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