I just made some computations under the assumption that John Connor is lynchable both days:
If we lynch every day:
31.3% John Connor is either lynched or killed by Terminator
40.9% chance game goes on and no terminator death, 4v2 after Judgement day.
20.2% chance terminator is lynched
7.8% chance both researchers die
If we never lynch:
11.1% chance John Connor is terminated
88.9% chance game goes on to 5v2v1 after Judgement Day
I actually kinda prefer the lynching strategy, although not by as much as I thought before I did the computation; we basically triple the chance of losing by not getting past judgment day, but we gain a chance to win before then and a chance to kill the terminator and go into post-judgement day in a much easier world for those who don't join skynet. Things get even better for us if you assume John is unlynchable on D3 but not today.
So, let's get this started.
-vote S-FM Sarge