Townies.  GOTO 2P 0 - 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 = 13/27) 48.1% Town win<br>
(1/9 + 2/9 + 2*2/9*1/3 = 7/27) 25.9% Town win<br>
(2/9*2/3 = 4/27) 14.8% Scum A win<br>
(2/9*2/3 = 4/27) 14.8% Scum A win<br>
(2/9*2/3 = 4/27) 14.8% Scum B win<br>
(2/9*2/3 = 4/27) 14.8% Scum B win<br>
(2/9) 22.2% Draw between Scum A and Scum B
(2*2/9 = 4/9) 44.4% Draw between Scum A and Scum B


===4P 1 - 2 - 1 (Night)===
===4P 1 - 2 - 1 (Night)===
Line 384: Line 384:
(1/5) 20.0% Scum A lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(1/5) 20.0% Scum A lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(1/5) 20.0% Scum B lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(1/5) 20.0% Scum B lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(3/5) 60.0% Town lynched.  GOTO 4P 2 - 1 - 1 (Night) (13/27 Town win; 4/27 either Scum win; 2/9 Draw)
(3/5) 60.0% Town lynched.  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*13/27 = 19/45) 42.2% Town win<br>
(2*1/5*1/3 + 3/5*7/27 = 13/45) 28.9% Town win<br>
(1/5*2/3 + 3/5*4/27 = 2/9) 22.2% Scum A win<br>
(1/5*2/3 + 3/5*4/27 = 2/9) 22.2% Scum A win<br>
(2/9) 22.2% Scum B win<br>
(2/9) 22.2% Scum B win<br>
(3/5*2/9 = 2/15) 13.3% Draw between Scum A and Scum B
(3/5*4/9 = 4/15) 26.6% Draw between Scum A and Scum B


===5P 2 - 2 - 1===
===5P 2 - 2 - 1===
(2/5) 40.0% Scum A lynched.  GOTO 4P 2 - 1 - 1 (Night) (13/27 Town win; 4/27 either Scum win; 2/9 Draw)<br>
(2/5) 40.0% Scum A lynched.  GOTO 4P 2 - 1 - 1 (Night) (7/27 Town win; 4/27 either Scum win; 4/9 Draw)<br>
(1/5) 20.0% Scum B lynched.  Scum A win.<br>
(1/5) 20.0% Scum B lynched.  Scum A win.<br>
(2/5) 40.0% Town lynched.  GOTO 4P 1 - 2 - 1 (Night) (2/3 Scum A win; 1/3 Draw)
(2/5) 40.0% Town lynched.  GOTO 4P 1 - 2 - 1 (Night) (2/3 Scum A win; 1/3 Draw)


(2/5*13/27 = 26/135) 19.2% Town win<br>
(2/5*7/27 = 14/135) 10.4% Town win<br>
(2/5*4/27 + 1/5 + 2/5*2/3 = 71/135) 52.6% Scum A win<br>
(2/5*4/27 + 1/5 + 2/5*2/3 = 71/135) 52.6% Scum A win<br>
(2/5*4/27 = 8/135) 5.9% Scum B win<br>
(2/5*4/27 = 8/135) 5.9% Scum B win<br>
(2/5*2/9 + 2/5*1/3 = 2/9) 22.2% Draw
(2/5*4/9 + 2/5*1/3 = 14/45) 31.1% Draw


===5P 1 - 2 - 2===
===5P 1 - 2 - 2===
*Premise: Townie is Kingmaker here. By lynching, they are consigning themselves to a 4P 1 - 2 - 1.  Thus, optimal play for Townie is to No Lynch and go to 5P 1 - 2 - 2 (Night).
*Premise: This is a [[Dilemma]]. The scum Draw by collaboratively lynching the Townie.


===5P 1 - 3 - 1===
===5P 1 - 3 - 1===
Line 412: Line 412:
(3/4*1/4 = 3/16) 18.8% As above, but swap scum.  1/3 Town win.<br>
(3/4*1/4 = 3/16) 18.8% As above, but swap scum.  1/3 Town win.<br>
(3/4*1/4 = 3/16) 18.8% Scum A and Scum B kill same Townie.  GOTO 4P 2 - 1 - 1 (Town win)<br>
(3/4*1/4 = 3/16) 18.8% Scum A and Scum B kill same Townie.  GOTO 4P 2 - 1 - 1 (Town win)<br>
(3/4*2/4 = 3/8) 37.5% Scum A and Scum B kill different Townies.  GOTO 3P 1 - 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 = 3/4) 75.0% Town win<br>
(1/16 + 2*3/16*1/3 + 3/16 = 3/8) 37.5% Town win<br>
(3/16*1/3 = 1/8) 12.5% Scum A win<br>
(3/16*1/3 = 1/8) 12.5% Scum A win<br>
(1/8) 12.5% Scum B win
(1/8) 12.5% Scum B win
(3/8) 37.5% Draw


