[locutus2002]

Hero can afford to take a flop and give up on it without affecting his stack. His priority should be to keep the pot small and maintain his chip lead.

I think that raising PF is a mistake given that villain should be willing to push a wide range of hands as the short stack and hero does not want to call off 540K even when he is ahead, even or worse.

the turn push is interesting because it's about the ace not about the jack.

Villain shouldn't push the jack here, but hero's hands for just calling PF and hitting the flop should not have many aces in them. Villain is representing the ace and giving up all the hands that hero has a Jack in them and probably an ace.

I'd guess its about 130 (~60 jacks; ~50 aces and some other junk) hands out of ~400-500 possible hands. So 2/3 of the time villain takes down 240K and the other 1/3 villain get stacked. It's a fair bet for villain if hero's range is wide.