JsAs versus confident pre-flop BB

[Buceph]

PokerStars No-Limit Hold'em, 1.1 Tournament, 400/800 Blinds 75 Ante (8 handed) - PokerStars Converter Tool from FlopTurnRiver.com

UTG+1 (t2725)
MP1 (t3160)
Hero (MP2) (t13970)
CO (t7075)
Button (t44921)
SB (t12900)
BB (t13775)
UTG (t7100)

Hero's M: 7.76

Preflop: Hero is MP2 with J, A
3 folds, Hero bets t1600, 3 folds, BB raises to t4000, Hero calls t2400

Flop: (t9000) K, 9, A (2 players)
BB bets t9700 (All-In)


I've hit a brick wall with this. It's the first time I've looked back through the big hands from a tournament and I really can't see if I did right or wrong with this. I think I'm just being pig headed about what I did here.

Basically this was a roll-of-the-dice tournament. Terrible bankroll management in that it was a $1 Satellite for a $100 Buy in Tournament (Single Guaranteed Ticket, escalated to four tickets in the end.) At the point of this hand the blinds were creeping up on pretty much everyone bar the top 5/10 people. There was a big balloon in the centre of the player list with everyone between 2 and 20 BBs and the seven or eight guys at the top having about 40-60. I would have been at the higher end of that balloon after getting lucky with pocket aces on two small-stack all-ins.

This to me still seems like a make-or-break hand.

[eamonhonda]

Shoving pre with this stack and position.
As played youve called 3 bet with Ace decent kicker. Youve hit your top pair on a safeish board. If your calling pre you have to be happy to call here.
AJ is a tricky hand but if youve decided to go with it pre and youve paired the ace you have to be willing to double up/ go broke with an all in on the flop imo

[LAPPIN]

shove pre.

As played, fold to 3bet.

As played preflop, stack off on this board.

[LTL]

shove pre.

As played, fold to 3bet.

As played preflop, stack off on this board.

This.

But is anyone opening and folding to 3bet as opposed to open jamming, and if not, how many BB's before you choose this option instead?