===5P 2 - 2 - 1 (Night)===
===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)<br>
(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)<br>
(1/3*2/4 = 1/6) 16.7% Scum A kills Scum B; Scum B kills Town. Scum A win.<br>
(1/3*2/4 = 1/6) 16.7% Scum A kills Scum B; Scum B kills Town. Scum A win.<br>
(2/3*2/4 = 1/3) 33.3% Scum A kills Town; Scum B kills Scum A.  GOTO 3P 1 - 1 - 1 (Town win).<br>
(2/3*2/4 = 1/3) 33.3% Scum A kills Town; Scum B kills Scum A.  GOTO 3P 1 - 1 - 1 (Draw).<br>
(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).<br>
(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).<br>
(2/3*1/4 = 1/6) 16.7% Scum A and Scum B kill different Townies.  Scum A win.
(2/3*1/4 = 1/6) 16.7% Scum A and Scum B kill different Townies.  Scum A win.


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


*Note that in this situation, Scum B is a [[Kingmaker]].
*Note that in this situation, Scum B is playing exclusively for the Draw.


===5P 1 - 2 - 2 (Night)===
===5P 1 - 2 - 2 (Night)===
(2/3*2/3 = 4/9) 44.4% Scum A and Scum B crosskill.  GOTO 3P 1 - 1 - 1 (Town win)<br>
(2/3*2/3 = 4/9) 44.4% Scum A and Scum B crosskill.  GOTO 3P 1 - 1 - 1 (Draw)<br>
(2/3*1/3 = 2/9) 22.2% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(2/3*1/3 = 2/9) 22.2% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(1/3*2/3 = 2/9) 22.2% As above, but reverse scum.  Scum B win.<br>
(1/3*2/3 = 2/9) 22.2% As above, but reverse scum.  Scum B win.<br>
(1/3*1/3 = 1/9) 11.1% Scum A and Scum B kill Townie.  Draw.
(1/3*1/3 = 1/9) 11.1% Scum A and Scum B kill Townie.  Draw.


*Premise: Thus, this is an extended [[Dilemma]]. The only winning move for scum is to hope the other player shoots the Townie. Thus, Town wins this by default.
(2/9) 22.2% Scum A win<br>
(2/9) 22.2% Scum B win<br>
(4/9+1/9) 55.6% Draw


===6P 4 - 1 - 1===
===6P 4 - 1 - 1===
(1/6) 16.7% Scum A lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(1/6) 16.7% Scum A lynched.  GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)<br>
(1/6) 16.7% Scum B lynched; 1/3 Town win.<br>
(1/6) 16.7% Scum B lynched; 1/3 Town win.<br>
(4/6) 66.7% Town lynched; GOTO 5P 3 - 1 - 1 (Night) (3/4 Town win; 1/8 either scum win)
(4/6) 66.7% Town lynched; 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*3/4 = 11/18) 61.1% Town win<br>
(2*1/6*1/3 + 2/3*3/8 = 13/36) 36.1% Town win<br>
(1/6*2/3 + 2/3*1/8 = 7/36) 19.4% Scum A win<br>
(1/6*2/3 + 2/3*1/8 = 7/36) 19.4% Scum A win<br>
(7/36) 19.4% Scum B win
(7/36) 19.4% Scum B win
(2/3*3/8 = 1/4) 25.0% Draw


===6P 3 - 2 - 1===
===6P 3 - 2 - 1===
(2/6) 33.3% Scum A lynched.  GOTO 5P 3 - 1 - 1 (Night). (3/4 Town win; 1/8 either scum win)<br>
(2/6) 33.3% Scum A lynched.  GOTO 5P 3 - 1 - 1 (Night). (3/8 Town win; 1/8 either scum win; 3/8 Draw)<br>
(1/6) 16.7% Scum B lynched.  Scum A win.<br>
(1/6) 16.7% Scum B lynched.  Scum A win.<br>
(3/6) 50.0% Town lynched.  GOTO 5P 2 - 2 - 1 (Night). (7/18 Town win; 5/9 Scum A win; 1/18 Draw)
(3/6) 50.0% Town lynched.  GOTO 5P 2 - 2 - 1 (Night). (1/18 Town win; 5/9 Scum A win; 7/18 Draw)


(2/6*3/4 + 1/2*7/18 = 4/9) 44.4% Town win<br>
(2/6*3/8 + 1/2*1/18 = 11/72) 15.3% Town win<br>
(2/6*1/8 + 1/6 + 3/6*5/9 = 35/72) 48.6% Scum A win<br>
(2/6*1/8 + 1/6 + 3/6*5/9 = 35/72) 48.6% Scum A win<br>
(2/6*1/8 + 1/24) 4.2% Scum B win<br>
(2/6*1/8 = 1/24) 4.2% Scum B win<br>
(3/6*1/18 = 1/36) 2.8% Draw
(2/6*3/8 + 3/6*7/18 = 23/72) 31.9% Draw


