What stage of the event? In SNG's and MTT's, survival is the name of the game. Is this the final table? If not, I think the long-term gain of minimizing our chance to bust out is best.
In a vacuum (assume: villain 3-bets from LB 15%):
Range pre-flop: 55+,A9s+,KTs+,QJs,JTs,T9s,ATo+,KJo+,QJo,JTo
*note: nothing ever happens to narrow this range. When Villain checks the turn, it could be with the intent to c/r. The only hands that might be ruled out are the AT hands.
I think a min-raise on the river just screams pay-me, pay-me, so it might not work if Villain has b/f discipline (but Hero wins the pot w/o showdown, ++). Also, what does Hero do if Villain shoves back? Can Hero reasonably think Villain is not at the top of his/her range? Can Hero possibly fold with 3.5:1 pot odds? Would Hero want to risk tournament life on this all-in call? Pokerstove has Hero as 85% favorite against Villain's range. Hero must call a shove here.
Another problem is that a min-raise of 16k leaves Hero 20k behind. Which means Hero should've shoved in the first place, bluff or made. The min-raise just doesn't feel like a bluff, and we want our villain to think we're bluffing at the flush.
So, let's say Hero shoves. If Villain is folding to a min-raise, then Villain is likely folding to a shove. If Villain is not folding to a min-raise, Villain will either shove or make a crying call. The only way to extract value here is with a min-raise, in my estimation.
The problem I have is that I want to stay alive in this tourney no matter what, so a call is my favorite. But, I want to bet with 85% equity, or I'll bust out later rather than sooner. But, but, even if we call behind and win, we're still chip-leader at this table which will have at least as much equity as extracting full value out of this one hand.
I just talked myself into calling. Is this a huge leak?