Jacks in SB, in the money, vs a MP 3bet and a button shove

[Swodaems]

This happened in Carbonpoker monthly 50k freeroll. Top 300 places pay out, and there are 176 players left. this is a minibubble as payout for 176th is $20, and payout for 175th is $25. I am currently ranked 139th/176 with about 10000 in chips with blinds at 600/1200. 6 hands ago, I had 1000, but won two big hands to put myself back in the running, however I am still very much in the short stack mindset. (I got queens in MP and more than doubled up when only the BB called my less than 1 bb shove. I then got 96 in BB, board came down q66, I checked the flop, then shoved when the sb raised Q10 on the turn.)
Then comes my SB and I find myself looking down at Jacks. Action folds to the guy directly across from me. (This is a 10 handed table by the way and he has about 16000 in chips.) He 3-bets, making me put him on either a high Ace or a lower pair. (I'm 90%+ sure that this is a high Ace (AQ or AK, maybe AJ if I'm lucky) from my read on the guy.) Action folds to the button, (who has 2000 in chips after I short stacked him last hand,) who shoves allin. This means very little to me as his range for shoving is almost anything after last hand.
My first instinct in this situation is to shove and try to get the 3-better of his high ace. However he may call anyway since he can afford to, putting me and him in a near coinflip situation on a minibubble. However, judicious use of my timebank should give the other tables enough time to eliminate someone.
If I merely call his 3bet, than I will having to make decisions against a player with position on me. I will also likely be pot commited with that much of my stack on the table.
As far as the option of folding goes, I have only once folded JJ preflop and I don't this will be the second time.

Can I get the numbers and your opinions for my proposed options?

(for those of you wondering about the BB, he has 3200 in chips including the BB he has on the table. He is a fairly timid player and is probably going to fold anything less than QQ in this situation.)

 

[josh_dei8]

I'm all in. You are in the money, I believe his shove is a steal knowing everyone else will fold to reach the next payout level. or just to isolate himself and the very short stack bb. You got a strong hand, shove and make him pay to beat you.

 

[wislim]

I agree ^^^with your reads on villians, just shove and win the race.

 

[Dorkus Malorkus]

Really need a HH here, but I'll bite. I'll assume MP is raising (not 3betting) to a standard ~3k.

It seems to be a routine shove.

As you said Button's range is basically two cards, meaning that while his 2k isn't 'dead' money per se, he is likely to have little equity.

Basically, you shove, one of four things happens.

(a) MP folds, you get HU with button with your JJ vs a range of any two cards and win a small sidepot for your troubles regardless of the result of the hand. This is good.

(b) MP calls with something you're flipping with. You have surplus money in the pot from Button and his any two cards, so even if you end up coinflipping here it's good unless Button happens to have a monster (unlikely).

(c) MP calls with a lower pair, which is obviously good.

(d) You run into MP's AA/QQ, which is bad.

Basically there are a lot of good things that can happen and very few bad things. Calling 30% of your stack off is almost always bad.

 

[robwhufc]

Mini bubble? Are you serious?

Yep, your recollection of hand is a bit muddled (a "3-bet" is a re-raise). Hand History would help, but this seems a pretty clear all-in. He'll either call or he'll fold, and he'll either beat you or you'll win, but you need to be accumulating chips in your situation, and you are very unlikely to get a better position than this.

And he can't afford to call you with junk- if he started with 16,000 (i'm guessing he's bet 3K?) then he'll only have 6K if he loses. And a call with a dominated hand would obviosuly be a good result here.

 

[Swodaems]

Glad to see that the consensus is biased towards shoving. That's what I did. I didn't blow my timebank however, because unless the button wins, he was going out ahead of me on the payout scale.
This is how things turned out:
The BB takes his sweet time about folding, actually going so far as to activate his time bank. Two of the other tables eliminate players during this time.
The MP raiser also takes a while to decide, but ends up calling. He showsdown AQ off and the button has A7 off. I relax a little because I'm about 60% to win the hand in this situation considering that one of the MP's outs is dead. Unfortunately, the flop contains 2 queens and I go out in 173rd earning $25. My opponent does very well and finishes 12th or 13th, earning him a prize of about $800.

(ps. Thanks for clearing up my confuson about the definition of 3betting. I am however sticking with minibubble.)