===6P 2 - 3 - 1===
===6P 2 - 3 - 1===
Line 462: Line 466:


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


(1/3 + 2*1/3*7/18 = 16/27) 59.2% Town win<br>
(2*1/3*1/18 = 1/27) 3.7% Town win<br>
(1/3*5/9 = 5/27) 18.5% Scum A win<br>
(1/3*5/9 = 5/27) 18.5% Scum A win<br>
(1/3*5/9 = 5/27) 18.5% Scum B win<br>
(1/3*5/9 = 5/27) 18.5% Scum B win<br>
(2*1/3*1/18 = 1/27) 3.7% Draw
(2*1/3*7/18 + 1/3 = 16/27) 59.2% Draw
 
*Town's chances are clearly maximized here by deliberately mislynching... IF [[Prisoner's Gambit]] is not considered.  This warrants further study.


===6P 4 - 1 - 1 (Night)===
===6P 4 - 1 - 1 (Night)===
Line 477: Line 479:
(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)<br>
(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)<br>
(4/5*1/5 = 4/25) 16.0% As above, but swap scum. (1/3 Town win; 2/3 Scum B win)<br>
(4/5*1/5 = 4/25) 16.0% As above, but swap scum. (1/3 Town win; 2/3 Scum B win)<br>
(4/5*1/5 = 4/25) 16.0% Scum A and Scum B kill same Townie. GOTO 5P 3 - 1 - 1 (19/45 Town win; 2/9 either scum win; 2/15 Draw)<br>
(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)<br>
(4/5*3/5 = 12/25) 48.0% Scum A and Scum B kill different Townies.  GOTO 4P 2 - 1 - 1 (Town win)
(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*19/45 + 12/25 = 781/1125) 69.4% Town win<br>
(1/25 + 2*4/25*1/3 + 4/25*13/45 + 12/25 = 757/1125) 67.3% Town win<br>
(4/25*2/3 + 4/25*2/9 = 32/225) 14.2% Scum A win<br>
(4/25*2/3 + 4/25*2/9 = 32/225) 14.2% Scum A win<br>
(32/225) 14.2% Scum B win<br>
(32/225) 14.2% Scum B win<br>
(4/25*2/15 = 8/375) 2.1% Draw
(4/25*4/15 = 16/375) 4.3% Draw


===6P 3 - 2 - 1 (Night)===
===6P 3 - 2 - 1 (Night)===
Line 489: Line 491:
(1/4*3/5 = 3/20) 15.0% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(1/4*3/5 = 3/20) 15.0% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(3/4*2/5 = 3/10) 30.0% Scum A kills Townie; Scum B kills Scum A.  GOTO 4P 2 - 1 - 1 (Town win)<br>
(3/4*2/5 = 3/10) 30.0% Scum A kills Townie; Scum B kills Scum A.  GOTO 4P 2 - 1 - 1 (Town win)<br>
(3/4*1/5 = 3/20) 15.0% Scum A and Scum B kill same Townie. GOTO 5P 2 - 2 - 1 (26/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 2/9 Draw)<br>
(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)<br>
(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)
(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*26/135 = 163/450) 36.2% Town win<br>
(1/10*1/3 + 3/10 + 3/20*14/135 = 157/450) 34.9% Town win<br>
(1/10*2/3 + 3/20 + 3/20*71/135 + 3/10*2/3 = 223/450) 49.6% Scum A win<br>
(1/10*2/3 + 3/20 + 3/20*71/135 + 3/10*2/3 = 223/450) 49.6% Scum A win<br>
(3/20*8/135 = 2/225) 0.9% Scum B win<br>
(3/20*8/135 = 2/225) 0.9% Scum B win<br>
(3/20*2/9 + 3/10*1/3 = 2/15) 13.3% Draw
(3/20*14/45 + 3/10*1/3 = 11/75) 14.7% Draw


===6P 2 - 3 - 1 (Night)===
===6P 2 - 3 - 1 (Night)===
Line 510: Line 512:
(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)<br>
(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)<br>
(2/4*2/4 = 1/4) 25.0% As above, but with reversed scum.<br>
(2/4*2/4 = 1/4) 25.0% As above, but with reversed scum.<br>
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill same Townie.  GOTO 5P 1 - 2 - 2 (Town win)<br>
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill same Townie.  GOTO 5P 1 - 2 - 2 (Draw)<br>
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill different Townies.  Draw.
(2/4*1/4 = 1/8) 12.5% Scum A and Scum B kill different Townies.  Draw.


