if NL:

IC doesn't die: (3/4)*(2/3) = 6/12 = 1/2
3p vote, IC doesn't die: 1/2 chance to lynch
= 1/4 chance to win

IC dies: 1/2
3p vote, IC dies: 1/3 chance to lynch
= 1/6 chance to win

1/4 + 1/6 = 5/12 chance to win

if randlynch:
D1: 1/5 lynch mafia, instantly win

If lynch IC:
(1/5) * (1/3) = 1/15 chance to win

If lynch vt:
IC dies at night: (3/5) * (1/3) * (1/3) = 1/15 chance to win
Ic lives: (3/5) * (2/3) * (1/2) = 6/30 = 1/5 chance to win

1/5 + 1/15 + 1/15 + 1/5 = 8/15 chance town wins

5/12 vs 8/15, randlynch increases chances by ~ 25%.