Sorry for bothering you with math, but I had nothing better to do.
Unsurprisingly, most people die during their first hunt. There seems to be no significant better chance of surviving your third hunt than your second.
The Tae mission has not been considered a proper hunt (put it under "risk of exposure"):
Survived first hunt
Sakata
Kaze
Inaba
Old Man
Hoi Hoi
Reika
Takeshi
Sakurai
Katou
Nishi
Kurono
Tetsuo
Hojo
Sadako
Kishimoto
Dog
Gang raper 4
Rape victim
Izumi
Killed first hunt
Onion 5
Tanaka 5
Buddha 9
Kappe 16
Ring 1
Oni 4
Total survived 22
Total killed 40
Total 62
Chance of surviving first hunt: 22 / 62 = 0.3548
Chance of dying on first hunt: 1 - 0.3548 = 0.6452
Died between first & second hunt
Tetsuo
Gang raper 2
Did not die between first & second hunt
Sakata
Kaze
Inaba
Old Man
Hoi Hoi
Reika
Sakurai
Katou
Nishi
Kurono
Hojo
Sadako
Kishimoto
Dog
Rape victim
Gang raper 2
Izumi
Died: 3
Survived: 18
Total: 21
Chance of death between first and second hunt: 3 / 21 = 0.1429
Chance of not surviving to start your second hunt: 0.3548 * 0.1429 = 0.0507
Chance of surviving to start your second hunt: 0.3548 - 0.0507 = 0.3041
Survived second hunt
Sakata
Kaze
Inaba
Old Man
Hoi Hoi
Reika
Sakurai
Katou
Nishi
Kurono
Kishimoto
Dog
Izumi
Killed second hunt
Hojo
Sadako
Rape victim
Gang raper 2
Total survived 13
Total killed 5
Total 18
Chance of surviving second hunt: 13 / 18 = 0.7222
Chance of surviving two hunts: 0.3041 * 0.7222 = 0.2196
Chance of dying on second hunt: 0.3041 - 0.2196 = 0.0845
Survived third hunt
Sakata
Kaze
Inaba
Old Man
Hoi Hoi
Reika
Kurono
Dog
Izumi
Killed third hunt
Sakurai
Katou
Kishimoto
Total survived 9
Total killed 3
Total 12
Chance of surviving third hunt: 9 / 12 = 0.75
Chance of surviving three hunts: 0.2196 * 0.75 = 0.1647
Chance of dying on third hunt: 0.2196 - 0.1647 = 0.0549
Killed first hunt: 0.6452
Died between 1st & 2nd: 0.0507
Killed second hunt: 0.0845
Killed third hunt: 0.0549
Survived 3 hunts: 0.1647


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