(1/4 + 1/8 = 3/8) 37.5% Town win<br>
(1/4) 25.0% Town win<br>
(1/4*2/3 = 1/6) 16.7% Scum A win<br>
(1/4*2/3 = 1/6) 16.7% Scum A win<br>
(1/4*2/3 = 1/6) 16.7% Scum B win<br>
(1/4*2/3 = 1/6) 16.7% Scum B win<br>
(2*1/4*1/3 + 1/8 = 7/24) 29.2% Draw
(2*1/4*1/3 + 2*1/8 = 5/12) 41.7% Draw


===7P 5 - 1 - 1===
===7P 5 - 1 - 1===
(1/7) 14.3% Scum A lynch; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)<br>
(1/7) 14.3% Scum A lynch; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)<br>
(1/7) 14.3% Scum B lynch; same as above (7/15 Town win; 8/15 Scum A win)<br>
(1/7) 14.3% Scum B lynch; same as above (7/15 Town win; 8/15 Scum A win)<br>
(5/7) 71.4% Town lynch; GOTO 6P 4 - 1 - 1 (Night). (781/1125 Town win; 32/225 either scum win; 8/375 Draw)
(5/7) 71.4% Town lynch; 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*781/1125 = 991/1575) 62.9% Town win<br>
(2*1/7*7/15 + 5/7*757/1125 = 967/1575) 61.3% Town win<br>
(1/7*8/15 + 5/7*32/225 = 8/45) 17.8% Scum A win<br>
(1/7*8/15 + 5/7*32/225 = 8/45) 17.8% Scum A win<br>
(8/45) 17.8% Scum B win<br>
(8/45) 17.8% Scum B win<br>
(5/7*8/375 = 8/525) 1.5% Draw
(5/7*16/375 = 16/525) 3.0% Draw


===7P 4 - 2 - 1===
===7P 4 - 2 - 1===
(2/7) 28.6% Scum A lynch; GOTO 6P 4 - 1 - 1 (Night) (781/1125 Town win; 32/225 either scum win; 8/375 Draw)<br>
(2/7) 28.6% Scum A lynch; GOTO 6P 4 - 1 - 1 (Night) (757/1125 Town win; 32/225 either scum win; 16/375 Draw)<br>
(1/7) 14.3% Scum B lynch; GOTO ~Mountainous~ 3 - 2 (2/15 Town win; 13/15 Scum A win)<br>
(1/7) 14.3% Scum B lynch; GOTO ~Mountainous~ 3 - 2 (2/15 Town win; 13/15 Scum A win)<br>
(4/7) 57.1% Town lynch; GOTO 6P 3 - 2 - 1 (Night) (163/450 Town win; 223/450 Scum A win; 2/225 Scum B win; 2/15 Draw)
(4/7) 57.1% Town lynch; 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*781/1125 + 1/7*2/15 + 4/7*163/450 = 1114/2625) 42.4% Town win<br>
(2/7*757/1125 + 1/7*2/15 + 4/7*157/450 = 154/375) 41.1% Town win<br>
(2/7*32/225 + 1/7*13/15 + 4/7*223/450 = 47/105) 44.8% Scum A win<br>
(2/7*32/225 + 1/7*13/15 + 4/7*223/450 = 47/105) 44.8% Scum A win<br>
(2/7*32/225 + 4/7*2/225 = 8/175) 4.6% Scum B win<br>
(2/7*32/225 + 4/7*2/225 = 8/175) 4.6% Scum B win<br>
(2/7*8/375 + 4/7*2/15 = 72/875) 8.2% Draw
(2/7*16/375 + 4/7*11/75 = 12/125) 9.6% Draw


===7P 3 - 3 - 1===
===7P 3 - 3 - 1===
(3/7) 42.8% Scum A lynch; GOTO 6P 3 - 2 - 1 (Night) (163/450 Town win; 223/450 Scum A win; 2/225 Scum B win; 2/15 Draw)<br>
(3/7) 42.8% Scum A lynch; GOTO 6P 3 - 2 - 1 (Night) (157/450 Town win; 223/450 Scum A win; 2/225 Scum B win; 11/75 Draw)<br>
(1/7) 14.3% Scum B lynch.  Scum A win.<br>
(1/7) 14.3% Scum B lynch.  Scum A win.<br>
(3/7) 42.8% Town lynch; GOTO 6P 2 - 3 - 1 (Night) (13/15 Scum A win; 2/15 Draw)
(3/7) 42.8% Town lynch; GOTO 6P 2 - 3 - 1 (Night) (13/15 Scum A win; 2/15 Draw)


(3/7*163/450 = 163/1050) 15.5% Town win<br>
(3/7*157/450 = 157/1050) 15.0% Town win<br>
(3/7*223/450 + 1/7 + 3/7*13/15 = 109/150) 72.7% Scum A win<br>
(3/7*223/450 + 1/7 + 3/7*13/15 = 109/150) 72.7% Scum A win<br>
(3/7*2/225 = 2/525) 0.4% Scum B win<br>
(3/7*2/225 = 2/525) 0.4% Scum B win<br>
(3/7*2/15 + 3/7*2/15 = 4/35) 11.4% Draw
(3/7*11/75 + 3/7*2/15 = 3/25) 12.0% Draw


