User blog:Dyaomaster/Statistics Analysis: Executioner's target is a jailed doctor the night jailor is stabbed by SK

I worked on this for an hour. My laptop battery is at 20% right now, but here goes...

Chance of 1 doctor: 1/2*13/14*29/30 =377/840

Chance of 2 doctors through RT: 1/2*1/14*29/30 =29/840

Chance of 2 doctors through Any: 1/2*13/14*1/30 =13/840

Chance of 3 doctors: 1/2*1/14*1/30 =1/840

Total chance of 1 doctor: 377/840

Total chance of 2 doctors: 42/840

Total chance of 3 doctors: 1/840

Expected amount of doctors: 58/105, ~0.55

Chance of 1 SK through NK: 1/3*29/30 =29/90

Chance of 1 SK through Any: 2/3*1/30 =2/90

Chance of 2 SKs 1/3*1/30 =1/90

Total chance of 1 SK: 31/90

Total chance of 2 SKs: 1/90

Expected amount of SKs: 32/90, ~0.36

Chance that, with SK, jailor does not jail SK n1:

1 SK: 13/14

2 SK: 12/14

Prob of 1 SK not jailed: 31/32*13/14 =403/448

Prob of 2 SK not jailed: 1/32*12/14 =12/448

Prob SK, but jailor does not jail: 415/448, ~0.93

Prob jailor jailed doc: (58/105)/14 =29/735, ~0.04

Prob jailor stab w/ 1 SK: 1/14

Prob jailor stab w/ 2 SK: 27/196

Prob 1 SK and jailor stabbed: 403/6272

Prob 2 SK and jailor stabbed: 81/21952

Prob jailor stabbed by SK not jailed: 2983/43904, ~0.07

Prob jailor jailed doc and got stabbed by SK: 2983/43094*29/735 =2983/1092210, ~0.0027

Prob there is an exe: 1/3

(assuming Any is not exe, otherwise SK/exe conflict gets too hard)

Prob jailed doc is exe's target: 1/7 (assuming Any is not town)

Prob both above are true: 1/21, ~0.05

Prob doc exe's target, doc is jailed, and SK stabs jailor: 2983/22936410,~0.00013

Probability town lynches doctor when all this happens: 1