$90 live MTT, roughly 60 players to start, 11 remaining on two tables. Blinds are 4,000/8,000 with an 8,000 BB ante. 7 players get paid.

Villain is big stack with 200k+ (not sure exactly, covers whole table). As you can see, stacks are getting very shallow, but I am far and away the short stack. Everyone else at both tables has at least 100k. Villain is raising almost every hand at this point as my table is 5 handed. He has shown up with some hands but I wanna say he's probably raised at least 6 of the 10 hands I've seen at this table so far, and maybe more. He's competent enough to know that he can bully the table, but I feel like his judgment is a little off.

I have 44,000 and am in the big blind with Q 6 off. I have 16,000 invested (BB and BB ante). Villain is UTG and raises to 31,000. CO, BTN, and SB fold.

Am I supposed to put in 28,000 (raise of 5k more that will obv be called) to win 84,000? Or am I supposed to fold, spend 4k on a SB and then have 3 chances to pick up a hand or try to get a double BB to fold when I shove 24k?

Just curious, I haven't gotten too deep in tournaments and been this short. I usually would have found a spot before this to shove, but with the Villain raising every hand (and getting some action here and there), it wasn't easy.

Wait and raise any two when the big stack has not put any money in the pot voluntarily. In this spot villian is going to pay you ( you don't have fold equity ) and it's better to shove with 72o with at least some fold equity than with Q6

I would say it's not even a question if this wasn't a BB ante tourney. Because when I do ultimately shove 24k do I really have fold equity against a guy who has 16k invested, and would need to call 16k more to win 60k? Seems like an any two call at that point. Only argument I'm curious about is is it more likely I'll get better than Q 6 off in the next 3 hands before I'm all in in the BB.

Your post and rationale are both off.

You do not have $16K invested - you have 8K plus the antes. So, you have to call a $23K RAISE or go all in for 36K total which will be snapped off by V here.

You state that V is competent. If so, his raise sizing is clearly trying to induce you. I fold here and look to GII better.

If I had Q-6 off that short and was first in, I would shove as we are just under 50/50 which is Q-7 if I remember correctly.

How exactly do I not have 16k invested? 16k of my chips that I had before the hand started are in the middle now. I have to put in $28k more to potentially have a stack of 84k if I win the hand.

We have to put 28k to win a pot that'll be 84k. 28/84=1/3
We have to take the pot 1/3rd of the times to make it a good call. Our hand is horrible but I guess we still have to go with it. Except if villain has us dominated we have our 33% equity + there is still a slight chance of us being ahead with Q high (vs JTs ot T9s for example).

+ villain is UTG, he'll be BB when we are SB, he won't be folding to our shove for 28k !