===7P 3 - 2 - 2===
===7P 3 - 2 - 2===
(2/7) 28.6% Scum A lynch.  GOTO 6P 3 - 2 - 1 (Night) (163/450 Town win; 223/450 Scum B win; 2/225 Scum A win; 2/15 Draw)<br>
(2/7) 28.6% Scum A lynch.  GOTO 6P 3 - 2 - 1 (Night) (157/450 Town win; 223/450 Scum B win; 2/225 Scum A win; 11/75 Draw)<br>
(2/7) 28.6% Scum B lynch.  As above, but with scum teams swapped.<br>
(2/7) 28.6% Scum B lynch.  As above, but with scum teams swapped.<br>
(3/7) 42.8% Town lynch. GOTO 6P 2 - 2 - 2 (Night). (3/8 Town win; 1/6 either scum win; 7/24 Draw)
(3/7) 42.8% Town lynch. GOTO 6P 2 - 2 - 2 (Night). (1/4 Town win; 1/6 either scum win; 5/12 Draw)


(2*2/7*163/450 + 3/7*3/8) 36.8% Town win<br>
(2*2/7*157/450 + 3/7*1/4 = 1931/6300) 30.6% Town win<br>
(2/7*223/450 + 2/7*2/225 + 3/7*1/6 = 97/450) 21.5% Scum A win<br>
(2/7*223/450 + 2/7*2/225 + 3/7*1/6 = 97/450) 21.5% Scum A win<br>
(97/450) 21.5% Scum B win<br>
(97/450) 21.5% Scum B win<br>
(2*2/7*2/15 + 3/7*7/24 = 169/840) 20.1% Draw
(2*2/7*11/75 + 3/7*5/12 = 551/2100) 26.2% Draw


===7P 5 - 1 - 1 (Night)===
===7P 5 - 1 - 1 (Night)===
Line 562: Line 564:
(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)<br>
(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)<br>
(5/6*1/6 = 5/36) 13.4% As above, but reverse scum.  7/15 Town win; 8/15 Scum A win.<br>
(5/6*1/6 = 5/36) 13.4% As above, but reverse scum.  7/15 Town win; 8/15 Scum A win.<br>
(5/6*1/6 = 5/36) 13.4% Scum A and Scum B kill same Townie.  GOTO 6P 4 - 1 - 1 (781/1125 Town win; 32/225 either scum win; 8/375 Draw)<br>
(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)<br>
(5/6*4/6 = 5/9) 55.6% Scum A and Scum B kill different Townies.  GOTO 5P 3 - 1 - 1 (19/45 Town win; 2/9 either scum win; 2/15 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*781/1125 + 5/9*19/45 = 989/2025) 48.8% Town win<br>
(1/36 + 2*5/36*7/15 + 5/36*13/36 + 5/9*13/45 = 53/144) 36.8% Town win<br>
(5/36*8/15 + 5/36*32/225 + 5/9*2/9 = 88/405) 21.7% Scum A win<br>
(5/36*8/15 + 5/36*7/36 + 5/9*2/9 = 97/432) 22.4% Scum A win<br>
(88/405) 21.7% Scum B win<br>
(97/432) 22.4% Scum B win<br>
(5/36*8/375 + 5/9*2/15 = 52/675) 7.8% Draw
(5/36*1/4 + 5/9*4/15 = 79/432) 18.3% Draw


===7P 4 - 2 - 1 (Night)===
===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)<br>
(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)<br>
(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)<br>
(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)<br>
(4/5*2/6 = 4/15) 26.6% Scum A kills Townie; Scum B kills Scum A.  GOTO 5P 3 - 1 - 1 (3/4 Town win; 1/8 either scum win)<br>
(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)<br>
(4/5*1/6 = 2/15) 13.3% Scum A and Scum B kill same Townie.  GOTO 6P 3 - 2 - 1 (4/9 Town win; 35/72 Scum A win; 1/24 Scum B win; 1/36 Draw)<br>
(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)<br>
(4/5*3/6 = 2/5) 40.0% Scum A and Scum B kill different Townies.  GOTO 5P 2 - 2 - 1 (26/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 2/9 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*3/4 + 2/15*4/9 + 2/5*26/135 = 263/675) 39.0% Town win<br>
(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<br>
(1/15*8/15 + 2/15*5/6 + 4/15*1/8 + 2/15*35/72 + 2/5*71/135 = 1229/2700) 45.5% Scum A win<br>
(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<br>
(4/15*1/8 + 2/15*1/24 + 2/5*8/135 = 167/2700) 6.2% Scum B win<br>
(4/15*2/9 + 2/15*1/24 + 2/5*8/135 = 239/2700) 8.8% Scum B win<br>
(2/15*1/36 + 2/5*2/9 = 5/54) 9.2% Draw
(4/15*4/15 + 2/15*23/72 + 2/5*14/45 = 643/2700) 23.8% Draw


===7P 3 - 3 - 1 (Night)===
===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)<br>
(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)<br>
(1/4*3/6 = 1/8) 12.5% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(1/4*3/6 = 1/8) 12.5% Scum A kills Scum B; Scum B kills Townie.  Scum A win.<br>
(3/4*3/6 = 3/8) 37.5% Scum A kills Townie; Scum B kills Scum A.  GOTO 5P 2 - 2 - 1 (26/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 2/9 Draw)<br>
(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)<br>
(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*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).
(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*26/135 = 67/720) 9.3% Town win<br>
(1/8*1/6 + 3/8*14/135 = 43/720) 6.0% Town win<br>
(1/8*5/6 + 1/8 + 3/8*71/135 + 1/8*13/15 + 1/4 = 113/144) 78.5% Scum A win<br>
(1/8*5/6 + 1/8 + 3/8*71/135 + 1/8*13/15 + 1/4 = 113/144) 78.5% Scum A win<br>
(3/8*8/135 = 1/45) 2.2% Scum B win<br>
(3/8*8/135 = 1/45) 2.2% Scum B win<br>
(3/8*2/9 + 1/8*2/15 = 1/10) 10.0% Draw
(3/8*14/45 + 1/8*2/15 = 2/15) 13.3% Draw


===7P 3 - 2 - 2 (Night)===
===7P 3 - 2 - 2 (Night)===
(2/5*2/5 = 4/25) 16.0% Scum A and Scum B crosskill.  GOTO 5P 3 - 1 - 1 (3/4 Town win; 1/8 either scum win)<br>
(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)<br>
(2/5*3/5 = 6/25) 24.0% Scum A kills Scum B; Scum B kills Townie.  GOTO 5P 2 - 2 - 1 (26/135 Town win; 71/135 Scum A win; 8/135 Scum B win; 2/9 Draw)<br>
(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)<br>
(3/5*2/5 = 6/25) 24.0% As above, but with reversed scum.
(3/5*2/5 = 6/25) 24.0% As above, but with reversed scum.<br>
(3/5*1/5 = 3/25) 12.0% Scum A and Scum B kill same Townie.  GOTO 6P 2 - 2 - 2 <FILLIN>
(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<br>
(4/25*2/9 + 6/25*71/135 + 6/25*8/135 + 3/25*5/27 = 223/1125) 19.8% Scum A win<br>
(223/1125) 19.8% Scum B win<br>
(4/25*4/15 + 2*6/25*14/45 + 3/25*16/27 + 6/25 = 566/1125) 50.3% Draw


===8P 6 - 1 - 1===
===8P 6 - 1 - 1===
(1/8) 12.5% Scum A lynch.  GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)<br>
(1/8) 12.5% Scum A lynch.  GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)<br>
(1/8) 12.5% Scum B lynch; 7/15 Townwin; 8/15 Scum A win.<br>
(1/8) 12.5% Scum B lynch; 7/15 Town win; 8/15 Scum A win.<br>
(6/8) 75.0% Town lynch; GOTO 7P 5 - 1 - 1 (Night) (989/2025 Town win; 88/405 either scum win; 52/675 Draw)
(6/8) 75.0% Town lynch; 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*989/2025 = 326/675) 48.3% Town win<br>
(2*1/8*7/15 + 6/8*2593/6480 = 3601/8640) 41.7% Town win<br>
(1/8*8/15 + 6/8*88/405 = 31/135) 23.0% Scum A win<br>
(1/8*8/15 + 6/8*97/432 = 677/2880) 23.5% Scum A win<br>
(31/135) 23.0% Scum B win<br>
(677/2880) 23.5% Scum B win<br>
(6/8*52/675 = 13/225) 5.8% Draw
(6/8*109/1296 = 109/1728) 6.3% Draw


===8P 5 - 2 - 1===
===8P 5 - 2 - 1===
(2/8) 25.0% Scum A lynch.  GOTO 7P 5 - 1 - 1 (Night) (989/2025 Town win; 88/405 either scum win; 52/675 Draw)<br>
(2/8) 25.0% Scum A lynch.  GOTO 7P 5 - 1 - 1 (Night) (53/144 Town win; 97/432 either scum win; 79/432 Draw)<br>
(1/8) 12.5% Scum B lynch.  GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)<br>
(1/8) 12.5% Scum B lynch.  GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)<br>
(5/8) 62.5% Town lynch.  GOTO 7P 4 - 2 - 1 (Night) (263/675 Town win; 1229/2700 Scum A win; 167/2700 Scum B win; 5/54 Draw)
(5/8) 62.5% Town lynch.  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*989/2025 + 1/8*1/6 + 5/8*263/675) 38.645% Town win<br>
(2/8*53/144 + 1/8*1/6 + 5/8*173/900 = 671/2880) 23.3% Town win<br>
(2/8*88/405 + 1/8*5/6 + 5/8*1229/2700) 44.298% Scum A win<br>
(2/8*97/432 + 1/8*5/6 + 5/8*433/900 = 3983/8640) 46.1% Scum A win<br>
(2/8*88/405 + 5/8*167/2700 = 241/2592) 9.3% Scum B win<br>
(2/8*97/432 + 5/8*239/2700 = 107/960) 11.1% Scum B win<br>
(2/8*52/675 + 5/8*5/54) 7.713% Draw
(2/8*79/432 + 5/8*643/2700 = 1681/8640) 19.4% Draw


===8P 4 - 3 - 1===
===8P 4 - 3 - 1===
(3/8) 37.5% Scum A lynch.  GOTO 7P 4 - 2 - 1 (Night) (263/675 Town win; 1229/2700 Scum A win; 167/2700 Scum B win; 5/54 Draw)<br>
(3/8) 37.5% Scum A lynch.  GOTO 7P 4 - 2 - 1 (Night) (173/900 Town win; 433/900 Scum A win; 239/2700 Scum B win; 643/2700 Draw)<br>
(1/8) 12.5% Scum B lynch.  Scum A win.<br>
(1/8) 12.5% Scum B lynch.  Scum A win.<br>
(4/8) 50.0% Town lynch.  GOTO 7P 3 - 3 - 1 (Night) (67/720 Town win; 113/144 Scum A win; 1/45 Scum B win; 1/10 Draw)
(4/8) 50.0% Town lynch.  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*263/675 + 4/8*67/720 = 1387/7200) 19.3% Town win<br>
(3/8*173/900 + 4/8*43/720 = 367/3600) 10.2% Town win<br>
(3/8*1229/2700 + 1/8 + 4/8*113/144 = 2477/3600) 68.8% Scum A win<br>
(3/8*433/900 + 1/8 + 4/8*113/144 = 157/225) 69.8% Scum A win<br>
(3/8*167/2700 + 4/8*1/45 = 247/7200) 3.4% Scum B win<br>
(3/8*239/2700 + 4/8*1/45 = 319/7200) 4.4% Scum B win<br>
(3/8*5/54 + 4/8*1/10 = 61/720) 8.5% Draw
(3/8*643/2700 + 4/8*2/15 = 1123/7200) 15.6% Draw


===8P 4 - 2 - 2===
===8P 4 - 2 - 2===
(2/8) 25.0% Scum A lynch.  GOTO 7P 4 - 2 - 1 (Night) (263/675 Town win; 1229/2700 Scum B win; 167/2700 Scum A win; 5/54 Draw)<br>
(2/8) 25.0% Scum A lynch.  GOTO 7P 4 - 2 - 1 (Night) (173/900 Town win; 433/900 Scum B win; 239/2700 Scum A win; 643/2700 Draw)<br>
(2/8) 25.0% As above, but with scum reversed.
(2/8) 25.0% As above, but with scum reversed.<br>
(4/8) 50.0% Town lynch.  GOTO 7P 3 - 2 - 2 (Night) <FILLIN>
(4/8) 50.0% Town lynch.  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<br>
(2/8*433/900 + 2/8*239/2700 + 4/8*223/1125) 24.152% Scum A win<br>
24.152% Scum B win<br>
(2*2/8*643/2700 + 4/8*566/1125) 37.063% Draw




Revision as of 02:40, 23 August 2011


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 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%.
  • 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.

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% 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 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

Nightless

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 Lynch 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.

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 lynch that would harm them and both other factions are doomed if they lynch, all players No Lynch 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 lynched. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/5) 20.0% Scum B lynched. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5) 60.0% Town lynched. 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 lynched. GOTO 4P 2 - 1 - 1 (Night) (7/27 Town win; 4/27 either Scum win; 4/9 Draw)
(1/5) 20.0% Scum B lynched. Scum A win.
(2/5) 40.0% Town lynched. 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 lynching 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.

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 lynched. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(1/6) 16.7% Scum B lynched; 1/3 Town win.
(4/6) 66.7% Town lynched; 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 lynched. GOTO 5P 3 - 1 - 1 (Night). (3/8 Town win; 1/8 either scum win; 3/8 Draw)
(1/6) 16.7% Scum B lynched. Scum A win.
(3/6) 50.0% Town lynched. 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 Lynch. GOTO 6P 2 - 3 - 1 (Night).

6P 2 - 2 - 2

(2/6) 33.3% Scum A lynched. GOTO 5P 2 - 2 - 1 (1/18 Town win; 5/9 Scum B win; 7/18 Draw)
(2/6) 33.3% Scum B lynched. As above, but with reversed scum.
(2/6) 33.3% Townie lynched. 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 lynch; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)
(1/7) 14.3% Scum B lynch; same as above (7/15 Town win; 8/15 Scum A win)
(5/7) 71.4% Town lynch; 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 lynch; GOTO 6P 4 - 1 - 1 (Night) (757/1125 Town win; 32/225 either scum win; 16/375 Draw)
(1/7) 14.3% Scum B lynch; GOTO ~Mountainous~ 3 - 2 (2/15 Town win; 13/15 Scum A win)
(4/7) 57.1% Town lynch; 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 lynch; 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 lynch. Scum A win.
(3/7) 42.8% Town lynch; 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 lynch. 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 lynch. As above, but with scum teams swapped.
(3/7) 42.8% Town lynch. 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 lynch. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win; 8/15 Scum B win)
(1/8) 12.5% Scum B lynch; 7/15 Town win; 8/15 Scum A win.
(6/8) 75.0% Town lynch; 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 lynch. GOTO 7P 5 - 1 - 1 (Night) (53/144 Town win; 97/432 either scum win; 79/432 Draw)
(1/8) 12.5% Scum B lynch. GOTO ~Mountainous~ 5P 3 - 2 (1/6 Town win; 5/6 Scum A win)
(5/8) 62.5% Town lynch. 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 lynch. 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 lynch. Scum A win.
(4/8) 50.0% Town lynch. 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 lynch. 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 lynch. 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


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

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 lynched for the Town win.
(1/5*3/4 = 3/20) Named claims; Town lynched; Named killed overNight. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)
(3/5*2/3 = 8/15) Town lynch; Town kill. GOTO ~Plus Innocent~ 3P 2 - 1 (1/2 Town win)
(3/5*1/3 = 4/15) Town lynch; Named kill. GOTO ~Mountainous~ 3P 2 - 1 (1/3 Town win)

(1/5 + 1/20 + 3/20*1/3 + 8/15*1/2 + 4/15*1/3 = 59/90) 65.6% Town win
(31/90) 34.4% Scum win

7P 6 - 1

(1/7) Scum gets counterclaimed for the Town win.
(1/7*1/6 = 1/42) Named claims; Scum lynched for the Town win.
(1/7*5/6 = 5/42) Named claims; Town lynched; Named killed overNight. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(5/7*4/5 = 4/7) Town lynch; Town kill. GOTO 5P 4 - 1 (59/90 Town win)
(5/7*1/5 = 1/7) Town lynch; Named kill. GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)

(1/7 + 1/42 + 5/42*7/15 + 4/7*59/90 + 1/7*7/15 = 209/315) 66.3% Town win
(105/315) 33.6% Scum win

7P 5 - 2

(2/7) Scum gets counterlynched; Named dies; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(1/7*2/6 = 1/21) Named claims; Scum lynched; Named dies; GOTO ~Mountainous~ 5P 4 - 1 (7/15 Town win)
(1/7*4/6 = 2/21) Named claims; Town lynched; Named dies; GOTO ~Mountainous~ 5P 3 - 2 (2/15 Town win)
(4/7*3/4 = 3/7) Town lynch; Town kill. GOTO ~Plus Innocent~ 5P 3 - 2 (1/6 Town win)
(4/7*1/4 = 1/7) Town lynch; 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 lynched for the Town win.
(1/9*7/8 = 7/72) Named claims; Town lynched; Named killed; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(7/9*6/7 = 2/3) Town lynch; Town kill; GOTO 7P 6 - 1 (209/315 Town win)
(7/9*1/7 = 1/9) Town lynch; Named kill; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)

(1/9 + 1/72 + 7/72*19/35 + 2/3*209/315 + 1/9*19/35 = 643/945) 68.0% Town win
(302/945) 32.0% Scum win

9P 7 - 2

(2/9) Scum gets counterlynched; Named dies; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(1/9*2/8 = 1/36) Named claims; Scum lynched; Named dies; GOTO ~Mountainous~ 7P 6 - 1 (19/35 Town win)
(1/9*6/8 = 1/12) Named claims; Town lynched; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(6/9*5/6 = 5/9) Town lynch; Town kill; GOTO 7P 5 - 2 (163/630 Town win)
(6/9*1/6 = 1/9) Town lynch; 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 counterlynched; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(1/9*3/8 = 1/24) Named claims; Scum lynched; Named dies; GOTO ~Mountainous~ 7P 5 - 2 (8/35 Town win)
(1/9*5/8 = 5/72) Named claims; Town lynched; Named dies; GOTO ~Mountainous~ 7P 4 - 3 (2/35 Town win)
(5/9*4/5 = 4/9) Town lynch; Town kill; GOTO ~Plus Innocent~ 7P 4 - 3 (1/15 Town win)
(5/9*1/5 = 1/9) Town lynch; 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

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